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UBC Theses and Dissertations

Signal and receiver design for high density digital magnetic tape recording Wood, Roger William 1979

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SIGNAL AND RECEIVER DESIGN FOR HIGH DENSITY DIGITAL MAGNETIC TAPE RECORDING b y ROGER WILLIAM WOOD B.Sc.(Eng.), U n i v e r s i t y C o l l e g e , London, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of E l e c t r i c a l Engineering) We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1979 Q Roger W i l l i a m Wood, 1979 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or. publ icat ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of E l e c t r i c a l E n g i n e e r i n g The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 24 Sept. 1979 ABSTRACT This thesis is concerned primarily xdth the improvement of data packing densities on magnetic tape. The concept of the 'magnetic recording channel' translates the thesis objectives into a concern for the maximization of channel data rate and minimization of error rate. A relatively comprehensive review provides background and indicates the present state of understanding for both magnetic recording and conventional communication channels. A helical-scan video-tape transport was selected as the vehicle for implementation and testing of signal and playback receiver designs. The recording channel was characterized by i t s response to balanced two-level record waveforms. The channel appeared approximately linear but was perturbed by moderate levels (-20dB) of additive noise as well as nonlinear behaviour. More serious degradations resulted from multiplicative noise (fading) manifest as extended (0.1 mm) regions of reduced playback level (dropouts). A prototype high-density recording system was constructed using non-return-to-zero signalling at 20 Mbit/s or 1.1 Mbit/m. The playback receiver comprised a fixed p r e - f i l t e r followed by an adaptive seven-tap transversal, f i l t e r . System performance, measured in terms of 'burst' and 'isolated' error rates, was investigated as a function of various parameters including signal record level, equalizer complexity, and head-preamplifier • coupling. Error control i s essential in many applications and higher-order error s t a t i s t i c s were-compiled i n order to estimate the efficacy of error correction techniques. In particular, erasure detection'and interleaved block coding proved to be useful techniques. i i The a p p l i c a t i o n of d e c i s i o n feedback was found to provide only marginal improvements i n performance. However, d e c i s i o n feedback was shown to provide a u s e f u l method of c o r r e c t i n g the d.c. channel n u l l . Concluding remarks i n d i c a t e the relevance of t h i s work to narrower t r a c k systems and suggest l i k e l y emphases f o r f u t u r e work. i i i TABLE OF CONTENTS page ABSTRACT i i TABLE OF CONTENTS. .v i v LIST OF TABLES v i - i i LIST OF FIGURES i x ACKNOWLEDGEMENTS x i i i I INTRODUCTION AND BACKGROUND 1 1.1 INTRODUCTION ,)1 1.2 OBJECTIVES 2 1.3 BACKGROUND 4 1.3.1 Magnetic r e c o r d i n g 4 1.3.2 D i g i t a l r e c ording 7 1.4 OUTLINE OF THESIS 11 I I REVIEW OF OTHERS' WORK 13 2.1 THE PHYSICS OF MAGNETIC RECORDING 13 2.1.1 Magnetic recording media 13 2.1.2 Magnetic record/playback heads 14 "2.1.3 The record and storage processes 17 2.1.4 The playback process 19 2.2 THE MAGNETIC TAPE RECORDER AS A COMMUNICATION CHANNEL . . . . 20 2.2.1 O v e r a l l response . 21 2.2.2 L i n e a r / n o n l i n e a r behaviour 23 2.2.3 A d d i t i v e noise sources 24 2.2.4 M u l t i p l i c a t i v e noise sources 26 2.3 SIGNAL AND RECEIVER DESIGN . . . . . . . . 28 2.3.1 Conventional data t r a n s m i s s i o n channels 28 2.3.2 Nonlinear channels 36 2.3.3 The magnetic r e c o r d i n g channel 37 I I I CHARACTERIZATION OF CHANNEL BEHAVIOUR . 43 3.1 INSTRUMENTATION 43 3.1.1 Tape transport 43 3.1.2 Record and playback a m p l i f i e r s 44 3.1.3 Tape crossover editor'!. . 45 i v 3.2 LINEAR AND NONLINEAR EFFECTS . . . 4 6 3.2.1,,, Tests of l i n e a r i t y 46 3.2.2 C h a r a c t e r i z a t i o n of channel n o n l i n e a r i t y 50 3.3 ADDITIVE NOISE . . ;. . ; 52 3.3.1 Tape noise 52 3.3.2 Playback p r e a m p l i f i e r noise 55 3.4 MULTIPLICATIVE NOISE • 56 3.4.1 Fade d i s t r i b u t i o n of s p e c t r a l components 56 3.4.2 Bandwidth of m u l t i p l i c a t i v e e f f e c t s 60 3.4.3 M o d e l l i n g of the record/playback process 61 3.4.4 Deduced d i s t r i b u t i o n f o r head-tape separation 62 3.5 OTHER CONSIDERATIONS 64 3.5.1 Timebase s t a b i l i t y 64 3.5.2 Tape-edge crossover 65 3.5.3 Tracking 6 7 3.5.4 Compatability 6 7 IV SIGNAL AND RECEIVER DESIGN CONSIDERATIONS 71 4.1 SIGNAL DESIGN 7 1 4.2 RECEIVER DESIGN 74 4.2.1 Receiver s t r u c t u r e s 74 4.2.2 Clock recovery 79 4.2.3 Adaptive f i l t e r i n g 79 4.3 PROTOTYPE :H3GH DENSITY MAGNETIC RECORDING SYSTEM 80 4.3.1 Record a m p l i f i e r 80 4.3.2 Playback p r e a m p l i f i e r 83 4.3.3 Automatic gain c o n t r o l 83 4.3.4 P r e f i l t e r 85 4.3.5 T r a n s v e r s a l f i l t e r :k. . 85 4.3.6 D e c i s i o n device 87 4.3.7 Tap adjustment / gain c o n t r o l 87 4.3.8 Clock recovery 89 4.4 DIFFICULTIES ENCOUNTERED 92 V PERFORMANCE MEASUREMENTS 95 5.1 TEST PATTERNS 95 5.1.1 Pseudo-random sequences 96 5.1.2 Sequence generation and e r r o r d e t e c t i o n 97 5.1.3 Burst e r r o r s 99 v 5.2 ANALOG MEASUREMENTS 1 0 0 5.2.1 Frequency domain 200 5.2.2 Time domain 2.08 5.2.3 S i g n a l - t o - n o i s e r a t i o s 2.H 5.3 ERROR RATES 1 ; L 1 5.3.1 E r r o r r a t e vs. record l e v e l and number of t r a n s v e r s a l f i l t e r taps H I 5.3.2 E r r o r r a t e vs. head/preamplifier c o u p l i n g 214 5.3.3 The n e c e s s i t y f o r p r e f i l t e r i n g . . ^  217 5.3.4 The advantages of adaptive e q u a l i z a t i o n 220 5.4 CONCLUSIONS 1 2Q VI ERROR CONTROL 1 2 3 6.1 SIGNAL AMPLITUDE DISTRIBUTIONS 1 2 3 6.1.1 Cumulative d i s t r i b u t i o n of equalized playback s i g n a l . 223 6.1.2 Deduced fade d i s t r i b u t i o n 225 6.2 HIGHER ORDER ERROR AND ERASURE STATISTICS 127 6.2.1 Measurement of multigap d i s t r i b u t i o n s 127 6.2.2 Derived s t a t i s t i c s , P(^m,n) and E(e^e^) 129 6.3 ERROR CORRECTION 133 6.3.1 Block codes 133 6.3.2 Int e r l e a v e d codes 135 6.3.3 Concatenated codes 137 6.4 CONCLUSIONS 139 V I I DECISION FEEDBACK EQUALIZATION ON THE MAGNETIC RECORDING CHANNEL 141 7.1 DECISION FEEDBACK EQUALIZATION 141 7.1.1 D e c i s i o n feedback / p a r t i a l response 141 7.1.2 E q u a l i z a t i o n of the d.c. n u l l 142 7.1.3 S e n s i t i v i t y to channel fades 144 7.2 RESULTS ON PROTOTYPE MAGNETIC RECORDING SYSTEM 149 7.2.1 E q u a l i z a t i o n of the d.c. n u l l 149' 7.2.2 M o d i f i c a t i o n of h.f. response 151 7.2.3 Attempts to compensate f o r channel fading 153 V I I I CONCLUSIONS 156 APPENDIX 1 EVALUATION OF THE RATIO OF SIGNAL TO TAPE-NOISE SPECTRAL. DENSITIES . 160 v i APPENDIX 2 DETAILS OF VIDEO TAPE TRANSPORT AND OF VIDEO TAPES . . . . 164 APPENDIX 3 ZERO-FORCING ADAPTIVE TRANSVERSAL FILTERING 165 REFERENCES 169 v i i LIST OF TABLES Table page 1.1 Comparison of recent h i g h - d e n s i t y d i g i t a l magnetic tape recorders 10 3.1 Mean playback l e v e l f o r the nine choices of record. and playback heads 68 6.1 O v e r a l l e r r o r r a t e s achieved by various 5/6 r a t e codes at high i n t e r l e a v i n g r a t i o s . The equalized magnetic recording channel i s quantized i n t o e i t h e r a b i n a r y or a f o u r - l e v e l erasure channel 139 v i i i LIST OF FIGURES F i g u r e page 1.1 Gross comparison of r e c o r d i n g d e n s i t i e s 2 1.2 H e l i c a l - s c a n tape format 6 2.1 a) Gapped r i n g head b) A p p r o x i m a t i o n t o gap f r i n g i n g f i e l d . 15 2.2 E m p i r i c a l response (2.9) f o r magnetic r e c o r d i n g c h a n n e l . . . . 22 2.3 Data t r a n s m i s s i o n c h a n n e l 29 2.4 R e c e i v e r s t r u c t u r e s 31 2.5 Magnetic r e c o r d i n g codes 38 3.1 Magnetic r e c o r d i n g c h a n n e l response to square wave, i =0.24 A- tape #1 48 m 1 3.2 Magnetic r e c o r d i n g c h a n n e l response t o 3 1 - b i t pseudo-random sequence, i m = o . 3 3 A , tape #1 48 3.3 C r o s s - c o r r e l a t i o n f u n c t i o n f o r e q u a l i z e d sampled magnetic r e c o r d i n g c h a n n e l , based on measurements o f Haynes [97] . . 51 3.4 S i g n a l and n o i s e s p e c t r a w i t h b e s t f i t t i n g e m p i r i c a l c u r v e s (2.9) and (2.11), u i n Mrad/s, i m=0.33.A, tape #1 . . . . 54 3.5 System used to measure s i g n a l p r o b a b i l i t y d i s t r i b u t i o n s . . . . 58 3.6 Cumulative p r o b a b i l i t y d i s t r i b u t i o n , F ( L ) , o f c h a n n e l output s i g n a l v s . output l e v e l , L; square wave i n p u t a t 1.5MHz, i m=0.33 A, tape#l 59 3.7 Cumulative s i g n a l d i s t r i b u t i o n , F ( L ) , v s . r e c o r d l e v e l , f o r L=-10dB and L=-20dB; based on f i f t h harmonic o f 1.0 MHz r e c o r d e d square wave 59 3.8 Comparison of measured c h a n n e l response w i t h response p r e d i c t e d by ( 3 . 1 ) ; head-tape s e p a r a t i o n , a=0.54 ym, a + d = 0 . 6 / t a n _ 1 ( 0 . 1 5 / i m ) , where d i s the e f f e c t i v e r e c o r d i n g depth and i m>2/0.15ir i s the r e c o r d l e v e l . . . . . 63 3.9 P r o b a b i l i t y o f head-tape s e p a r a t i o n b e i n g exceeded v s . head-tape s e p a r a t i o n ; d e r i v e d from f i g s . 3 . 6 - 3 . 8 . . . . 63 3.10 P l a y b a c k r e s p o n s e s around tape edge c r o s s o v e r 66 3.11 Channel response f o r v a r i o u s c h o i c e s o f r e c o r d and p l a y b a c k heads. Based on spot f r e q u e n c y measurements a t 1,3,5,7,9,11,13 MHz. Record l e v e l , i m = 0 . 5 3 A , tape #1 . . . 69 i x Figure Page 4.1 C a l c u l a t e d e f f e c t i v e SNR vs. l i n e a r recording d e n s i t y ; p a r t i a l response s i g n a l l i n g and f l a t e q u a l i z a t i o n 76 4.2 Prototype high-density magnetic r e c o r d i n g system 81 4.3 Record A m p l i f i e r . . . . ; 82 4.4 Playback p r e a m p l i f i e r 82 4.5 Automatic gain c o n t r o l a m p l i f i e r 84 4.6 P r e f i l t e r 84 4.7 Tr a n s v e r s a l f i l t e r 86 4.8 D e c i s i o n device (quantizer) 86 4.9 Automatic tap adjustment (see a l s o Appendix 3) 88 4.10 Clock recovery 90 5.1 Sequence.generator/ e r r o r d e t e c t o r 98 5.2 I d e n t i f i c a t i o n of i s o l a t e d and burst e r r o r s 98 5.3 Playback s i g n a l s p e c t r a vs. record l e v e l 101 5.4 S i g n a l s p e c t r a i l l u s t r a t i n g the a c t i o n of the p r e f i l t e r . . . . 103 5.5 Spectra i l l u s t r a t i n g the a c t i o n of the t r a n s v e r s a l f i l t e r ; i m=0.53 A-; tape #3 . 104 5.6 Spectrum of equalized playback s i g n a l v s . number of t r a n s v e r s a l f i l t e r taps; i m=0.53 A, tape #3 104 5.7 Equalized s i g n a l and noise sp e c t r a vs. record l e v e l , tape #3 . 105 5.8 Phase response before and a f t e r e q u a l i z a t i o n , i m=0.53 A . . . . 107 5.9 Responses to a 31-bit pseudo-random sequence i l l u s t r a t i n g a c t i o n of p r e f i l t e r and t r a n s v e r s a l f i l t e r ; d e c i s i o n sampling i n s t a n t s i n d i c a t e d , i m=0.53 A, tape #3 109 5.10 S i g n a l e q u a l i z a t i o n vs. record l e v e l - eye diagrams, tape #3 . n o 5.11 C r o s s - c o r r e l a t i o n of equalized playback s i g n a l against 31-bit pseudo-random input sequence; i m=0.53 A, tape #3 . 112 5.12 Measured s i g n a l - t o - n o i s e r a t i o s a f t e r e q u a l i z a t i o n 112 x Figure page 5.13 E r r o r r a t e vs. record l e v e l and number of e q u a l i z e r taps; tapes #2,#3 113 5.14 E r r o r r a t e vs. record l e v e l and number of e q u a l i z e r taps; tape #4 115 5.15 Head c o u p l i n g : v a r i a t i o n of n a t u r a l frequency, f ^ , and Q w i t h shunt capacitance, C s^, and r e s i s t a n c e , R s^ 116 5.16 E r r o r r a t e s vs. head/preamplifier c o u p l i n g ; i m=0.44 A, tape #4. 118 5.17 I s o l a t e d e r r o r r a t e vs. record l e v e l and number of e q u a l i z e r taps; p r e f i l t e r absent, tape #3 119 5.18 E r r o r r a t e s v s . record l e v e l f o r adaptive and non-adaptive e q u a l i z e r s ; tape #4 119 5.19 E r r o r r a t e s vs. head/preamplifier c o u p l i n g ; non-adaptive t r a n s v e r s a l f i l t e r , i m=0.44 A, tape #4 121 6.1 Measurement of cumulative d i s t r i b u t i o n f o r the equalized playback s i g n a l conditioned on a recorded '1' . . 124 6.2 Cumulative d i s t r i b u t i o n of playback s i g n a l at sampling i n s t a n t s ; conditioned on '1' recorded, equalized by p r e f i l t e r and seven-tap, z e r o - f o r c i n g t r a n s v e r s a l f i l t e r , record l e v e l i m=0.35 A 124 6.3 Cumulative d i s t r i b u t i o n s f o r p r e a m p l i f i e r noise and f o r p r e a m p l i f i e r noise + a.c.-bias tape n o i s e ; e q u a l i z a t i o n s as f o r f i g . 6.2, tape #1 126 6.4 Fade d i s t r i b u t i o n derived from f i g s . 6.2 and 6.3; tape #1 . . 126 6.5 Measurement of multigap d i s t r i b u t i o n s 128 6.6 P r o b a b i l i t y of two b i t s both being i n c o r r e c t , E(eQe^), as a f u n c t i o n of t h e i r r e l a t i v e displacement; derived from the multigap e r r o r s t a t i s t i c s f o r a simulated b i n a r y s i g n a l l i n g channel w i t h a d d i t i v e Gaussianinoise 131 6.7 P r o b a b i l i t y of two b i t s both being i n c o r r e c t , E(eQejj), as a f u n c t i o n of t h e i r r e l a t i v e displacement, N; derived from the measured multigap e r r o r s t a t i s t i c s f o r the b i n a r y magnetic r e c o r d i n g channel 131 6.8 P r o b a b i l i t y of two b i t s both being erased as a f u n c t i o n of t h e i r r e l a t i v e displacement; derived from the measured multigap erasure s t a t i s t i c s f o r the magnetic rec o r d i n g channel . 132 x i Figure Page 6.9 Geometric mean c o n d i t i o n a l p r o b a b i l i t i e s , E(ejj|eQ=l), . ... from f i g u r e s 6.7 and 6.8 132 6.10 P r o b a b i l i t y , P($m,n), that n consecutive b i t s i n c l u d e at l e a s t m e r r o r s ; derived from the measured multigap e r r o r s t a t i s t i c s f o r the b i n a r y magnetic r e c o r d i n g channel 134 6.11 O v e r a l l e r r o r r a t e s , p Q , on the b i n a r y magnetic r e c o r d i n g channel f o r v a r i o u s codes w i t h rates of approximately 5/6 136 6.12 O v e r a l l e r r o r r a t e s , p Q , on the magnetic re c o r d i n g channel f o r i n t e r l e a v e d coding at approximately 5/6 r a t e 136 7.1 I l l u s t r a t i n g the use of DFE to compensate f o r the d.c. n u l l : i n the magnetic re c o r d i n g channel 143 7.2 Feedback f i l t e r amalgamating compensation f o r the d.c. '. n u l l w i t h c l a s s I p a r t i a l , response s i g n a l l i n g : . . 1 4 3 7.3 D i s c r e t e time model of the magnetic recording channel w i t h DFE re c e p t i o n 146 7.4 C a l c u l a t e d e f f e c t of applying.reduced feedback w i t h p a r t i a l response (ternary :eye) s i g n a l l i n g ; based on measured a d d i t i v e noise and fade d i s t r i b u t i o n s . . . . 147 7.5 E r r o r r a t e vs. bandwidth of d.c. n u l l , w i t h and without DFE, i m=0.5 A, mk=0.83 150 7.6 E f f e c t of reducing feedback l e v e l , t\, i m=0.5 A, T/ITRC=0.02 150. 7.7 E r r o r r a t e vs. l e v e l of feedback from immediately preceding b i t : l . f . feedback a p p l i e d w i t h T/TTRC=0.02, mk=0.8, i m=0.50 152 7.8 E f f e c t upon d.c. n u l l compensation of i n t r o d u c i n g erasure region as i n f i g . 7.9a; T/TTRC=0.02, mk=0.8, i m=0.5A . . 1 5 2 7.9 Attempts to compensate f o r channel fading by the use of erasure decoding 154 A3.1 E q u a l i z a t i o n e r r o r r e s u l t i n g from the use of a 7-tap z e r o - f o r c i n g t r a n s v e r s a l f i l t e r upon a s i g n a l of the form, e - a l w l 168 x i i ACKNOWLEDGEMENT S I should l i k e to thank the Canadian people f o r t h e i r generous f i n a n c i a l support through the U n i v e r s i t y of B r i t i s h Columbia and the N a t i o n a l Research C o u n c i l (Grant A-3308). A Frank A. Cowan Award administered by the I n s t i t u t e of E l e c t r i c a l and E l e c t r o n i c Engineers was a l s o g r a t e f u l l y accepted. The t h e s i s t o p i c was suggested by Dr. Robert W. Donaldson who has provided sound guidance and s u c c i n c t advice thoughout. I am p a r t i c u l a r l y g r a t e f u l f o r h i s a s s i s t a n c e i n the pr e p a r a t i o n of p u b l i c a t i o n s associated wit h t h i s work and h i s c o n s t r u c t i v e c r i t i c i s m of the t h e s i s i t s e l f . I am indebted to many members of the f a c u l t y , s t a f f , and student population of the Dept. of E l e c t r i c a l Engineering f o r t h e i r advice, a s s i s t a n c e , and t o l e r a n c e . In p a r t i c u l a r , Mrs. Shih-Ying Hoy and Miss L i s a O h r l i n g typed the bulk of the t h e s i s . Despite the many s a c r i f i c e s which a student budget imposes, my w i f e , Carole, has provided immeasurable support and encouragement throughout my s t u d i e s . x i i i I INTRODUCTION AND BACKGROUND 1.1 INTRODUCTION Over some f i v e m i l l e n n i a the progress of human s o c i e t y has been marked by the e v o l u t i o n of i n c r e a s i n g l y s o p h i s t i c a t e d methods of r e c o r d i n g i n f o r m a t i o n . This e v o l u t i o n , from e a r l y pictographs through symbolic r e p r e s e n t a t i o n to modern alphabets, makes the n a t u r a l advantages of d i g i t a l formats apparent. D i g i t a l i n f o r m a t i o n can be recorded upon a v a r i e t y of media ranging from the f a m i l i a r p r i n t e d page to the high speed storage r e g i s t e r s w i t h i n an e l e c t r o n i c computer. The development of magnetic r e c o r d i n g has been regarded as an e v o l u t i o n a r y step of s i g n i f i c a n c e comparable to the p r i n t i n g press [ 1 ] . The ubiquitous magnetic tape provides the primary r e c o r d i n g medium f o r audio and video s i g n a l s i n analog format. In d i g i t a l format, magnetic media are used almost e x c l u s i v e l y f o r storage or exchange of machine readable records. Even i n f i e l d s where more d i r e c t p r e s e n t a t i o n i s intended, d i g i t a l magnetic rec o r d i n g i s becoming i n c r e a s i n g l y i n v o l v e d i n p r e p a r a t i o n and storage; examples i n c l u d e cartography, p u b l i s h i n g and audio r e c o r d i n g . In the context of the current " i n f o r m a t i o n e x p l o s i o n " , one of the more important c o n s i d e r a t i o n s i s the sheer p h y s i c a l bulk of recorded i n f o r m a t i o n . Figure 1...1 -is a gross comparison of the i n f o r m a t i o n packing d e n s i t i e s of two f a m i l i a r h i s t o r i c a l records [2,3], an e a r l y 800 b i t s per i n c h magnetic tape format, and a r e c e n t l y discussed h i g h d e n s i t y r e c o r d i n g system [ 4 ] . A l s o i n d i c a t e d i s the d e n s i t y achieved by an i s o l a t e d s t r a n d of deoxyribonuceic a c i d (DNA). DNA provides primary storage of b i o l o g i c a l i n f o r m a t i o n and a l l o w s , perhaps, the u l t i m a t e comparison. - 1 -R o s e t t a S t one , 196 B.C. Domesday Book, 1086 8 0 0 b . p . i . Tape, 1967 H igh D e n s i t y Tape , 1978 S t r a n d o f DNA w////////////////////////////.//m 10 •15 DENSITY 10 5 ( b i t s / u m 3 ) 1 0 + 5 F i g u r e 1.1 Gros s Compar i son o f r e c o r d i n g d e n s i t i e s I t i s , of course, u n f a i r to compare p a c k i n g : d e n s i t i e s without regard to the f u n c t i o n of the records or the system supporting them. Nevertheless F-ig.l-l suggests s u b s t a n t i a l improvements i n d e n s i t y commensu-ra t e w i t h t e c h n o l o g i c a l developments. Such improvements r e f l e c t human s o c i e t y ' s i n c r e a s i n g requirement f o r and dependence upon recorded informa-t i o n [5,6]. I t i s t h i s observation which provides the e s s e n t i a l m o t i v a t i o n f o r the work presented here. 1.2 OBJECTIVES The o v e r a l l o b j e c t i v e of t h i s t h e s i s i s to develop techniques which f u r t h e r f a c i l i t a t e the storage and recovery of d i g i t a l i n f o r m a t i o n . The s e l e c t i o n of magnetic r e c o r d i n g technology to f u l f i l t h i s o b j e c t i v e a r i s e s from i t s assured continued preeminence [7,8] and from the promise of la r g e performance improvements [9]. Recording at high d e n s i t y eases the d i f f i c u l t i e s of storage and t r a n s p o r t a t i o n of l a r g e q u a n t i t i e s of informa-t i o n , allows more economic use of the r e c o r d i n g medium, and o f t e n leads to - 2 -higher record/playback r a t e s and improved r e l a t i v e access time. Such improvements are however compromised by a v a r i e t y of f a c t o r s such as the v e r a c i t y of reproduction,system c o s t , d u r a b i l i t y o f . r e c o r d i n g medium and s u b s t r a t e , and i n some s i t u a t i o n s the requirement f o r backwards t e c h n o l o g i c a l c o m p a t a b i l i t y . The o b j e c t i v e i s t h e r e f o r e to maximise the b u l k data packing d e n s i t y upon the magnetic tape r e c o r d i n g medium w h i l e m a i n t a i n i n g acceptable system performance. The record/playback process i s e s s e n t i a l l y confined to a two-dimensional i n t e r f a c e and the problem of maximising the a r e a l data d e n s i t y can be considered l a r g e l y independently of tape t h i c k n e s s . While r e d u c t i o n of the medium and sub s t r a t e thicknesses (which the tape t h i c k n e s s comprises) i s of d i r e c t value i n maximising bulk d e n s i t y , the problems i n v o l v e d are of a mechanical and chemical nature and do not c o n s t i t u t e the major focus of t h i s t h e s i s . The r e c o r d i n g process normally i n v o l v e s the p l a c i n g of data sequences i n w e l l defined t r a c k s . A r e a l data d e n s i t y i s thus the product of t r a c k and l i n e a r d e n s i t i e s . Some of the problems a s s o c i a t e d w i t h maximiz-i n g track d e n s i t y are of a mechanical n a t u r e , but the achievable l i n e a r d e n s i t y i s s t r o n g l y dependent upon t r a c k w i d t h . Thus the question of trackw i d t h a r i s e s i n t i m a t e l y i n the design of the playback s i g n a l processor. Trackwidth is,.however, determined d i r e c t l y by the p h y s i c a l w i d t h of the rec o r d head and represents one of the l e s s f l e x i b l e parameters a v a i l a b l e f o r study i n t h i s t h e s i s . The o b j e c t i v e s of the t h e s i s are thus approached p r i m a r i l y by an attempt to maximize l i n e a r r e c o r d i n g d e n s i t y . The motion of the rec o r d / playback head along the t r a c k t r a n s l a t e s s i g n a l design problems i n t o the time domain. The r e c o r d i n g and subsequent r e t r i e v a l of i n f o r m a t i o n can be - 3 -considered akin to the transmission and reception of information over a communication channel. In this context the "magnetic recording channel" i s defined and the maximization of data rate, with due regard to the error rate and the nature of those errors, becomes the principal task. 1.3 BACKGROUND 1.3.1 Magnetic Recording One of the earliest references to magnetic recording was made in 1888 by 0. Smith [10] whose machine recorded upon cotton cord impregnated with iron dust. Subsequent improvements by Poulsen [11]., recording upon steel wire, f i r s t enabled the reproduction of speech and music. Further advances awaited the introduction of de Forest's triode amplifier [12] which, however, made apparent the high levels of distortion and noise on early direct recordings. Two engineers working at the U.S. Naval research Laboratory noted a sudden improvement in quality which they eventually attributed.to the spontaneous os c i l l a t i o n of an amplifying stage [13]. By 1927 the two engineers, Carlson and Carpenter, had obtained a patent [14] which included the.technique of a . c . - bias recording. In the same year O'Neill was granted a patent [15] for a paper tape coated with magnetic material. These two inventions set the stage for modern audio tape recording. By the end:of the second World War the 'Magnetophon' [16] had emerged as the preferred type of recording machine. This machine employed both coated tape and a.c- bias recording and was the prototype for modern high quality audio and instrumentation machines. Professional audio machines use stationary record/playback heads and reel-to^reel tape motion; these machines enjoy 60-65 dB signal-to-noise ratio (15 KHz bandwidth) with 0.3% third harmonic distortion and up to 24 - 4 -p a r a l l e l channels on two-inch tape [ 1 ] . Tape consumption remains s u r p r i s i n g l y h i g h at 0.76 m/sec. The more general c l a s s of i n s t r u m e n t a t i o n machines i n c l u d e s p r e c i s e l y engineered and designed recorders f o r a p p l i c a -t i o n s i n t e l e m e t r y , geophysics, medicine and other s c i e n t i f i c f i e l d s . These recorders employ high q u a l i t y tapes burnished to a surface f i n i s h of o p t i c a l q u a l i t y and c a r e f u l l y s l i t . A c c u r a t e l y formed heads w i t h gaps below 0.5 um enable wavelengths as short as 0.75 um to be s u c c e s s f u l l y recovered [ 1 ] . The a.c. - b i a s l e v e l and s i g n a l l e v e l are c a r e f u l l y adjusted to maximize high frequency recovery and minimize n o n l i n e a r d i s t o r t i o n ; d.c. balance currents are a p p l i e d t o the r e c o r d i n g head to cancel the e f f e c t s of ambient f i e l d s . The r e c o r d i n g of video s i g n a l s has n e c e s s i t a t e d development of techniques somewhat d i f f e r e n t to those employed i n audio and i n s t r u m e n t a t i o n machines. The l a r g e bandwidth and h i g h timebase s t a b i l i t y r e q u i r e d by video s i g n a l s motivated the c l a s s of r o t a t i n g head machines which o f f e r high r e l a t i v e head^tape speed and good timebase s t a b i l i t y governed by the r o t a t i n g head's i n e r t i a . In the transverse format four heads mounted on a r o t a t i n g drum scan d i r e c t l y across the width of the tape at 39 m/s g i v i n g broadcast q u a l i t y r eproduction. For the consumer market, q u a l i t y i s n e c e s s a r i l y compromised. Remarkable performance i s nevertheless achieved [17-19] w i t h up to four hours of r e c o r d i n g on a s i n g l e r e e l . Consumer video machines employ h e l i c a l scan i n v a r i o u s formats. The a-format i s depicted i n F i g . 1.2: tape i s wrapped i n a s i n g l e h e l i c a l t u rn around a c y l i n d r i c a l drum. A narrow c e n t r a l s e c t i o n of the drum r o t a t e s c a r r y i n g a r e c o r d / playback head d i a g o n a l l y across the tape width. The fi-format using 180° tape wrap and two heads has become more popular s i n c e i t advantageously allows t r a c k s to be recorded w i t h a l t e r n a t e l y s l a n t e d azimuth [17]. - 5 -I I I I I ROTATES AT ^ 60 Hz FIGURE 1-2 STATIONARY CYLINDRICAL DRUM HELICAL-SCAN TAPE FORMAT The most popular video and audio machines take advantage of the convenience of c a s s e t t e l o a d i n g . The a d d i t i o n a l tape p r o t e c t i o n thus a f f o r d e d helps to maintain clean tape surfaces and permits the use of t h i n n e r , l e s s robust tapes. 1.3.2 D i g i t a l Recording Q u a n t i z a t i o n ( d i g i t i z a t i o n ) of i n f o r m a t i o n has been i m p l i c i t i n the development of spoken and then w r i t t e n languages. I t has been r e i n f o r c e d by the i n t r o d u c t i o n of p r i n t i n g i n 1455 and t y p i n g [20] i n 1873; indeed, modern language may be adequately expressed by a few as t h i r t y symbols. Reductions to b i n a r y code were f i r s t made by B r a i l l e [20] i n 1829 and Morse [21] i n 1837. Although a magnetic recorder was used as e a r l y as 1912 to record telegraph s i g n a l s [12], the r e c o r d i n g of elementary b i n a r y data d i d not become widespread u n t i l the i n t r o d u c t i o n of d i g i t a l machines around 1948. Computer memories are normally organized i n t o a h i e r a r c h y of i n c r e a s i n g access time but decreasing c o s t . D i g i t a l magnetic tape r e c o r d i n g f u l f i l s almost u n i v e r s a l l y the r o l e of b u l k storage at low c o s t . Paper tape and cards are used but o f f e r very poor packing d e n s i t y . Large memories w i t h improved access are obtained on magnetic d i s c s [22] or w i t h v e r y - l a r g e - s c a l e i n t e g r a t i o n (VLSI) technologies [23 - 29]. R i g i d substrates do not f a c i l i t a t e h i g h volume storage d e n s i t i e s . The advantages of s t r u c t u r e d s u b s t r a t e s (VLSI) w i t h t h e i r freedom from mechanical motion are o f f s e t by the high cost of p r o c e s s i n g , by t h e i r i n t o l e r a n c e to surface d e f e c t s , and by the d i f f i c u l t y of i n t e r c o n n e c t i n g and packing l a r g e numbers of moderately s i z e d memory 'chips'. - 7 -Competition to high d e n s i t y d i g i t a l magnetic tape systems has been considered only on homogeneous substrates where memory s t r u c t u r e i s superimposed by mechanical movement and/or beam addressing. E l e c t r o n beams are e a s i l y focussed and d e f l e c t e d ; such systems [30], however, have l i m i t e d c a p a c i t y because of the need to work i n vacuo ( p r e c l u d i n g l a r g e s c a l e mechanical movement). V i s i b l e l i g h t beams are a t t r a c t i v e i n view of the transparency of a i r and the a v a i l a b i l i t y of o p t i c a l components. S u i t a b l e l i g h t beams a r e , however, more d i f f i c u l t to generate and to d e f l e c t r a p i d l y and e f f i c i e n t l y through l a r g e angles [31]. Permanent records may be w r i t t e n upon photographic emulsion [32] but g e n e r a l l y i n v o l v e the inconvenience of wet processing. This inconvenience may be avoided by thermal w r i t i n g w i t h a high power l a s e r upon a m e t a l l i c s u r f a c e [33]. A l t e r a b l e bulk data stores using o p t i c a l technology do not appear to be commercially a v a i l a b l e . Systems have been i n v e s t i g a t e d which i n v o l v e Curie p o i n t (or thermomagnetic c o e r c i v i t y change) w r i t i n g and Faraday r o t a t i o n 2 12 readout [34,35]. D e n s i t i e s of 10,000 bits/mm and c a p a c i t i e s of 10 b i t s (comparable w i t h h i g h - d e n s i t y magnetic tape systems) have been demonstrated on a magnetooptic tape system [31]. D i f f r a c t i o n l i m i t s have been approached 9 on magnetooptic d i s c s [36] y i e l d i n g around 10 b i t s per d i s c s u r f a c e . Problems i n c l u d e h i g h system costs and low t r a n s f e r r a t e s . Holographic data storage i s s i m i l a r l y d i f f r a c t i o n l i m i t e d [37]. However, t o l e r a n c e t o medium i m p e r f e c t i o n s , the p o s s i b i l i t y of high t r a n s f e r r a t e s i n the absence of moving p a r t s , and the p o s s i b i l i t y of r e c o r d i n g d i r e c t l y w i t h i n the volume of the medium [38] combine to make holographic>.systerns p o t e n t i a l l y a t t r a c t i v e . The p a r a l l e l nature of input and output leads to questions of c o m p a t a b i l i t y w i t h extant s e r i a l l y -o r i e n t e d d i g i t a l systems. This f a c t o r together w i t h h i g h system cost and - 8 -the d i f f i c u l t i e s of r e a l i z i n g the promised t h e o r e t i c a l d e n s i t i e s have discouraged commercial development to date. The ubiquitous magnetic tape has been i n v o l v e d from the i n c e p t i o n of d i g i t a l e l e c t r o n i c machines [39,40]. The e a r l i e s t formats [41,42] were d i c t a t e d by s i x b i t t r a n s m i s s i o n codes and i n v o l v e d d i r e c t r e c o r d i n g of data i n seven ( i n c l u d i n g p a r i t y ) p a r a l l e l t r a c ks at 200, 556, or 800 b i t s per i n c h (b.p.i) on h a l f - i n c h tape. Although most data i s p r e s e n t l y recorded at 63 bits/mm (1600 b. p. i . ) w i t h nine t r a c k s , i t i s a n t i c i p a t e d that 244 bits/mm (6250 b.p.i.) w i l l become the i n d u s t r y standard. These formats o f f e r only moderate storage d e n s i t i e s and do not approach p h y s i c a l l i m i t a t i o n s on l i n e a r or t r a c k d e n s i t y . Much higher l i n e a r and t r a c k d e n s t i e s have been demonstrated on d i s c s , and on i n s t r u m e n t a t i o n and video machines. High-density tape systems were f i r s t attempted us i n g l o n g i t u d i n a l t r a n s p o r t s and met w i t h v a r y i n g degrees of success i n terms of data d e n s i t y , r e l i a b i l i t y , and c o s t . Table 1.1 i n d i c a t e s the important c h a r a c t e r i s t i c s of h i g h - d e n s i t y magnetic tape r e c o r d i n g systems developed over the l a s t few 2 years. On l o n g i t u d i n a l systems a d e n s i t y of 1400 bits/mm was achieved [46]. L o n g i t u d i n a l r e c o r d e r s , however, s u f f e r two d i s t i n c t disadvantages. High r e l a t i v e head-tape speed i s d e s i r e d to f a c i l i t a t e s i g n a l recovery and high t r a n s f e r r a t e s ; s t a t i o n a r y heads th e r e f o r e l e a d to excessive tape v e l o c i t y and consumption. High t r a c k d e n s i t y on l o n g i t u d i n a l machines i m p l i e s expensive m u l t i - t r a c k head assemblies and extensive d u p l i c a t i o n of record and playback c i r c u i t s . Higher data d e n s i t i e s and t r a n s f e r r a t e s have thus been achieved on r o t a t i n g head machines. Recently a high d e n s i t y recorder has been reported by M a l l i n s o n [4] o f f e r i n g s i g n i f i c a n t improvements i n a r e a l and - 9 -DENSITY/mm11 LONGITUDINAL HELICAL BIT ERROR YEAR LINEAR TRACK AREA VOLUME TRANSVERSE RATE RATE CODE REF. 1968 1600 bpi 63 0.71 40 860 L 1 Mb/s -9 <10 • Bi0 1973 Bell & Howell 1140 0.55 630 L 37 Mb/s 7/8 ENRZ [43] 1973 HDMR (RCA) 800 1.77 1420 52,000 L 240 Mb/s 2x l 0 - 6 Bi<J> [42] 1973 Miniscan (Ampex) 200 7.4 1500 H 5 Mb/s i o " 5 F.M. 1974 MMR-1 (IVC) 284 1160 40,700 8 Mb/s i o " 6 M i l l e r [44] 1974 TBM (Ampex) 300 7.4 1100 T : 6 Mb/s IO" 1 0 F.M. [45] 1975 Sangamo 1310 1.1 1400 L 4 Mb/s 28 Channels i o " 7 NRZ [46] 1975 3850 (IBM) 110 3.5 300 2,500 H [47] 1975 MacDonald Dettwiler Assoc., Vancouver 600 4.1 2200 51,000 H 10 Mb/s mean IO" 6 7/8 ENRZ 1977 Prototype (UBC) 1080 4.1 4030 92,000 H 18 Mb/s mean <10-5 NRZ 1978 Ampex 393 26.3 10300 190,000 H X 30 Mb/s 25 Channels < i o " 6 M2 [4] TABLE 1.1 Comparison of Recent High-Density D i g i t a l Magnetic Tape Recorders o i volume d e n s i t i e s . These improvements have been achieved at moderate l i n e a r d e n s i t y but by almost an order of magnitude decrease i n t r a c k width (39 um). Problems are being overcome i n the f a b r i c a t i o n of narrow-track multi-head assemblies and i n the c o n t r o l of c r o s s t a l k between heads/tracks. C a r e f u l design of the head-tape i n t e r f a c e [48,49,4] and, i n p a r t i c u l a r the use of a s e r v o - c o n t r o l l e d a u t o - t r a c k i n g head assembly [50,51,4] have been important steps i n the development of t h i s h i g h d e n s i t y recorder. 1.4 OUTLINE OF THESIS Chapter two contains a review of the l i t e r a t u r e appropriate to the t h e s i s t i t l e . The u n d e r l y i n g p h y s i c a l processes are f i r s t d iscussed and the present s t a t e of understanding i n d i c a t e d . The record/playback process may be modelled as a communication channel. In t h i s l i g h t v a r i o u s process c h a r a c t e r i s t i c s i n c l u d i n g d i s p e r s i o n , n o n l i n e a r behaviour, a d d i t i v e n o i s e and f a d i n g are examined. A b r i e f review f o l l o w s of the techniques used on current data t r a n s m i s s i o n channels and of attempts to extend t h e i r a p p l i c a t i o n to n o n l i n e a r data channels. The chapter concludes w i t h a d i s c u s s i o n of techniques which have been a p p l i e d t o , or considered f o r , the d i g i t a l magnetic r e c o r d i n g channel. Chapter three deals w i t h the c h a r a c t e r i z t i o n of a t y p i c a l magnetic record/playback channel. A h e l i c a l - s c a n video tape t r a n s p o r t i s s e l e c t e d f o r c o n s i d e r a t i o n and appropriate record/playback c i r c u i t r y and t e s t c i r c u i t r y are developed. Measurements are made to c h a r a c t e r i z e the channel i n terms of l i n e a r / n o n l i n e a r behaviour, a d d i t i v e n o i s e , m u l t i p l i c a t i v e n o i s e , and other e f f e c t s of secondary importance. The i n v e s t i g a t i o n of m u l t i p l i c a t i v e n o i s e i s extended i n an attempt to describe the u n d e r l y i n g p h y s i c a l processes. - 11 -Chapter four considers signal and receiver (playback circuitry) design for digital magnetic recording channels in general and for the channel characterized above in particular. The results of those considerations are embodied in a prototype Recording system which is described in the remainder of the chapter. Chapter five deals initially with the selection of test sequences but is essentially concerned with analog and digital measures of the prototype system performance. Of particular interest is the minimization of error rate as a function of system parameters such as the record level, head-preamplifier coupling, and receiver complexity. For many applications the raw error rates available from high density recording schemes are unacceptable. The efficacy of error control techniques are therefore assessed in Chapter six. The assessment requires the measurement of higher order error statistics and of the distribution of the equalized playback signal level. Chapter seven deals with the application of decision feedback to the magnetic recording channel. A novel method of compensating the d.c. null is described. In the presence of decision feedback further measurements of the prototype system performance are made. The final chapter provides a brief review of the work accomplished in this thesis. The concluding remarks consider the trend toward narrower tracks and indicate the probable emphases of future work. - 12 -I I REVIEW OF OTHERS' WORK The f i r s t s e c t i o n of t h i s review deals w i t h the p h y s i c a l , magnetic and e l e c t r i c a l processes of magnetic r e c o r d i n g . Understanding of these processes has allowed s i g n i f i c a n t improvements i n modelling d i g i t a l magnetic r e c o r d i n g . The second s e c t i o n considers the c h a r a c t e r i s t i c s of the 'magnetic re c o r d i n g channel' such as noise sources, f a d i n g behaviour, and no n l i n e a r e f f e c t s . The f i n a l s e c t i o n deals w i t h s i g n a l and r e c e i v e r design ( i n c l u d i n g a p p l i c a t i o n s to nonl i n e a r channels) and w i t h techniques used on d i g i t a l magnetic recorders. 2.1 THE PHYSICS OF MAGNETIC RECORDING 2.1.1 Magnetic recording media Magnetic tape comprises a t h i n p l a s t i c s u b s t r a t e coated w i t h magnetic m a t e r i a l . The sub s t r a t e must be s t r o n g , dimensionally s t a b l e , and s u i t a b l e f o r a r c h i v a l storage. Paper, c e l l u l o s e a c e t a t e , and p o l y v i n y l c h l o r i d e preceded the present p o l y e s t e r substrates [8, 13, 52. 53]. The magnetic m a t e r i a l should have high remnance and c o e r c i v i t y . However the wide choice of a v a i l a b l e m a t e r i a l s i s r e s t r i c t e d by two s p e c i a l requirements. The p a r t i c l e s or grains of the magnetic medium should be s u f f i c i e n t l y s m a l l and independent to enable recording at high d e n s i t y w i t h adequate s i g n a l - t o -noise r a t i o (SNR). I t must a l s o be p o s s i b l e to coat onto the sub s t r a t e a t h i n , f l e x i b l e l a y e r of the medium w i t h an e x c e p t i o n a l l y smooth surface [54], Current tapes are coated to a thickness of about 2 um w i t h s m a l l magnetic p a r t i c l e s suspended i n an organic binder. Most tapes use elongated p a r t i c l e s of Y-Fe20 3 t y p i c a l l y 0.2 um long w i t h a 5:1 a x i a l r a t i o [55] and o r i e n t e d along the length of the recorded t r a c k s . The e f f e c t s of self-demagnetiza-t i o n [56] l i m i t high frequency (h.f.) response. The recent 'high energy' - 13 -tapes (with c o b a l t doped y-Fe203 [57] or C r p 2 [58]) attempt to reduce s e l f -demagnetization by i n c r e a s i n g c o e r c i v i t y . M e t a l l i c p a r t i c l e coatings have been announced [59] which give considerable advantage i n SNR [54]. Steps must be taken to prevent the o x i d a t i o n of the Fe or Fe-Co p a r t i c l e s . In p a r t i c u l a t e media i t i s d e s i r a b l e to have a s m a l l spread i n magnetic c h a r a c t e r i s t i c s , a uniform d i s t r i b u t i o n throughout the b i n d i n g m a t e r i a l , a high packing f r a c t i o n , and good o r i e n t a -t i o n . The tardy i n t r o d u c t i o n of m e t a l l i c p a r t i c l e coatings-has a r i s e n from p r a c t i c a l d i f f i c u l t i e s i n a c h i e v i n g the above goals [1,8]. P l a t e d m e t a l l i c media have not found a p p l i c a t i o n i n systems employing f l e x i b l e tape. Further d i s c u s s i o n of r e c o r d i n g media may be found i n [1,8,52,54,55,57,60-62]. 2.1.2 Magnetic record/playback heads The gapped r i n g head, F i g . 2.1a, has c o n v e n t i o n a l l y been used to provide the sharply defined magnetic f i e l d s e s s e n t i a l f o r high d e n s i t y r e -cording. The nature of the gap f r i n g i n g f i e l d i s of fundamental importance i n the theory of magnetic re c o r d i n g . The manner i n which the K a r l q u i s t [63] approximation a r i s e s i s i n d i c a t e d below and i n F i g . 2.1b. The x - a x i s l i e s along the d i r e c t i o n of head-tape motion, the y-a x i s i n t o the depth of the tape, and the extent of the head i n the z - d i r e c t i o n determines the t r a c k width. The f i e l d , h ( x , y ) , produced by a s e m i - i n f i n i t e head of high p e r m e a b i l i t y i s i d e n t i c a l to that produced by a z - d i r e c t e d current f i l a m e n t , i m . (constant f a c t o r s are ignored) h x (x,y) = i m . y/(x 2+y 2) - (2.1a) - 14 -pole face / " n e a d 9°P magnetizing -S> current •m \head coil Fig. 2-1 a Gapped ring head 2-directed current filament z-directed current Fig. 2-1 b Approximation to gap fringing field - 15 -The F o u r i e r transform (along the x-axis) of t h i s f i e l d component i s H x(k,y) = i m . j exp (-ky) k > 0 (2.1b) where the conjugate nature of the transform f o r k<0 i s presumed. The f i n i t e gap, 2g, i s approximated by a current sheet of s i m i l a r width; the assumption being that the f r i n g i n g f i e l d at the head surface remains p a r a l l e l to that surface. Thus h x(x,y) = i m . t a n " 1 [ 2 y g / ( x 2 + y 2 - g 2 ) ] (2.2a) H x(k,y) = 1^ . j exp(-ky) s i n kg/kg k>0 (2.2b) Fan [64] has confirmed the accuracy of (2.2) i n p r a c t i c a l a p p l i c a t i o n s . The extent of the head i n the z-dimension (typically>100g) g e n e r a l l y j u s t i f i e s the two-dimensional treatment. Continuing reductions i n t r a c k -width have, however, prompted s t u d i e s of the s i d e f r i n g i n g f i e l d [4, 65-67] which extends beyond the gap ends. I t s behaviour i n the z-dimension has proven s i m i l a r to that of the gap f r i n g i n g f i e l d i n the y-dimension. With the exception of magnetooptic devices [31] a l l magnetic record/playback transducers r e l y on high p e r m e a b i l i t y m a t e r i a l s to d e f i n e r e s o l u t i o n . Mallinson.[68] has shown that a l l such heads d i s p l a y the same behaviour, exp(-,k/y), i n the y-dimension and that h x and hy n e c e s s a r i l y form a H i l b e r t transform p a i r along the x - a x i s . M a l l i n s o n a l s o recognised t h a t , w h i le the gap-width determines h.f. response, low frequency (31. f.) response i s determined by the o v e r a l l head dimensions. This f a c t i s manifest on i n t e g r a t e d heads [69] as f i e l d s around the outer edges of the pole face; these f i e l d s should be i n c l u d e d i n d e s c r i p t i o n s of the read and w r i t e - 16 -processes. The p o s s i b i l i t y of commercial a p p l i c a t i o n seems c l o s e f o r both i n t e g r a t e d magnetodynamic heads [70] and t h i n - f i l m magnetoresistive playback heads [71,72]. The record head gap i s not c r i t i c a l s i n c e record r e s o l u t i o n i s p r i m a r i l y determined by f i e l d g radients at the t r a i l i n g gap edge. A m a t e r i a l w i t h high s a t u r a t i o n l e v e l i s r e q u i r e d to a l l o w r e c o r d i n g on high c o e r c i v i t y tapes. The playback head should have a narrow gap and be made of a h i g h -p e r m e a b i l i t y , l o w - l o s s , non-magnetostrictive m a t e r i a l . The mechanical behaviour of the head-tape i n t e r f a c e i s of c r u c i a l importance i n high d e n s i t y recording. The recovered s i g n a l s present a r a p i d l y decreasing f u n c t i o n of head-tape s e p a r a t i o n . U n f o r t u n a t e l y reduced separation leads to excessive head wear ( F e r r i t e heads are chosen as much fo r t h e i r e x c e l l e n t wear r e s i s t a n c e as f o r t h e i r h.f. performance). Smooth tape surfaces are e s s e n t i a l to minimise f l u c t u a t i o n s i n head-tape se p a r a t i o n . Measurement [48,73,74] and design [4,49] f o r the head-tape i n t e r f a c e are reasonably understood, 0.3 um s e p a r a t i o n r e p r e s e n t i n g a reasonable compromise between head-wear and s i g n a l l o s s . 2.1.3 The record and storage processes The processes occurring-as the -tape--,passes -the -recordings head, are the l e a s t understood i n magnetic recording theory. The instantaneous magnet-i z a t i o n , M ( r , t ) , at time, t , and at a p o i n t , r , f i x e d w i t h i n the medium, i s a f u n c t i o n of the i n i t i a l s t a t e , M(r, 0 ) , and the time h i s t o r y , over a l l x < t , of the l o c a l f i e l d , H ( r , t ) , JO M(r\ t ) = f T < t [ H £ ( ? , x ) , M(r, 0)] (2.3) where f [?] i s the vector M - H c h a r a c t e r i s t i c . T<t J The l o c a l f i e l d i s i t s e l f a f u n c t i o n of the l o c a l magnetization as w e l l as the a p p l i e d gap f r i n g i n g f i e l d , h ( r - i v t ) , where i v i s the r e l a t i v e head-tape v e l o c i t y ; i . e . H^(r, t) = h ( r - i v t ) - JV.M(r, t ) ( r - r ) / | r - r | .dr (2.4) Image terms, generated by the pr o x i m i t y of the high p e r m e a b i l i t y head, have been omitted from (2.4). D i f f i c u l t i e s i n the s o l u t i o n of (2.3-2.4) a r i s e p r i n c i p a l l y from the l a c k of adequate d e s c r i p t i o n s of the M-H c h a r a c t e r i s t i c . This c h a r a c t e r i s t i c a r i s e s s t a t i s t i c a l l y from the r e o r i e n t a t i o n of magnetic domains and, i n p a r t i c u l a t e media, i s h i g h l y dependent upon the s i z e , shape, d i s p e r s i o n , method of p r e p a r a t i o n , and surface b i n d i n g of the p a r t i c l e s [54]. The d i f f i c u l t y of d e s c r i b i n g even s c a l a r M—H curves i s noted [75]. Frequently the w r i t e process has been s i m p l i f i e d by assuming t r a n s i -t i o n s between recorded b i t s to have an arctangent form i n M^x) (My and dK^/dy being ignored) [76-78], as f o l l o w s : M x(x) = (2M r /TT) t a n - 1 ( x / J l ) (2.5) where M r i s the remanence, and I, the t r a n s i t i o n l e n g t h , takes the l e a s t value which avoids self-demagnetization. Other models [56, 79-81] a r r i v e at a f i n a l t r a n s i t i o n shape by s e l f - c o n s i s t e n t computations on a one-dimensional w r i t e process/ These analyses are more a p p l i c a b l e to saturated r e c o r d i n g and t h i n media ( d i s c s and low-density tape). Modern media e x h i b i t good o r i e n t a t i o n j u s t i f y i n g n e glect of the perpendicular component, My . At high d e n s i t i e s the medium depth becomes s i g n i f i c a n t and the y - v a r i a t i o n must be included [82-85]. Measurements of magnetization d i s t r i b u t i o n s and more q u a l i t a t i v e models are contained i n [86,87]. The record process has a l s o been described w i t h curved [88,89] or t i l t e d [90] magnetic t r a n s i t i o n s corresponding to the contour upon which the a p p l i e d f i e l d i s equal to the medium c o e r c i v i t y . Ortenburger and P o t t e r [50] seem to have developed the most complete modelling. P a r t i c l e s w i t c h i n g energies exceed thermal energies by a f a c t o r which t y p i c a l l y exceeds 10 3 . The permanence of the recorded data i s thus w e l l assured; no superparamagnetic decay occuring w i t h i n conceivable time spans. Some p a r t i c l e s are i n e v i t a b l y s u s c e p t i b l e to superparamagnetic e f f e c t s and, i n conjunction w i t h f i e l d s from adjacent l a y e r s of tape, the phenomenon of 'print-through' occurs ( t y p i c a l l y -50 dB down [ 1 ] ) . In the absence of l a r g e ambient magnetic f i e l d s , the chemical s t a b i l i t y of p a r t i c l e s , b i n d e r , and s u b s t r a t e become paramount f o r a r c h i v a l storage. 2.1.4 The playback process In c o n t r a s t to the h i g h l y n o n l i n e a r record process, the playback process i s l i n e a r . Subsequent to the remagnetization induced by 'keeper' a c t i o n at the l e a d i n g edge of the pole face, the recorded s i g n a l s are l i n e a r l y transduced as they pass the head gap and couple i n t o the head c o i l . This l i n e a r t r a n s d u c t i o n i s most s u c c i n c t l y expressed by the r e c i p r o c i t y p r i n c i p l e [91]; the f l u x , <()(t) , threading the head c o i l i s <Kt) = j W - i v t ) . M ( r ' ,<*>) dr' (2.6) where M(r ,°°) represents the recorded magnetization. From (2.2) the response to an element, v S t , of x - d i r e c t e d magnetization i s , 5 $ x ( t ) = t a n " 1 { 2 y g / ( v t ) 2 +y 2-g 2)} v 6 t (2.7a) - 19 -the constant f a c t o r again being omitted. The F o u r i e r transform of <j>x(t) i s 6$ (co) = j exp (-coy/v)sin(cdg/v)/(ci)g/v)6t co>0 (2.7b) I n t e g r a t i n g (2.7b) w i t h respect to y, over the medium t h i c k n e s s , d, gives the f a m i l i a r Wallace output voltage spectrum [92], co > 0 E x(w) = j v [ l - exp(wd/v)] exp(-coa/v)sin(tog/ v)/(wg/y) (2.8) where a i s head-tape se p a r a t i o n . Equation (2.8) describes the voltage response of the playback head to a s i n u s o i d a l x - d i r e c t e d magnetization, uniform over y w i t h wavenumber, k=w/v. The constant, v, i n d i c a t e s the dependence of recovered s i g n a l energy upon r e l a t i v e head-tape v e l o c i t y . The f a c t o r , l-exp(-a)d/v), i s sometimes termed the t h i c k n e s s l o s s and introduces a d.c. n u l l i n the vo l t a g e response. The f a c t o r , exp(-coa/v), i l l u s t r a t e s the importance of minimising head tape separation ( t h i s 'spacing l o s s ' amounts to 54.5 dB per wavelength). The f i n a l f a c t o r , sin(u>g/v) / (cog/v) , represents the e f f e c t s of a f i n i t e gap, 2g. Because the f r i n g i n g f i e l d s a t i s f i e s Laplace's equation V 2h = 0, the response, Ey(to) , to an element of y - d i r e c t e d magnetization, i s the H i l b e r t transform of E x ( u ) . Measured responses d i f f e r from the i d e a l i z e d response (2.8) p r i n -c i p a l l y i n pe r t u r b a t i o n s of l.f. response due to f i n i t e pole pieces [68] and i n the 'gap l o s s ' f a c t o r [64] due to the approximation i n (2.2). 2.2 THE MAGNETIC TAPE RECORDER AS A COMMUNICATION CHANNEL The response of a magnetic recording channel i s defined i n terms of the record currents and the subsequent playback v o l t a g e s . The t o p i c of l i n e a r / n o n l i n e a r behaviour i s discussed as w e l l as noise which a r i s e s from a v a r i e t y of sources and i s l o o s l y c l a s s i f i e d as a d d i t i v e or m u l t i p l i c a t i v e (signal-dependent). - 20 -2.2.1 O v e r a l l response The magnetic recording channel i s both h i g h l y d i s p e r s i v e and h i g h l y n o n l i n e a r . Generalized d e s c r i p t i o n s (such as the V o l t e r r a expansion [93]) of nonli n e a r d i s p e r s i v e channels conceal s u r p r i s i n g complexity and d i f f i c u l t y of c h a r a c t e r i z a t i o n [94]. Nor does the use of such d e s c r i p t i o n s f o r s i g n a l and r e c e i v e r design appear v i a b l e i n view of the s e v e r i t y of the n o n l i n e a r i t y and the e s s e n t i a l l y i n f i n i t e memory. D e s c r i p t i o n s of the magnetic r e c o r d i n g channel have ther e f o r e only been developed f o r very s p e c i f i c a l l y constrained s i g n a l s ; notably those f o r which the channel appears approximately l i n e a r . The simultaneous a p p l i c a t i o n of an analog s i g n a l together w i t h a high, l e v e l , high frequency a.c. b i a s causes the s c a l a r magnetization to trac e a decreasing sequence of minor M-H loops. The f i n a l magnetization s t a t e i s almost independent of the i n i t i a l s t a t e and i s s i n g l e valued. F u r t h e r , i f the s i g n a l i s a p p r o p r i a t e l y constrained to a sm a l l c e n t r a l p o r t i o n of the r e s u l t i n g a n h y s t e r e t i c M-H c h a r a c t e r i s t i c , an approximately l i n e a r r e l a t i o n -ship between recorded magnetization and input current can be maintained. Such i s the b a s i s of audio tape recording. The o v e r a l l channel response f o r the above s i t u a t i o n i s described i n essence by (2.8) w i t h the assumptions of a w e l l o r i e n t e d medium and no y v a r i a t i o n . The re d u c t i o n i n s i g n a l l e v e l r e q u i r e d to ensure reasonable l i n e a r i t y p a r t i a l l y a l l e v i a t e s s elf-demagrietization. Self-demagnetization can, i n any case, be adequately included i n the r e l a t i v e l y s t r a i g h t f o r w a r d s i t u a t i o n s where e i t h e r a si n e wave or balanced b i n a r y s i g n a l i s recorded [77]. In the l a t t e r s i t u a t i o n the abrupt s i g n a l t r a n s i t i o n s are taken to assume an arctangent form (2.5) under the e f f e c t s of self- d e m a g n e t i z a t i o n . - 21 -The t r a n s i t i o n l e n g t h , I, i s determined i n a manner s i m i l a r to [78, 95]. The o v e r a l l response i n c l u d i n g self-demagnetization may be conveniently expressed i n the frequency domain as f o l l o w s , and p l o t t e d i n F i g . 2.2 f o r OJ»0. CO Figure 2.2 E m p i r i c a l response (2.9) f o r magnetic r e c o r d i n g channel, g<a+£ The arctangent t r a n s i t i o n l e n g t h , £, i s seen to be i n d i s t i n g u i s h a b l e from the head-tape s e p a r a t i o n , a. In f a c t (2.9) can provide a u s e f u l d e s c r i p t i o n of channel behaviour i n a v a r i e t y of s i t u a t i o n s ; the exponent, a + A , i s considered an a d j u s t a b l e parameter which inc l u d e s both spacing l o s s and record process l o s s e s . Haynes has derived [89] the f o l l o w i n g expression w i t h s i m i l a r behaviour f o r a c y l i n d r i c a l w r i t e contour. E(o J)/I m(w)={jv M J + d ) {[l+(Wv]-[l+co(a+d)/v]e - a ) d / v} . e - W a / v . S i n ( " g / V ) co > 0 (2.10) lOg/V - 22 -Haynes a l s o c a l c u l a t e d a phase response n u m e r i c a l l y . No attempt was made to i n c l u d e record process l o s s e s . Binary s a t u r a t i o n r e c o r d i n g may be considered as a degenerate form of a n h y s t e r e t i c r e c o r d i n g . Responses of the form of (2.9) or (2.10) are t h e r e f o r e u s e f u l i n d e s c r i b i n g d i r e c t b i n a r y r e c o r d i n g as w e l l as a.c. b i a s r e c o r d i n g . The gradual t r a n s i t i o n from a.c. b i a s to d i r e c t r e c o r d i n g and the s i m i l a r i t y of responses are w e l l depicted i n [96,97]. By s i m i l a r arguments the response to frequency or phase modulation may a l s o be described by (2.9) or (2.10). Playback responses have a l s o been determined f o r some of the more complete models of the record process r e f e r r e d to i n § 2.1.3. Non-l i n e a r behaviour becomes apparent i n these more complete models and the derived responses have been s p e c i f i c to the r e c o r d i n g of i s o l a t e d t r a n s i t i o n s , to groups of 2 or 3 t r a n s i t i o n s , or to s i n e wave rec o r d i n g . No g e n e r a l i z e d models of the m u l t i l e v e l or analog, d i r e c t - r e c o r d e d , magnetic r e c o r d i n g channel are known. 2.2.2 L i n e a r / n o n l i n e a r behaviour I f s u p e r p o s i t i o n holds i n the playback response f o r the recording of adjacent data symbols (not n e c e s s a r i l y f o r a r b i t r a r y record waveforms) a l i n e a r data channel may be defined and intersymbol i n t e r f e r e n c e can be el i m i n a t e d by the use of l i n e a r f i l t e r i n g . A wealth of analyses and tech-niques (§2.3) are a p p l i c a b l e to l i n e a r data channels. The question of l i n e a r i t y or s u p e r p o s i t i o n i s th e r e f o r e c r u c i a l i n the design of high d e n s i t y recorders. Unfortunately the d i s t i n c t i o n between l i n e a r and n o n l i n e a r - 23 -d i s t o r t i o n has not always been appreciated and system degradations have g e n e r a l l y been lumped under the term 'peakshift* [80, 98-101] which r e l a t e s to a common method of data d e t e c t i o n . Nonlinear e f f e c t s s p e c i f i c a l l y have been assessed by t e s t i n g the v a l i d i t y of s u p e r p o s i t i o n upon simulated [56, 77, 79, 80, 86, 102-104] or measured [77, 79, 86, 102, 105, 106] rec o r d i n g channels; v a r y i n g degrees of no n l i n e a r behaviour being reported. The u s e f u l -ness of l i n e a r treatments i s a t t e s t e d to by the widespread use of l i n e a r e q u a l i z a t i o n i n video and data a p p l i c a t i o n s [1]. Middleton and Wisely [85] suggest that w h i l e s u p e r p o s i t i o n holds c l o s e l y i t may not be best expressed i n terms of the s u p e r p o s i t i o n of i s o l a t e d t r a n s i t i o n s . The l a c k of a c o n s i s t e n t , q u a n t i t a t i v e measure of no n l i n e a r behaviour i s apparent i n the i n v e s t i g a t i o n s r e f e r r e d to above. This de-f i c i e n c y has r e c e n t l y been redressed by Wood and Donaldson [107]. Their method, based on the V o l t e r r a expansion, was suggested by the graphic non-l i n e a r i t i e s presented i n Haynes' r e s u l t s [97]. Nonlinear e f f e c t s are aggravated by high l i n e a r r e c o r d i n g d e n s i t i e s and w i l l become i n c r e a s i n g l y important i n channel modelling [108] and system design. C u r r e n t l y , improvement of t r a c k d e n s i t y r a t h e r than l i n e a r d e n s i t y has done much to m i t i g a t e the problem. 2.2.3 A d d i t i v e noise sources In a w e l l designed system the bulk of a d d i t i v e noise a r i s e s from the p a r t i c u l a t e nature of the rec o r d i n g medium. In the unmagnetized medium p a r t i c l e s are assumed to be randomly o r i e n t e d and d i s t r i b u t e d . The c o r r e -sponding noise power s p e c t r a l d e n s i t y [109] observed through the playback head f o r co > 0 i s ( o m i t t i n g constant f a c t o r s ) - 24 -S n(u) = vLo[l-exp(-2tod'/v) ]exp(-2o)a/v) .sin 2(wg/v)/(cog/v) a (2.11) where d' represents the medium thickness r a t h e r than recording depth. By comparison w i t h the s i g n a l t r a n s f e r f u n c t i o n s , (2.9) or (2.10), tape noise i s seen to predominate at high frequencies. Although i t might be a n t i c i p a t e d that tape noise decreases as the medium i s magnetized, inhomogeneities i n the p a r t i c u l a t e d i s p e r s i o n cause increased noise l e v e l s (§ 2.3.3). P a r t i c u l a t e tape noise (a.c. erase noise) thus provides an upper bound to performance i n both analog and d i g i t a l systems [109]. M a l l i n s o n [110] d e r i v e s an approximate expression f o r maximum l i n e a r d e n s i t y w i t h b i n a r y s i g n a l l i n g and a l s o d e r i v e s the Shannon c a p a c i t y f o r the analog channel. The d e r i v a t i o n of narrowband s i g n a l - t o - n o i s e r a t i o (SNR) i s c l a r i f i e d i n Appendix 1. Receiver noise i s s i g n i f i c a n t only i n r e l a t i o n to playback s i g n a l energy. The l a t t e r can g e n e r a l l y be arranged (with s u i t a b l y high head-tape v e l o c i t y ) to provide an adequate s i g n a l to r e c e i v e r - n o i s e r a t i o . In f e r r i t e heads Barkenhausen and thermal shock noise are s m a l l . S i g n i f i c a n t n o i s e can be introduced by mechanical shock a s s o c i a t e d w i t h the head-tape i n t e r f a c e [111] and a f e r r i t e must be chosen w i t h low m a g n e t o s t r i c t i o n [1]. The head noise f a c t o r i s l i m i t e d by i t s o v e r a l l e f f i c i e n c y i n combination w i t h r e -s i s t i v e and h y s t e r e t i c l o s s e s . P r i n t - t h r o u g h between adjacent l a y e r s of tape, occurs at wavelengths greater than the tape thickness [1] but does not g e n e r a l l y present problems. The presence of d.c. or l i n e frequency f i e l d s can introduce d i s t o r t i o n and noise [87, 112]. A more severe noise source a r i s e s from the e f f e c t s of p r e v i o u s l y recorded unknown data [113]. A separate erase c y c l e may be necessary. - 25 -2.2.4 M u l t i p l i c a t i v e noise sources The f o l l o w i n g noise sources are s i g n a l dependent but non-determi-n i s t i c and can g e n e r a l l y be i n t e r p r e t e d as causing f l u c t u a t i o n s i n channel gain and/or s p e c t r a l response. Poor t r a c k i n g , head skew and v a r i a t i o n s i n head response can introduce ft.f. or d.c. m u l t i p l i c a t i v e noises which o f t e n appear as a compat-i b i l i t y problem between t r a n s p o r t s . The a p p l i c a t i o n of s e r v o - c o n t r o l l e d heads [4, 50, 51] to h e l i c a l - s c a n machines has allowed accurate f o l l o w i n g of narrow t r a c k s . Head skew r a i s e s problems only on wide t r a c k s by reducing the h.f. response. Channel gain and s p e c t r a l response are a l s o a f u n c t i o n of the head gap and of the pole-face p r o f i l e which determines the mean head-tape sep a r a t i o n . Although noise from a uniform d i s t r i b u t i o n of p a r t i c l e s i s .. approximately Gaussian and a d d i t i v e , p a r t i c l e clumping, v o i d s , and other inhomogeneities give r i s e to more extreme behaviour which may be considered as m u l t i p l i c a t i v e [114-117]. Such defects w i t h i n the magnetic medium would appear to be the p r i n c i p a l source of e r r o r s on d i s c systems which have t h i n , smooth coatings and high head-medium sep a r a t i o n . Media defects are g e n e r a l l y s m a l l , 6-30 um, and y i e l d short w e l l defined e r r o r b u r s t s or channel gain r e d u c t i o n s . Bulk inhomogeneities are undoubtedly present i n tape media but are b e l i e v e d to play a secondary r o l e . Intimate head-tape contact ensures that surface defects and.the presence of f o r e i g n p a r t i c l e s become paramount i n determining the performance of tape systems. The a s s o c i a t e d v a r i a t i o n s i n e f f e c t i v e head-tape separation can give r i s e to severe reductions i n channel gain (dropouts). - 26 -Carson [118] as e a r l y or 1962 reported a comprehensive study of ... the length and depth d i s t r i b u t i o n s of dropouts (the medium len g t h of 3 dB dropouts was 0.4 mm) and noted a dependency on head-tape contact pressure. The bulk of dropouts appeared on a l l playback runs. However, w i t h the tape re-recorded between runs as many as 20% of dropouts occurred only on a s i n g l e run. These f a c t s v e r i f y t h a t , f o r tape systems, dropouts are p r i m a r i l y caused by defects r e l a t i v e l y s e c u r e l y f i x e d to the s u r f a c e , and suggest that t h e i r e f f e c t s are more severe during the record process. E l d r i d g e [115] d i s c r i m i n a t e d between bulk inhomogeneity n o i s e predominating under d.c. e r a s e c o n d i t i o n s , and surface induced noise pre-dominating at low record l e v e l . From E l d r i d g e ' s measurements D a n i e l [119] c a l c u l a t e d a c h a r a c t e r i s t i c l e n g t h of 0.5 mm f o r surface d e f e c t s . Shmelkov [120] a s c r i b e d frequency dependent noise to v a r i a b l e head-tape contact r e -p o r t i n g a modulation noise bandwidth of 130 Cycles/m at a wavelength of 12 ym Baker [121] examined s e l e c t e d defects w i t h a microscope and p r o f i l m e t e r , r e v e a l i n g lumps or 'stubble' around 2.5 ym high. The tape was assumed to ' l i f t o f f i n a quadratic manner as the defect passed the head gap. The model provides a poor f i t of deep fades. Hoagland et a l . [122] w i t h an e l e c t r o n microscope revealed t y p i c a l defects to be ' f l a k e - l i k e ' i n appearance 25-75 ym i n diameter and p a r t i a l l y embedded i n the tape s u r f a c e ; dropouts were almost independent of t r a c k width but h i g h l y dependent upon the l i n e a r r e c ording d e n s i t y . Recently A l s t a d and Haynes [123] have compiled dropout s t a t i s t i c s (median length 0.3 mm) remarkably s i m i l a r to those of Carson [118] s i x t e e n years e a r l i e r ; d e f e c t heights of 2-3 ym are suggested by t h e i r Gaussian ' l i f t o f f model. Wood and Donaldson [107] model both the record and playback processes to deduce that head-tape se p a r a t i o n exceeds lym w i t h p r o b a b i l i t y 10 5. A l l of the above experiments were conducted on l o n g i t u -d i n a l machines w i t h the exceptions of [122], on f l e x i b l e d i s c , and [107], on h e l i c a l scan. In view of the obvious s e n s i t i v i t y of the head-tape i n t e r f a c e to tape surface p r e p a r a t i o n , head p r o f i l e , tape s t i f f n e s s , head pressure, e t c . , the above r e s u l t s are remarkably c o n s i s t e n t . 2.3 SIGNAL AND RECEIVER DESIGN 2.3.1 Conventional data t r a n s m i s s i o n channels Figure 2.3 shows the elements of a data tra n s m i s s i o n channel. The waveform channel introduces s i g n a l degradations i n c l u d i n g a d d i t i v e and m u l t i p l i c a t i v e n o i s e s , d i s p e r s i o n , and n o n l i n e a r behaviour. With some l o s s of g e n e r a l i t y [ ± 2 4 •] the f u n c t i o n s of encoding and modulation have been d i s t i n g u i s h e d at the t r a n s m i t t e r , together w i t h t h e i r counterparts at the r e c e i v e r . The o v e r a l l design process i s thus s i m p l i f i e d . The modulator/ demodulator i s designed to match the channel response and n o i s e , minimising e r r o r s i n the r e c e i v e d sequence {a}. The encoder/decoder i s designed to provide e r r o r c o n t r o l on {b}. (a) Modulation/demodulation. Loading ( l i n e a r e q u a l i z a t i o n ) was found necessary i n the e a r l i e s t t r ansmission systems [21] to reduce the e f f e c t s of h.f. a t t e n u a t i o n . With the advent of e l e c t r o n i c a m p l i f i e r s [12] the fundamental, l i m i t i n g nature of thermal noise became evident. This s i g n a l l i n g environment ( l i n e a r d i s -p e r s i o n and a d d i t i v e Gaussian noise) i s commonly encountered. With concern f o r bandwidth e f f i c i e n c y l i n e a r modulation ( i n c l u d i n g baseband schemes) i s g e n e r a l l y found most appropriate .for t h i s environment [124]. Data r e c e i v e r s - 28 -COMMUNICATION T R A N S M I T T E R CHANNEL RECE IVER Encoder Modulator Waveform channel Demodulator Decoder — ^ ^ to H y(t) r(t) . N3 Input data sequence Output data sequence Figure 2.3 Data transmission channel f o r l i n e a r modulation/transmission systems can be broadly c a t e g o r i z e d as l i n e a r or n o n l i n e a r . Matched f i l t e r i n g [124] followed by sampling at the baud r a t e i s known [125] to be in f o r m a t i o n l o s s l e s s . Any r e c e i v e r may thus be represented w i t h a matched f i l t e r f o l l o wed by a t r a n s v e r s a l f i l t e r (or l i n e a r d i s c r e t e - t i m e f i l t e r ) as i n F i g . 2.4. Li n e a r r e c e i v e r s detect symbols independently at the t r a n s v e r s a l f i l t e r output. Nonlinear r e c e i v e r s take advantage of the d i s c r e t e nature of proximate symbols. O p t i m i z a t i o n of l i n e a r r e c e i v e r s [124] and j o i n t o p t i m i z a t i o n of t r a n s m i t t e r / r e c e i v e r [126] are w e l l understood. The performance of such ... systems under various degradations and c o n s t r a i n t s i s s t i l l the obje c t of a t t e n t i o n [127-129]. Linear r e c e i v e r s can provide c l o s e to maximum l i k e l i -hood (ML) performance when the narrowband SNR i s roughly f l a t across the folded Nyquist [124] spectrum. N u l l s or dips i n t h i s s p e c t r a l SNR lead to high l e v e l s of noise and/or intersymbol i n t e r f e r e n c e ( I S I ) . D e c i s i o n feedback e q u a l i z a t i o n (DFE) takes advantage of the d i s c r e t e nature of I S I from preceding symbols [130]. A l t e r n a t i v e l y the feedback f i l t e r may be regarded as r e c o n s t r u c t i n g those missing or attenuated p a r t s of the s i g n a l spectrum [131, 132]. Because of e r r o r propagation the performance of DFE i s not e a s i l y assessed [133]. In c e r t a i n s i t u a t i o n s I S I may be advanta-geously constrained to form a m u l t i l e v e l eye which can be quantized d i r e c t l y without recourse to DFE. This technique of " p a r t i a l response" s i g n a l l i n g [134, 135] provides performance comparable to that of a corresponding DFE r e c e i v e r . Because of the b i t - b y - b i t nature of DFE and the c o n s t r a i n t that . the feedback be c a u s a l , ML performance i s not always a t t a i n e d . P r a c t i c a b l e - 30 -Baud M a t c h e d r a t e sampler D i s c r e t e t i m e ** f i l ter 1/T l i n e a r f i l t e r (a) L I N E A R R E C E I V E R FORWARD F I L T E R D i s c r e t e Matched ' ^ t i m e f i l ter 1/T l inear f i l t e r ( b ) D E C I S I O N F E E D B A C K R E C E I V E R Quantizer Quant izer D i s c r e t e t ime I inear f i l ter received sequence > 0} {a} F E E D B A C K F I L T E R D i s c r e t e N o n l i n e a r M a t c h e d t i m e (wi th m e m o r y ) > f i l ter 1/T l inear f i l t e r p r o c e s s o r ® (c) M A X I M U M - L I K E L I H O O D R E C E I V E R Y I T E R B I P R O C E S S O R Figure 2.4 Receiver structures - 3 1 -ML r e c e p t i o n was f i r s t approached by Forney's r e c o g n i t i o n [125] that the V i t e r b i a l g o r i t h m [136] could be a p p l i e d to the problem. The V i t e r b i a l g o r i t h m had been p r e v i o u s l y developed to decode c o n v o l u t i o n a l codes [137] and i s s i m i l a r i n concept to dynamic programming [138]. Implementation of the a l g o r i t h m can present a formidable task, r e q u i r i n g M m squaring opera-t i o n s [125] or d i s c r e t e by analog m u l t i p l i c a t i o n s [139] per symbol p e r i o d (M-ary s i g n a l l i n g w i t h m symbols channel memory). Recently analog techniques [140] have been a p p l i e d at data r a t e s up to 50 Mbit/s. P r a c t i c a l i t i e s such as f i n i t e t r a n s v e r s a l f i l t e r s , t o l e rances on r e c e i v e r components, and c a r r i e r / c l o c k inaccuracy a l l tend to degrade per-formance. The channel model i m p l i c i t -in the r e c e i v e r may be i n a c c u r a t e or the channel may i n c l u d e n o n l i n e a r behaviour or non-Gaussian noi s e . Adaptive r e c e p t i o n and the e f f e c t s of r e c e i v e r p r a c t i c a l i t i e s and channel degradations are discussed i n [124, 126, 127, 130, 141, 142] f o r l i n e a r r e c e i v e r s , [130, 132, 133, 143-146] f o r DFE, and [125, 139, 144, 145, 147, 148] f o r ML r e c e i v e r s . In general terms i t has been found that DFE gives considerable improvement over l i n e a r .reception, on channels w i t h s p e c t r a l nulls." The e r r o r performance fo r ML r e c e p t i o n w h i l e c o n c e p t u a l l y simpler than f o r DFE i s not e a s i l y computed without r e s o r t to exhaustive techniques. Magee and P r o a k i s [149] provide estimated upper bounds w h i l e Forney [150] and Mazo [151] provide lower bounds. I t has been shown that i n many circumstances ML performance d i f f e r s by only a small f a c t o r from the matched f i l t e r bound on i s o l a t e d symbols [125], The above r e c e i v e r s a l l r e q u i r e accurate knowledge of the incoming c l o c k (and c a r r i e r ) phase. The subject of c a r r i e r / c l o c k recovery has r e -ceived considerable a t t e n t i o n [124, 152, 153]. C a r r i e r recovery can be - 32 -avoided by the use of incoherent r e c e p t i o n techniques such as envelope d e t e c t i o n or d i f f e r e n t i a l l y - c o h e r e n t p h a s e - s h i f t keying (DCPSK). Such techniques g e n e r a l l y i n v o l v e only a few dB l o s s w h i l e considerably s i m p l i f y ^ -ing r e c e i v e r s t r u c t u r e . The p a r t i c u l a r s e n s i t i v i t y of DCPSK to r e s i d u a l I S I has, however, been demonstrated by Wood [154]. A v a r i e t y of n o n l i n e a r modulation techniques are a l s o a v a i l a b l e . However, n o n l i n e a r modulation g e n e r a l l y i n v o l v e s increased bandwidth i n exchange f o r s i m p l i c i t y of implementation. Pulse p o s i t i o n modulation or pulse i n t e r v a l modulation are v a r i a n t s of frequency modulation and thus of phase modulation. Under pressure of increased bandwidth e f f i c i e n c y , pulse width and frequency modulations tend to degenerate i n t o forms of l i n e a r modulation. A most common form of waveform channel degradation i s m u l t i p l i c a -t i v e n o i s e , o f t e n encounted as fading on c a r r i e r systems. Such f a d i n g may have a Rayleigh or R i c i a n d i s t r i b u t i o n [155]. Performance of modulation/ demodulation schemes under f a d i n g c o n d i t i o n s has been i n v e s t i g a t e d by s e v e r a l authors [155, 156-158], (b) Channel encoding The source sequence {b:}. i s assumed to be a stream of equiprobable bi n a r y d i g i t s which are to be encoded i n such a manner as to e f f e c t e r r o r c o n t r o l on the system. Shannon [159] i n 1948 proved the p o s s i b i l i t y of v i r t u a l l y e r r o r - f r e e t ransmission of i n f o r m a t i o n over channels used below t h e i r c a p a c i t y . This goal proved d i f f i c u l t to a t t a i n . However, a consi d e r -ably body of l i t e r a t u r e now e x i s t s 1124, 160-165] and c o n t r o l of e r r o r s by coding has become a p r a c t i c a b l e p r o p o s i t i o n [166]. E r r o r c o r r e c t i n g codes - 33 -are best implemented i n s i t u a t i o n s where r e l a t i v e l y wide bandwidth i s a v a i l a b l e (e.g. space probes [167]). At high data r a t e s some decoding algorithms become d i f f i c u l t to implement. On bandlimited channels increased separation of codewords does not n e c e s s a r i l y imply increased s e p a r a t i o n of the r e c e i v e d waveforms. On channels used c l o s e to the Nyquist r a t e [124]. e r r o r c o n t r o l may thus be i n e f f e c t i v e . The system designer has a wide choice of codes a v a i l a b l e . Block codes are more appropriate to computer systems where data i s handled i n b l o c k s , whereas c o n v o l u t i o n a l codes are appropriate to communication channels c a r r y i n g a continuous stream of i n f o r m a t i o n [166]. On r e a l channels e r r o r s may not be randomly d i s t r i b u t e d . While the occurrence of e r r o r s i n b u r s t s a c t u a l l y increases channel c a p a c i t y , the l o c a l l y increased e r r o r d e n s i t i e s can f r u s t r a t e the decoding processes f o r codes of moderate c o n s t r a i n t l e n g t h . Codes capable of c o r r e c t i n g b u r s t e r r o r s or both burst and random e r r o r s are a v a i l a b l e [124, 162, 163, 168]. The decoding complexity of long c o n s t r a i n t - l e n g t h codes w i t h high r a t e makes the technique of i n t e r l e a v i n g [169-171] a t t r a c t i v e . By t h i s means e r r o r bursts are dispersed a l l o w i n g the use of sh o r t e r codes, although c o n s i d e r -able memory i s r e q u i r e d . The performance of e r r o r c o n t r o l schemes i s very dependent upon the nature of the d i g i t a l t ransmission channel. The G i l b e r t model [172] o f f e r s a simple approach to channel modelling w i t h the channel taken to be :. i n e i t h e r a good or bad s t a t e . Chien et a l . [173] consider extensions to the two-state G i l b e r t model and introduce gap d i s t r i b u t i o n models. Kanal and Sastry provide a review [174] of d i g i t a l channel models. - 34 -(c) Hybrid modulation/coding Often i t i s i n e x p e d i t i o u s to separate the fun c t i o n s of coding and modulation at the t r a n s m i t t e r or demodulation and decoding at the r e c e i v e r . Although s p e c t r a l energy d i s t r i b u t i o n i s p r i m a r i l y determined by the choice of modulation waveform, the encoding process can be used f o r s p e c t r a l shaping. At the r e c e i v e r demodulation/quantization p r i o r to decoding can destroy some of the a v a i l a b l e i n f o r m a t i o n . The design of codes a f f e c t i n g s p e c t r a l d i s t r i b u t i o n i s u s u a l l y aimed s p e c i f i c a l l y at channel 'impairments' such as the d.c. n u l l or the poor h.f. response. In these contexts the concepts of d i g i t a l sum v a r i a t i o n [175] and r u n - l i m i t e d coding [176] are u s e f u l . The former provides an e x c e l -l e n t measure of £.f. behaviour which can be c o n t r o l l e d by the use of 'low d i s p a r i t y ' block codes [177, 178]. Clock recovery and l.f. performance are associated w i t h the maximum separation between data t r a n s i t i o n s w h i l e h.f. performance i s a s s o c i a t e d w i t h the minimum separation. D i f f e r e n t i a l l y en-coded (d,k) r u n - l i m i t e d codes [176, 179-181] ensure a minimum d+1, and maximum k+1, b i t i n t e r v a l s between t r a n s i t i o n s . Franaszek [179] has developed synchronous, r u n - l i m i t e d , v a r i a b l e - l e n g t h codes notable f o r t h e i r ease of implementation. Encoding f o r e r r o r c o n t r o l i s normally envisaged on a d i g i t a l channel. I t i s , however, p o s s i b l e and advantageous to make use of the analog informa-t i o n present at the r e c e i v e r . 'Soft d e c i s i o n decoding' [166, 182-186] describes the technique of i n c r e a s i n g the number of quantized l e v e l s at the r e c e i v e r thus a l l o w i n g s i g n a l s to be c l a s s i f i e d as ' r e l i a b l e ' , 'ambiguous', ' u n r e l i a b l e ' , e t c . Decoding w i t h channel measurement in f o r m a t i o n i s taken here to r e f e r to r e c e i v e r s making use of estimated channel parameters (channel g a i n , c a r r i e r / c l o c k phase, e t c . ) - The use of such estimates to optimise d e c i s i o n and de-coding s t r a t e g i e s i s mentioned i n [45, 170, 187, 188]. Sequential decoders and M.L. r e c e i v e r s among others advantageously combine the fu n c t i o n s of demodulation and decoding [139, 140, 182, 186]. 2.3.2 Nonlinear channels The assumption of channel l i n e a r i t y i s i m p l i c i t i n much of the preceding s e c t i o n . Real channels i n e v i t a b l y r e v e a l some measure of n o n l i n e a r behaviour when examined i n d e t a i l [189, 190]. Some trans m i s s i o n [191-193] and some storage [106, 194, 195] channels e n t a i l severe n o n l i n e a r i t y . The performance of systems i n the presence of non l i n e a r behaviour and the c o r r e -sponding task of system design are th e r e f o r e of some s i g n i f i c a n c e . The d i f f i c u l t i e s inherent i n c h a r a c t e r i z a t i o n and s i g n a l design f o r n o n l i n e a r despersive channels are mentioned i n §2.2 and §4.1. S i g n a l designs f o r n o n l i n e a r channels have g e n e r a l l y been based upon the s e l e c t i o n of s i g n a l l i n g formats which minimise n o n l i n e a r behaviour; f o r example, the use of frequency modulation on t r a v e l l i n g - w a v e a m p l i f i e r s . Work has concentrated on e v a l u a t i n g the performance, i n the presence of nonlinear 'degradation', of designs adopted from l i n e a r channels. J a i n and Blachman [196] consider the trans m i s s i o n of phase s h i f t keying through a n o n l i n e a r i t y and show that some advantage can accrue on repeated systems. Benedetto et a l . [197] i n v e s t i g a t e m u l t i l e v e l baseband s i g n a l l i n g w i t h cubic n o n l i n e a r i t y . Forsey and Gooding [198] g e n e r a l i z e J a i n and Blachman's r e s u l t s and apply them to the s a t e l l i t e channel. Attempts to optimise r e c e p t i o n on n o n l i n e a r channels have been made by Mesiya et a l . [199] f o r the l i n e a r r e c e i v e r . Nonlinear s t r u c t u r e s have - 36 -been proposed by Lawless and Schwartz [200]. Forney's maximum l i k e l i h o o d (ML) r e c e i v e r was extended to the n o n l i n e a r binary channel by Mesiya et a l . [201], and f i n a l l y extended to the g e n e r a l i z e d n o n l i n e a r d i s p e r s i v e data channel by Wood [202]. Performance of ML r e c e i v e r s may be guaged by the methods of [151, 203]. Recently Falconer [204] has simulated a r e c e i v e r s t r u c t u r e of considerable f l e x i b i l i t y . The r e c e i v e r a d a p t i v e l y accommodates to the channel n o n l i n e a r i t y ; i t s s t r u c t u r e i n c l u d e s n o n l i n e a r processing of both the incoming analog s i g n a l and the recent d e c i s i o n s . S i g n i f i c a n t improvements i n performance have been demonstrated. 2.3.3 The magnetic r e c o r d i n g channel (a) Modulation/coding R e l a t i v e l y few d i s t i n c t code/modulation formats are used on extant high d e n s i t y tape recorders. With the exception of the use of incoherent frequency modulation at lower l i n e a r d e n s i t i e s , t a b l e 1.1 and F i g . 2.5; r e v e a l s i g n a l l i n g formats to be e s s e n t i a l l y b i n a r y w i t h various code options. Waveforms are i d e a l i z e d as r e c t a n g u l a r although the recorded patterns are determined p r i m a r i l y by the p o s i t i o n and amplitude of successive waveform peaks. Non-return-to-zero (NRZ) s i g n a l l i n g i s used widely on computer tapes w i t h clock recovery assured by an odd p a r i t y check across the nine recorded t r a c k s . The l a c k of d.c. response and the e f f e c t s of head skew prompted the use of bi-phase modulation, F i g . 2.5 ;r, on 1600 b.p.i., machines [8]. Phase modulation i s u n s u i t a b l e f o r use at high l i n e a r d e n s i t y because of the small separation between t r a n s i t i o n s . Such c o n s i d e r a t i o n s suggested the use of r u n - l i m i t e d codes [179]. M i l l e r code [205], a l s o known as delay - 37 -N O N - R E T U R N T O Z E R O ( N R Z ) B I - P H A S E M O D U L A T I O N "_n_j M I L L E R C O D E S T A T E T R A N S I T I O N D I A G R A M ( M I L L E R ) Figure 2.5 Magnetic recording codes - 38 -modulation or modified frequency modulation, i s a i - r a t e code w i t h 1, l i , or 2 s o u r c e - b i t i n t e r v a l s between adjacent t r a n s i t i o n s . Clock recovery i s f a c i l i t a t e d by the high t r a n s i t i o n d e n s i t y but, compared w i t h NRZ, M i l l e r code i s s u s c e p t i b l e to cl o c k inaccuracy and a l s o incurs, a 3 dB performance penalty. Because of lower d.c. content the e f f e c t s of the d.c. n u l l are r e -duced. The 4/5-rate code (used i n 6250 b . p . i . standard format) maps four b i t s i n t o f i v e ensuring c l o c k recovery and reducing d i s p a r i t y . This code has higher d.c. content than M i l l e r but o f f e r s greater e f f e c t i v e SNR at a l l but the highest r e c o r d i n g d e n s i t i e s . The 3PM code, introduced by Jacoby [206], maps three b i t s i n t o s i x w i t h minimum t r a n s i t i o n s e p a r a t i o n of l i s o u r c e - b i t i n t e r v a l s . V a r i a b l e - l e n g t h , r u n - l i m i t e d codes [176] have been considered. Run-limited codes are not i n general d.c. f r e e . Codes w i t h low d i s p a r i t y are discussed by Davidson et..al. [177]. By r e l a x i n g the maximum run-length c o n s t r a i n t , M i l l e r type codes may be made d.c. f r e e ; examples in c l u d e zero-modulation [207] and M 2 code [205]. Such codes are p a r t i c u l a r l y i n s e n s i t i v e to low frequency shortcomings i n the record/playback channel. Performance comparisons [177, 206, 208, 209] tend to r e v e a l t h i s advantage. C a s t l e [46] and Lindholm [210] i n v e s t i g a t e the sp e c t r a of magnetic recording codes. Two stu d i e s i n p a r t i c u l a r do not adhere to bin a r y s i g n a l l i n g formats. Dent and Schneider [211] attempt to reduce the e f f e c t s of dropouts by spread-ing each b i t i n t o a much longer Huffman sequence ( c f . pulse compression r a d a r ) . These overlapping sequences are recovered by pulse compression i n a t r a n s v e r s a l f i l t e r . D i f f i c u l t i e s i n c l u d e requirements f o r a l i n e a r channel w i t h wide dynamic range and f o r a t r a n s v e r s a l f i l t e r w i t h s u f f i c i e n t l ength - 39 -and accuracy. P r i c e et a l . [187] consider three and four l e v e l s i g n a l l i n g on a l i n e a r i z e d channel but r e q u i r e only l i m i t e d dynamic range. R e l a t i v e l y l i t t l e work has been done on coding f o r e r r o r c o n t r o l . Standard computer data formats i n c l u d e an odd p a r i t y check across the recorded tracks and a l o n g i t u d i n a l c y c l i c redundancy check [8]. These checks o f f e r s i g n i f i c a n t e r r o r c o r r e c t i o n c a p a b i l i t y . On r o t a t i n g head machines i n t e r -t r a c k checks are not normally a v a i l a b l e . E r r o r c o r r e c t i o n has been implemented by d u p l i c a t e r e c o r d i n g [45] w i t h channel measurement i n f o r m a t i o n (amplitude sensing) and by an i n t e r l e a v e d (3,2) block code [170] w i t h e i t h e r amplitude sensing or c y c l i c redundancy check. Several e r r o r c o r r e c t i n g codes [42, 47, 212, 213] have been considered f o r use on the magnetic r e c o r d i n g channel. Varaiya [168] implements a G i l b e r t burst e r r o r c o r r e c t i n g code capable of c o r r e c t i n g a 32 b i t b u r s t i n a 2279 b i t block. In connection w i t h audio or video r e c o r d i n g the technique of e r r o r concealment [170, 212] i s discussed. The e r r o r d e t e c t i o n capacity of p a r i t y checks are f r e q u e n t l y used to i n s t i g a t e a p h y s i c a l r e ^ w r i t e or re-read operation. This technique i s s i m i l a r to the use of a feedback communication channel [214] and can provide considerable economy over forward e r r o r - c o r r e c t i o n techniques. (b) Data recovery From the i n c e p t i o n of magnetic r e c o r d i n g the l a c k of d.c. response was recognized i n that the o p e n - c i r c u i t head voltage i s the d e r i v a t i v e of the recorded magnetization. The playback s i g n a l thus r e f l e c t s changes i n magnetization. For t h i s reason d i f f e r e n t i a l precoding was i n e v i t a b l y used and reproduction o r i e n t e d toward d e t e c t i n g data t r a n s i t i o n s . This o r i e n t a l t i o n permeates the magnetic r e c o r d i n g l i t e r a t u r e i n code s e l e c t i o n [205] - 40 -and data recovery [8]. The use of measures such as 'peak s h i f t ' make appre-c i a t i o n of recovery or r e c e p t i o n techniques d i f f i c u l t i n terms of communication theory. At low d e n s i t i e s , t w o - l e v e l r e c o r d i n g i s reproduced as a sequence of i s o l a t e d pulses of a l t e r n a t i n g p o l a r i t y . 'Amplitude d e t e c t i o n ' [8] i d e n t i f i e s data t r a n s i t i o n s as points at which the playback s i g n a l exceeds a c e r t a i n magnitude. Amplitude d e t e c t i o n may thus be considered a crude form of p a r t i a l response s i g n a l l i n g [134]. The use of/.'peak d e t e c t i o n ' [8,208] was prompted by the s e n s i t i v i t y of amplitude d e t e c t i o n to v a r i a t i o n s i n channel gain. The s i g n a l i s d i f f e r -e n t i a t e d converting pulse 'peaks' i n t o z e r o - c r o s s i n g s . Data may be recovered d i r e c t l y w i t h a comparator/sampler provided that run-lengths are short or the comparator contains some h y s t e r e s i s . Peak d e t e c t i o n i s e s s e n t i a l l y a form of l i n e a r r e c e p t i o n w i t h a d i f f e r e n t i a t o r forming the e q u a l i z e r . In the frequency domain t h i s e q u a l i z a t i o n corresponds to a f a c t o r , j o i , m u l t i p l y i n g (2.9) or (2.10). The TT/2 phase s h i f t i s thus removed ( F i g . 2.2) and the h.f. response f l a t t e n e d . The £.f. response i s degraded. Peak d e t e c t i o n i s the prevalent means of data recovery. Attempts have been made to improve upon the l i n e a r r e c e p t i o n i m p l i c i t above. L i n e a r e q u a l i z a t i o n has received considerable a t t e n t i o n [1, 215-217] on audio and instrumentation machines. On d i g i t a l machines, S i e r r a [218] made one of the e a r l i e s t c o n t r i b u t i o n s a pplying 'pulse slimming' to counteract h.f. r o l l - o f f . Jacoby [219] a p p l i e s amplitude and phase c o r r e c t i o n p r i n c i p a l l y to bi-phase s i g n a l l i n g . Tachibana e t a l . [220] con-s i d e r lumped component f i l t e r s and a nine-tap t r a n s v e r s a l f i l t e r p r o v i d i n g minimum mean square e r r o r on M i l l e r code. Ashlock [221] discusses the opt-imum l i n e a r r e c e i v e r a p p l i e d to bi-phase s i g n a l l i n g . A t r a n s v e r s a l type - 41 -f i l t e r i s used in[98] to e f f e c t pulse slimming. Schneider [222] complements t h i s technique w i t h i.f. i n t e g r a t i o n p r o v i d i n g wideband, f l a t e q u a l i z a t i o n . Tahara e t a l . [208] optimise a lumped component f i l t e r on M i l l e r and 4/5-rate codes. Optimum f i l t e r s which e l i m i n a t e 'peak s h i f t ' r a t h e r than 'amplitude s h i f t ' caused by ISI are considered i n [220,223]. Geffron [224] formulates an e q u a l i z a t i o n scheme which e l i m i n a t e s both peak s h i f t and amplitude s h i f t . Huber [225] borrows techniques from the radar f i e l d to reduce the si d e l o b e l e v e l of i s o l a t e d pulses. Nonlinear ( i n c l u d i n g p a r t i a l response) r e c e i v e r s allow s p e c t r a l d e f i c i e n c i e s to be p a r t i a l l y avoided. The d.c. n u l l and acute h.f. r o l l - o f f make the use of no n l i n e a r r e c e p t i o n appear a t t r a c t i v e f o r the magnetic r e c o r d -i n g channel. The p a r a l l e l between amplitude d e t e c t i o n and p a r t i a l response s i g n a l l i n g has been noted above. D e c i s i o n feedback i s i m p l i c i t i n the h y s t e r e s i s commonly introduced i n the peak d e t e c t i o n scheme to compensate f o r the absence of d.c. tr a n s m i s s i o n . A simple and more e f f e c t i v e a p p l i c a t i o n of d e c i s i o n feedback to the d.c. n u l l i s implemented by Wood and Donaldson [131]. Nonlinear r e c e i v e r s are, however', s e n s i t i v e to channel gain f l u c t u a t i o n s . P r i c e et a l . [187] i n c l u d e automatic gain c o n t r o l i n t h e i r m u l t i l e v e l p a r t i a l response system. In t h i s case the c l a s s of response [135] i s chosen appro-, p r i a t e to both the d.c. n u l l and the h.f. r o l l - o f f . The same system [187] a l s o i n c l u d e s p a r t i c u l a r l y comprehensive e q u a l i z a t i o n ; the three stage d e r i v a t i v e e q u a l i z e r i s followed by a 25-tap t r a n s v e r s a l f i l t e r . One of the f i r s t a p p l i c a t i o n s of the V i t e r b i a l g o r i t h m to analog r e c e p t i o n was made by Kobayashi [226] i n the context of the magnetic record-i n g channel. The complexity of such r e c e i v e r s and t h e i r s e n s i t i v i t y to channel gain v a r i a t i o n s has apparently precluded t h e i r f u r t h e r c o n s i d e r a t i o n i n the f i e l d of magnetic r e c o r d i n g . - 42 -I l l CHARACTERIZATION OF CHANNEL BEHAVIOUR Information storage may be regarded as the tr a n s m i s s i o n of i n f o r -mation through a temporal r a t h e r than a s p a t i a l dimension. A storage channel may thus be c h a r a c t e r i z e d by observation of the playback response to a known record waveform. The a r b i t r a r y nature of storage channel delay n e c e s s i t a t e s the l o c a l generation of a timing reference during playback. In c o n t r a s t to the l a b o r a t o r y t e s t i n g of tr a n s m i s s i o n channels, i t i s not p o s s i b l e take advantage of the f a m i l i a r 'cheat w i r e s ' which c a r r y i n f o r m a t i o n about c l o c k phase or t e s t sequence d i r e c t l y from t r a n s m i t t e r to r e c e i v e r . The f i r s t s e c t i o n of t h i s chapter describes the instrumentation used i n the measurements. The f o l l o w i n g s e c t i o n examines the extent to which the channel may be considered l i n e a r and describes a method of charac-t e r i z a t i o n f o r the no n l i n e a r e f f e c t s . Sections three and four deal w i t h measurements of a d d i t i v e and m u l t i p l i c a t i v e noises r e s p e c t i v e l y . A v a r i e t y of e f f e c t s of l e s s d i r e c t importance are discussed i n the f i n a l s e c t i o n . D e t a i l s of the tr a n s p o r t and tapes used may be found i n Appendix 2. 3.1 INSTRUMENTATION 3.1.1 Tape tr a n s p o r t Although high l i n e a r d e n s i t i e s have been demonstrated [43, 46] on l o n g i t u d i n a l t r a n s p o r t s , the highest a r e a l d e n s i t i e s r e q u i r e very narrow t r a c k s n e c e s s i t a t i n g expensive multihead assemblies and a m u l t i p l i c i t y of record/playback c i r c u i t s . The need f o r high t r a n s f e r r a t e s and high head-tape speed can lead to excessive tape v e l o c i t y and consumption on l o n g i t u -d i n a l t r a n s p o r t s . - 43 -Rotating-head t r a n s p o r t s a l l o w head-tape v e l o c i t y and t r a c k -width to be chosen independently of tape-speed and number-of-heads respec-r t i v e l y . The i n e r t i a of the r o t a t i n g head assembly ensures good timebase s t a b i l i t y . The transverse format used f o r broadcast q u a l i t y video r e c o r d i n g i s being superceded by the h e l i c a l - s c a n format w i t h s e r v o - p o s i t i o n e d heads [51]. The disadvantages of rotating-head t r a n s p o r t s p e r t a i n to the a d d i t i o n a l l e v e l s of s y n c h r o n i z a t i o n r e q u i r e d , to the d i s c r e t e t r a c k - l e n g t h , to the rotary-head c o u p l i n g , to the slow access times, and to the d i f f i c u l t i e s of e r a s i n g / r e - r e c o r d i n g short data segments. However, h e l i c a l recorders are p r e s e n t l y the object of intense economic and t e c h n o l o g i c a l competition aimed at the consumer video market. The machine used i n t h i s study i s .de-s c r i b e d i n Appendix 2 and was t y p i c a l of higher q u a l i t y h e l i c a l - s c a n machines intended f o r use i n e d u c a t i o n a l , medical, or business environments. 3.1.2 Record and playback a m p l i f i e r s . I n i t i a l assessment of the channel c h a r a c t e r i s t i c s revealed that (at optimum h.f. record l e v e l ) the narrowband SNR dropped r a p i d l y below 20 dB near 10 MHz (.5 Mcycles/m). In a d d i t i o n , the f i r s t gap n u l l was a n t i c i p a t e d [64] i n the region 12-15 MHz. Record and playback a m p l i f i e r s were t h e r e f o r e constructed to observe,in p a r t i c u l a r , channel responses around the a n t i -c i p a t e d u s e f u l bandedge. A m p l i f i e r design i s complicated by the i n d u c t i v e nature of the record/playback head. The head impedance was determined by . d i r e c t measurement, and confirmed by observation of the playback a m p l i f i e r response to a step change i n magnetic f i e l d , the head being shunted w i t h known reactances. The playback a m p l i f i e r ( s i m i l a r to F i g . 4.4) was designed around a d i f f e r e n t i a l video i n t e g r a t e d c i r c u i t . The head inductance resonated w i t h - 44 -the a m p l i f i e r input capacitance around 10 MHz maximising s i g n a l t r a n s f e r and f a c i l i t a t i n g higher frequency observations. The record a m p l i f i e r r e q u i r e d a choice of source impedance. A voltage source (fed by the d e r i v a t i v e of the re q u i r e d head current) reduces the e f f e c t s of shunt capacitance. A current source, however, extends l.f. performance s i n c e the inductance of the interposed r o t a r y transformer appears i n s e r i e s w i t h that of the record head. This l a t t e r mode was chosen; shunt capacitances resonated w i t h the head inductance around 15 MHz and small amounts of p a r a l l e l and s e r i e s damping reduced overshoot/ISI. The record a m p l i f i e r used i n t h i s s e c t i o n i s s i m i l a r to that shown i n F i g . 4.3. Because of the balanced c o n f i g u r a t i o n and high source impedance the head currents were not e a s i l y observed. I t was p o s s i b l e to e x t r a p o l a t e observations of w r i t e current decay to a time constant of 8.3 us. From the record v o l t a g e s , the measured c h a r a c t e r i s t i c of the r o t a r y transformer, and the head impedence, the h.f. response was presumed to extend w e l l beyond 10 MHz. 3.1.3 Tape crossover e d i t o r The e f f e c t s of the tape edge crossover (§3.5.2) extend through approximately 54° of the head r o t a t i o n . The tape crossover e d i t o r , synchro-n i z e d from a s i g n a l a v a i l a b l e at the t r a n s p o r t , ensured that measurements were not made i n the crossover r e g i o n . In p r a c t i c e the a c t i v e p o r t i o n of the head r o t a t i o n was reduced to 263° thus avoiding i n t e r f e r e n c e from l o n g i -t u d i n a l c o n t r o l t r a c k s recorded c l o s e to the tape edge. - 45 -3.2 LINEAR AND NONLINEAR EFFECTS 3.2.1 Tests of l i n e a r i t y The magnetic recording channel i s extremely n o n l i n e a r . However, under the c o n s t r a i n t of a n h y s t e r e t i c recording or t w o - l e v e l balanced r e c o r d -i n g an approximately l i n e a r data channel may be defined. Such a channel allows the adaption of a wide v a r i e t y of techniques developed f o r l i n e a r communication channels (§2.3.1). For reasons i n d i c a t e d i n §4.1 balanced tw o - l e v e l recording appeared the more a p p r o p r i a t e , at l e a s t f o r i n t i a l s t u d i e s . The f o l l o w i n g t e s t s r e f l e c t t h i s f a c t and concentrate on c h a r a c t e r i z i n g the magnetic recording channel f o r such recordings under a v a r i e t y of c o n d i t i o n s . L i n e a r i t y has f r e q u e n t l y been assessed by r e c o r d i n g two adjacent t r a n s i t i o n s and a l l o w i n g t h e i r s e p a r a t i o n to approach zero [56, 79, 86, 105, 106]. The presence of a r o t a r y coupling transformer precludes such t e s t s on h e l i c a l - s c a n t r a n s p o r t s . However, s i m i l a r t e s t s may be performed by a l t e r i n g the p e r i o d of a recorded square wave (a s e r i e s of equispaced t r a n s i t i o n s ) . Although comparisons i n the time domain appeared to confirm the v a l i d i t y of s u p e r p o s i t i o n , such responses tend to r e f l e c t the s p e c t r a l dominance of low to medium frequencies. More accurate comparisons ( i n v o l v i n g measurement of d i s c r e t e s p e c t r a l energies) can be made i n the frequency domain and r e l a t e d d i r e c t l y to an e q u a l i z e d channel by using l o g a r i t h m i c amplitude s c a l i n g . The a s s o c i a t e d l o s s of phase in f o r m a t i o n i s of l i t t l e consequence both because of the d i f f i c u l t y of c o n c e i v i n g a s i t u a t i o n i n which a channel appears l i n e a r i n amplitude but not phase response, and because of the i n i t i a l confirmations of s u p e r p o s i t i o n i n the time domain. - 46 -The l i n e a r channel response, F i g . 3.1, was assessed by the r e c o r d -i n g and playback of square waves at s e v e r a l frequencies. Harmonic responses were correct e d by a f a c t o r n 2 (n=harmonic number) to allow f o r t h e i r reduced l e v e l . No c o r r e c t i o n s were made f o r the response of the head-preamplifier coupling. The responses i n F i g . 3.1 trac e a w e l l defined bandshape; c e r t a i n l y up to 13 MHz. The l e v e l of no n l i n e a r behaviour may a l s o be assessed. At 6 MHz, f o r example, the fundamental response d i f f e r s from the t h i r d harmonic response of 2 MHz by 1/2 dB. Such d i f f e r e n c e s are t y p i c a l up to 13 MHz. Above 13 MHz the di s c r e p a n c i e s become more severe, p a r t l y r e f l e c t i n g the d i f f i c u l t y of measuring the low energy l e v e l s i n v o l v e d . Below 13 MHz the d i s c r e t e s p e c t r a l responses d i f f e r by l e s s than 0.2 dB r.m.s. from the mean s p e c t r a l response. Nonlinear e f f e c t s are thus suggested to be b e t t e r than 30 dB below the l i n e a r response. More r e a l i s t i c t e s t s may be performed with pseudo-random sequences [227] at s u i t a b l e b i t r a t e s . Figure 3.2 shows r e s u l t s w i t h a 31 b i t sequence at 20 Mbit/s (1.1 Mbit/m). Nonlinear e f f e c t s give r i s e to the r i p p l e i n the amplitudes of successive harmonic responses. Nonlinear e f f e c t s can a l s o be assessed i n F i g . 3.2 by comparison w i t h the co r r e c t e d harmonics of a 20/31 MHz square wave. The e f f e c t s appear more s i g n i f i c a n t here, exceeding ±1 dB r e l a t i v e to a mean response. The r.m.s. d e v i a t i o n remains below 10% and corresponds to about -19 dB of no n l i n e a r I S I . The response to the pseudo-random sequence i s c o n s i s t e n t l y 1 dB below that of the square wave, and w h i l e t h i s r e s u l t i s d i f f i c u l t to i n t e r p r e t , the r i p p l e i n the former's s p e c t r a l response i s amenable to explanation as i n §3.2.2. The l i n e a r frequency response of the magnetic r e c o r d i n g channel has been described by e m p i r i c a l formulae (2.9, 2.10). Such d e s c r i p t i o n s - 47 -09 0 ro rt H-n i-i to o o i-i H-3 lew o 3* B 3 fD i-i ro CD ' 1 3 cn rt> I rf O n TO m D cz m z _ , n 0 -< 2 I CHANNEL RESPONSE AMPLITUDE (dB] p o i Ul o I Ul I o I OI 5 c m z n •< m ? n -< o r-m cn i o I I ro O o I > • Oa o + x CO -< CD o O o o < m ' -n"n TOCZ ii. to w r ' f ? ? o o o o b c n o u i M C > ui n •<: X N m a i + x 4> cx X +> x > JO o + • D TO C ro U3 co 3 , ro, rt' H-n i-i • ro o o a.. 3 W n 3' . 3 3 ro ro cn O 3 cn ro rr O o NJ cn oo I ro > 555 Z ro C o m fo CD ro m I Ul CHANNEL RESPONSE AMPLITUDE (dB) i i i i to to ro ro I -n TO m _» o o c m z " n -< o have proven remarkably accurate i n the s i t u a t i o n of balanced t w o - l e v e l recording. In order to compare (2.9) w i t h the measured responses ( F i g s . 3.1 and 3.2) i t i s necessary to evaluate the e f f e c t s of the hea d - a m p l i f i e r c o u p l i n g . The.-head-preamplifier response was evaluated experimentally using a c u r r e n t -source feeding a s m a l l r e s i s t o r i n s e r i e s w i t h the head. These r e s u l t s were checked against and supplemented by the response c a l c u l a t e d from measured head and p r e a m p l i f i e r impedances (§3.1.2). A mean channel response was constructed from F i g s . 3.1 and 3.2, and from a d d i t i o n a l measurements based on square-wave harmonics i n the range 10 to 18 MHz. The mean frequency response so constructed was d i v i d e d by the head-preamplifier response p r e v i o u s l y derived. The r e s u l t i n g curve i s shown i n F i g . 3.4 but d i s c u s s i o n of i t s f i t against (2.10) i s postponed u n t i l §3.3 where the tape noise s p e c t r a l d e n s i t y i s introduced. The s p e c t r a l response of the record/playback processes i s , of course, a s t r o n g l y n o n l i n e a r f u n c t i o n of record l e v e l . High record l e v e l s r e s u l t i n reduced h.f. response w h i l e lower l e v e l s y i e l d inadequate SNR. Such behaviour was observed during t e s t recordings of the 31-bit sequence, however the nonl i n e a r p e r t u r b a t i o n s proved r e l a t i v e l y independent of record l e v e l . Q u a n t i t a t i v e measurements of the change i n s p e c t r a l response w i t h record l e v e l may be found i n §3.4.2. I t has thus been i l l u s t r a t e d that although n o n l i n e a r e f f e c t s are present, an o v e r a l l s p e c t r a l response can be c l e a r l y i d e n t i f i e d . Nonlinear e f f e c t s appear to be about 20 dB below the l i n e a r response, suggesting that the channel may w e l l respond to the a p p l i c a t i o n of techniques adapted from l i n e a r communication channels. - 49 -3.2.2 C h a r a c t e r i z a t i o n of channel n o n l i n e a r i t y The magnitudes of the nonl i n e a r e f f e c t s q u a l i t a t i v e l y determined i n the preceding s e c t i o n appear u n l i k e l y to cause severe performance degra-d a t i o n or to i n v a l i d a t e the a p p l i c a t i o n of techniques from l i n e a r data channels. Nevertheless, the c h a r a c t e r i z a t i o n of no n l i n e a r data channels i s a t o p i c of wide a p p l i c a t i o n . Nonlinear behaviour occurs i n a v a r i e t y of data tran s m i s s i o n [189-193] and storage [194, 195] channels, however, there e x i s t s a s u p r i s i n g p a u c i t y of methods f o r channel c h a r a c t e r i z a t i o n . For the binary channel Herrmann [228] suggests measurement of the response to each b i t sequence ( w i t h i n the memory c o n s t r a i n t l e n g t h ) ; the V o l t e r r a c o e f f i c i e n t s being derived from these responses v i a an in v e r s e Hadamard transform. Wood and Donaldson [107] independently suggest a s i m i l a r approach but based on time-average measurements ( i n p a r t i c u l a r , c r o s s - c o r r e l a t i o n ) . : , Such measurements are more convenient i n many s i t u a t i o n s and lead more d i r e c t l y to the V o l t e r r a C o e f f i c i e n t s . The f o l l o w i n g example from [107] i s based on Haynes' comprehensive measurements on a bi n a r y magnetic recording channel [97]. Haynes derive s both amplitude and phase responses f o r the channel. Due to no n l i n e a r e f f e c t s both responses e x h i b i t d i s t i n c t i v e r i p p l e s which cannot be a l l e v i a t e d by l i n e a r e q u a l i z a t i o n . The c r o s s - c o r r e l a t i o n f u n c t i o n corresponding to the equalized and sampled channel response i s shown i n F i g . 3.3. Three d i s t i n c -t i v e spikes occur w e l l d i s p l a c e d from the regions where l i n e a r channel r e -sponses occur. These spikes a r i s e where no n l i n e a r e f f e c t s generate widely d i s p l a c e d copies of the d r i v i n g sequence, a •; property p e c u l i a r to maximal-length pseudo-random sequences [227]. The p o s i t i o n s of the spikes permit a s s o c i a t i o n w i t h s p e c i f i c n o n l i n e a r i n t e r a c t i o n s . The recei v e d samples, v^, - 50 -o UJ or cr o o I i n i n o or 0 - 0 3 0 0 2 0 0 1 0 0 0 - 0 0 1 - 0 0 2 - 0 0 3 - 0 0 4 - 0 0 5 1-0 0 ' 1 j M I j I ' • 4 H T E R M S AR IS ING FROM L INEAR CHANNEL 11 * 4 10 2 0 3 0 4 0 5 0 DISPLACEMENT (bits) arbitrary zero • . > 6 0 Figure 3.3 Cross-correlation", function for equalized sampled^magnetic' recording channel based on measurements of Haynes [97{]-\ - 51 -f o r the e q u a l i z e d channel described above may be approximated as f o l l o w s [107] where a k=±l; v k = a k - 0.044 a k _ 2 a k _ i a k - 0.026 a ^ a ^ + 0 .'024-. a ^ a ^ (3.1) As i n the case of the h e l i c a l - s c a n r e c o r d e r , the n o n l i n e a r e f f e c t s determined on Haynes 1 l o n g i t u d i n a l recorder are r e l a t i v e l y small and do not present a serious problem i n the c o n s i d e r a t i o n of a l i n e a r r e c o r d i n g channel.-. More severe e f f e c t s would be u n l i k e l y to prompt the use of r e c e i v e r s designed f o r the n o n l i n e a r channel [133], s i n c e n o n l i n e a r i n t e r a c t i o n s g e n e r a l l y de-crease the minimum s i g n a l l i n g d i s t a n c e causing i r r e v e r s i b l e degradation. Nonlinear pre-emphasis complementing the a n t i c i p a t e d d i s t o r t i o n appears to be a more u s e f u l approach [107, 228]. 3.3 ADDITIVE NOISE A d d i t i v e noise i s generated p r i m a r i l y by the magnetic medium (tape noise) and by the playback p r e a m p l i f i e r . Tape n o i s e , a r i s i n g from the p a r t i c u l a t e nature of the recording medium, provides fundamental l i m i t s on l i n e a r data d e n s i t y . With the a v a i l a b l e heads and t r a n s p o r t , however, p r e a m p l i f i e r n o i se exceeds tape noise over much of the u s e f u l bandwidth. 3.3.1 Tape noise The presence of high l e v e l s of p r e a m p l i f i e r noise makes measurement of tape noise d i f f i c u l t , p a r t i c u l a r l y at higher frequencies and at very low frequencies. Tape noise s p e c t r a l d e n s i t y was measured as the change i n noise l e v e l when the head-tape motion was a r r e s t e d . A 300 KHz observation band-width was s e l e c t e d to provide 'high < s e n s i t i v i t y w i t h reasonable r e s o l u t i o n . - 52 -A f t e r c o r r e c t i o n f o r the e f f e c t s of head-preamplifier c o u p l i n g the measured tape noise s p e c t r a l d e n s i t y i s d i s p l a y e d i n F i g . 3.4. This f i g u r e a l s o i n d i c a t e s the p r e a m p l i f i e r noise (§3.3.2), the s i g n a l s p e c t r a l d e n s i t y (§3.2.1), and the best f i t t i n g e m p i r i c a l curves (2.9) and (2.11). The c o e f f i c i e n t s i n d i c a t e d f o r (2.9) and (2.11) i n F i g . 3.4 pro-vide minimum mean square l o g a r i t h m i c f i t s of s i g n a l and tape noise s p e c t r a l d e n s i t i e s , r e s p e c t i v e l y . The corresponding parameters are: head-tape se p a r a t i o n , 0.59 um, record depth, 1.07 pm, and t r a n s i t i o n - l e n g t h / r e c o r d -p r o c e s s - l o s s e s , 0.35 um. These values compare favourably with those obtained by others [48, 73, 229]. The gap l o s s f a c t o r , sin(cog/v)/(wg/v), i s omitted, being absorbed by the exponents of the e m p i r i c a l formulae. The head gap i s nominally 1.2 pm, however, t h i s i s understood to be a lower bound. There i s no evidence of a w e l l defined s p e c t r a l n u l l i n the responses below 20 MHz suggesting that the gap i s l e s s than 0.9 pm. Mi c r o s c o p i c examination revealed a gap of t h i s order of magnitude but wi t h obvious v a r i a t i o n s along i t s length. Such v a r i a t i o n s would tend to destroy a w e l l defined s p e c t r a l n u l l . The absolute l e v e l of s i g n a l s p e c t r a l d e n s i t y i s not d i r e c t l y a v a i l a b l e from the d i s c r e t e s p e c t r a l measurements presented i n §3.2.1. The s i g n a l s p e c t r a l d e n s i t y was measured as the response to a 2 2 1 +-1 b i t pseudo-random sequence s i m u l a t i n g the d i r e c t recording of random data at 20 Mbit/s. The s p e c t r a l response proved s i m i l a r to that traced by the d i s c r e t e s p e c t r a l components from sho r t e r t e s t sequences and was used to f i x the l e v e l of s i g n a l s p e c t r a l density i n F i g . 3.4. The narrowband SNR peaks at approximately 44 dB near 2 MHz. Although formulae have been derived which c o r r e c t l y d escribe the o v e r a l l SNR on an equalized channel [109, 110], i n c o n s i s t e n c i e s i n the - 53 -- 5 t (dB) -10 -15+ i A x A N \ . 0-58(1-e-»°- 2 7> w). a-2(0 032)< .» A N x \ A \ A | 7-7(1-e- 0- 5 8") ^ - ( a 0 3 2 * 0 - 0 1 9 ) w \ X \ SPECTRAL DENSITIES x Signal A Tape noise (x 10* ) o Preamplifier noise »x \ I \ FREQUENCY 10 ( MHz) Figure 3.4 Signal arid;'noise spectra with best f i t t i n g empirical curves (2.9) and (2.11). win Mrad/s. i =0.33A-,-tape. #1 - 54 -d e r i v a t i o n s preclude comparison of the r e l a t i v e l e v e l s of s i g n a l and tape noise s p e c t r a l d e n s i t i e s . This s i t u a t i o n i s r e c t i f i e d i n Appendix 1 where (A1.5) describes the narrowband SNR. S i g n a l to tape-noise r a t i o i s a f u n c t i o n of the f o l l o w i n g : trackwidth and medium depth (known), recording depth ( e s t i -mated above), a parameter, f, which describes the l e v e l of magnetization due to the s i g n a l (assumed c l o s e to s a t u r a t i o n , f - l ) , and the bulk p a r t i c l e d e n s i t y . This l a s t parameter i s c a l c u l a t e d from the measured narrowband SNR by s u b s t i t u t i o n i n (A1.5). The c a l c u l a t e d d e n s i t y , 210 p a r t i c l e s / u m 3 , may be compared w i t h 230 p a r t i c l e s / u m 3 reported f o r s i m i l a r m a t e r i a l [57]. 3.3.2 Playback p r e a m p l i f i e r noise Although p r e a m p l i f i e r noise does not give r i s e to fundamental l i m i t a t i o n s on l i n e a r data d e n s i t y , data must be recovered i n f i n i t e time. Noise l e v e l s i n the playback system cannot t h e r e f o r e be ignored and, i n f a c t , provide an upper bound to data recovery r a t e f o r s i g n a l s of a given energy. Conventional magnetodynamic heads, however, acquire t h e i r s i g n a l energy from the r e l a t i v e head-tape motion. Since s i g n a l energy v a r i e s as the square of the head-tape v e l o c i t y , p r e a m p l i f i e r noise provides a lower bound to t h i s v e l o c i t y and to the data recovery r a t e ! By a t t e n t i o n to the head-tape v e l o c i t y , the head e f f i c i e n c y , and the p r e a m p l i f i e r noise f i g u r e , p r e a m p l i f i e r noise can be made subordinate to tape n o i s e . On the a v a i l a b l e t r a n s p o r t t h i s goal i s not achieved ( F i g . j 3.4) l a r g e l y because of the r e l a t i v e l y low head-tape v e l o c i t y but a l s o because of the poor p r e a m p l i f i e r noise f i g u r e (-9 dB). Much higher v e l o c i t i e s are f e a s i b l e [4] and heads can be designed f o r high e f f i c i e n c y [17]. The design of low noise p r e a m p l i f i e r s i s outside the scope of t h i s t h e s i s . -.55 -However, design of the c r i t i c a l h ead-preamplifier i n t e r f a c e i s an important c o n s i d e r a t i o n which i s introduced i n §3.1.2 and i s the subject of performance measurements i n §5.3.2. The a v a i l a b l e s i g n a l to p r e a m p l i f i e r noise r a t i o exceeds 25 dB (over a 10 MHz bandwidth). Although the i m p l i e d e r r o r r a t e at t h i s SNR i s n e g l i g i b l e , e r r o r s a r i s i n g from fading behaviour are aggravated by the presence of a d d i t i v e noise. 3.4 MULTIPLICATIVE NOISE Noise which i s s i g n a l dependent but n o n - d e t e r m i n i s t i c i s r e f e r r e d to as m u l t i p l i c a t i v e n o i s e s i n c e i t i s p a r t i c u l a r l y c h a r a c t e r i z e d by reduc-t i o n s i n channel gain which p e r s i s t through many b i t s of recorded i n f o r m a t i o n . M u l t i p l i c a t i v e n o i s e i s a l s o known as modulation n o i s e , amplitude i n s t a b i l i t y , channel gain i n s t a b i l i t y , or may be considered as fading bahaviour. Severe reductions i n s i g n a l l e v e l are r e f e r r e d to as dropouts and represent the p r i n c i p a l e r r o r mechanism on d i g i t a l magnetic recording systems. The char-a c t e r i z a t i o n of m u l t i p l i c a t i v e noise i s thus of some s i g n i f i c a n c e . The cumulative d i s t r i b u t i o n of m u l t i p l i c a t i v e n o i s e (fade d i s t r i b u t i o n ) together w i t h s t a t i s t i c s such as the mean dropout length are e s s e n t i a l c o n s i d e r a t i o n s i n the design of s i g n a l s and r e c e i v e r s f o r magnetic r e c o r d i n g systems. Some i n s i g h t may a l s o be gained i n t o the mechanical and p h y s i c a l processes which cause fad i n g . 3.4.1 Fade d i s t r i b u t i o n of s p e c t r a l components Although fading reduces the mean s i g n a l l e v e l , the e f f e c t s are more severe upon the h.f. s i g n a l components. The f o l l o w i n g measurements determine the fade d i s t r i b u t i o n s of s e v e r a l s p e c t r a l components i n the frequency range of i n t e r e s t . A square wave at 1.5 MHz was recorded and the - 56 -fade d i s t r i b u t i o n s of the f i r s t , t h i r d , f i f t h and seventh harmonics assessed using the system of F i g . 3.5. The magnitude of each harmonic was observed through a bandwidth of ±150 KHz; however, no change i n d i s t r i b u t i o n r e s u l t e d u n t i l the observation bandwidth was reduced to ±15 KHz when small but con-s i s t e n t reductions i n the p r o b a b i l i t y of deeper fades occurred. In the f i r s t t e s t the p r o b a b i l i t y d i s t r i b u t i o n at each fade l e v e l was estimated using d i f f e r e n t 2 to 3 minute segments of tape. However, tape surface c h a r a c t e r i s t i c s v a r i e d considerably over the segments, w i t h the r e s u l t that the cumulative d i s t r i b u t i o n s obtained were not n e c e s s a r i l y monotonic with fade l e v e l making i n t e r p r e t a t i o n d i f f i c u l t . The t e s t s were repeated on a f i x e d three minute s e c t i o n of tape; these r e s u l t s were monotonic and confirmed the general behaviour observed i n the f i r s t t e s t . F i g . 3.6 shows the cumulative fade p r o b a b i l i t y d i s t r i b u t i o n observed. The most s t r i k i n g feature of the d i s t r i b u t i o n i s the presence of a background fade p r o b a b i l i t y of 1 0 - 5 which i s approached by fades as small as -6 dB. A second feature seen i n F i g . 3.6 i s the frequency dependence of the d i s t r i b u -t i o n . The 1 0 i MHz component i s considerably more s u s c e p t i b l e to s m a l l fades of approximately -3dB than are the lower frequency components. Fade p r o b a b i l i t i e s are a f u n c t i o n of record l e v e l . F i g . 3.7 shows fade p r o b a b i l i t i e s at -lOdB and -20dB as defined on the a b s c i s s a of F i g . 3.6, to be decreasing fun c t i o n s of head current f o r a 5 MHz s i g n a l . U n f o r t u n a t e l y , i n c r e a s i n g the record l e v e l to combat fading enhances self-demagnetization which reduces the a v a i l a b l e bandwidth and aggravates the d i f f i c u l t i e s of e q u a l i z a t i o n . - 57 -mm csiro L O L O min. c o cor Q_ X Cr: LU < CO I- . 2 : LU LU X cr i — CJ LU D_ CO COMPARATOR LOG AMPLIFIER NARROW-BAND FILTER AND POWER DETECTOR COUNTER 1MHz CLOCK ATTENUATOR TAPE CROSSOVER EDITOR PLAYBACK PREAMP WRITE AMPLIFIER HEAD SCAN SYNC. PULSE VIDEO TAPE RECORDER 1.5 MHz SQUARE WAVE Figure 3.5 System used to measure s i g n a l p r o b a b i l i t y d i s t r i b u t i o n s - 58 -x -1.5 MHz + -4.5 MHz o -7.5MHz A -10.5 MHz -6 -8 -10 -12 -14 OUTPUT LEVEL (dB) 16 -18 -20 Figure 3.6 Cumulative p r o b a b i l i t y d i s t r i b u t i o n , F(L) , of channel output s i g n a l vs. output l e v e l , L. i m=0.33 A, square wave input at 1.5 MHz, tape #1 > co < 03 o DC D_ < 2 CD CO 1 — zz> D_ to o iu > 1 — < 1 r> z 10 " 3 , 10-4 10 -5 10~6 0.2 * L= -10dB o L = -20dB 0.3 0.4 0-5 0-6 RECORD LEVEL im(At) Figure 3.7 Cumulative s i g n a l • ^ d i s t r i b u t i o n , F(L) , vs. record l e v e l , <f or." ; » L=-10dB and L=-20dB. Based on f i f t h harmonic of 1 MHz recorded square wave - 59 -This work confirms observations by E l d r i d g e [115] that non-saturated modulation noise i s f i x e d r e l a t i v e to tape p o s i t i o n , being a t t r i b u t e d to tape surface d e f e c t s . During the above measurements fades at lower p r o b a b i l i t i e s were seen to occur through a l l frequencies at s p e c i f i c repeatable p o s i t i o n s on the tape. I t f o l l o w s that i f the fading p r o b a b i l i t y d i s t r i b u t i o n can be uniquely r e l a t e d to a s i n g l e u n d e r l y i n g process, then fade depth vs. harmonic frequency at a given p r o b a b i l i t y of occurence a l s o s p e c i f i e s the instantaneous channel frequency response vs. p r o b a b i l i t y . Thus, the frequency response of the magnetic r e c o r d i n g channel changes during a fade and can be r e l a t e d to fade depth (a f a c t a l s o i l l u s -t r a t e d by the model developed i n §3.4.3) and can be assigned a p r o b a b i l i t y of occurence. On the channel i n v e s t i g a t e d the frequency response decreased across the band by at l e a s t an a d d i t i o n a l 0.17 dB/MHz f o r 1% of the time and 0.36 dB/MHz f o r 0.01% of the time. On a 10 MHz bandwidth the 0.36 dB/ MHz decrease amounts to -20 dB r.m.s. e r r o r i n a c t u a l frequency response r e l a t i v e to a f l a t response. The change i n frequency response a s s o c i a t e d w i t h fades would seem to be of secondary importance p a r t i c u l a r l y i f exact e q u a l i z a t i o n i s arranged at a fade depth where the system i s more s u s e p t i -b l e to e r r o r s . This p r a c t i c e i s r e f e r r e d to as "over e q u a l i z a t i o n " [219]. 3.4.2 Bandwidth of m u l t i p l i c a t i v e e f f e c t s As noted above, s l i g h t changes i n fade d i s t r i b u t i o n occurred as the observation bandwidth was reduced to 15 KHz. In p a r t i c u l a r , the prob-a b i l i t i e s of deep fades were s i g n i f i c a n t l y reduced under a narrow observa-t i o n bandwidth. A time constant of the order of 10 ps (0.2 mm) may thus be a s s o c i a t e d w i t h deep fades. D i r e c t observation of s i g n a l envelopes - 60 -i n the time domain revealed 10 dB fades which p e r s i s t t y p i c a l l y f o r 5 ys but which range from 0.1 ys to 25 .ys. The a s s o c i a t e d time constant, perhaps 2 ys (0.04 mm) i s considerably l e s s than suggested by the preceding methods. This l a s t method however attaches equal weight to short fades which c o n t r i b u t e l i t t l e to e i t h e r the envelope s p e c t r a l d e n s i t y or the d i s t r i b u t i o n f u n c t i o n . The c h a r a c t e r i s i t c dimensions of m u l t i p l i c a t i v e noise have been v a r i o u s l y quoted or i m p l i e d to be: 1.2 mm [120], 0.5 mm [119], 0.03 mm [111]. This l a s t r e s u l t i s based on a study of tape induced v i b r a t i o n s . Dropouts have been i n d i c a t e d w i t h lengths ranging from 0.05 to 0.5 mm [52] and more r e c e n t l y w i t h a t y p i c a l l ength of 0.4 mm [123]. S e c t i o n 6.2 contains a more complete examination of fading behaviour on the d i g i t a l channel. 3.4.3 M o d e l l i n g of the record/playback process The dominant fading process on the magnetic r e c o r d i n g channel i s assumed to i n v o l v e v a r i a t i o n s i n head-tape s e p a r a t i o n which are repeatable on a l l record/playback runs. This assumption i s supported by the observed narrow bandwidth of the process and the p e r s i s t e n c e of deep fades through a l l r e cordings. In order to deduce from F i g s . 3.6 and 3.7 a p r o b a b i l i t y d i s t r i b u t i o n f o r head-tape s e p a r a t i o n , i t i s f i r s t necessary to e s t a b l i s h the accuracy of channel behaviour as described by (2.9) or (2.10) as w e l l as the a s s o c i a t e d parameter values. Behaviour as p r e d i c t e d by (2.9) and (2.10) was compared w i t h channel measurements over the a c c e s s i b l e v a r i a b l e s , namely record l e v e l and frequency. Recording f i e l d r a d i u s , a+d, was assumed to vary as g/tan ( K / i m ) , where 2g i s the head gap, i m the record current l i n k a g e , and K describes the medium's c o e r c i v i t y r e l a t i v e to the head e f f i c i e n c y . In (2.9) Z was chosen as 0.44d on the b a s i s of Lindholm's work [78] and a s i m i l a r s elf-demagnetization f a c t o r , exp[-0.44dco(2a+d)/ - 61 -2v(a+d)], was introduced i n t o (2.10). The l a t t e r f a c t o r i s based on the assumption that self-demagnetization i s r e l a t e d to the i n t e g r a l of magnetic moment over the recording depth [79]. The response (2.10) becomes E(w) / l m(a))=jv[l+toa/v-(l+o)(a+d) /v]exp(-cod/v)] ;. exp (-coa/v) exp [-0.44cod(2a+d)/2v(a+d)]v/u>(a+d) (3.2) The parameters a and d were adjusted to minimise the mean square e r r o r between a c t u a l and p r e d i c t e d behaviour. The r e s i d u a l mean square e r r o r was 0.03 (normalized against mean output s i g n a l power) f o r both mathematical models. Figure 3.8 shows the nature of the discrepency f o r the model based on (3.2). Attempts to improve the f i t by f u r t h e r r e f i n i n g the w r i t e process model met w i t h l i m i t e d success. For example, a l l o w i n g the constant, a, to be a uniform d i s t r i b u t i o n r a t h e r than a d i s c r e t e value gave only marginal improvement as d i d the i n t r o d u c t i o n of a minimum recorded t r a n s i t i o n l e n g t h . An exponential decay of magnetization beyond the w r i t e f i e l d r adius reduced the mean square e r r o r to 0.023. V a r i a t i o n s i n head response (§3.5.4), and u n c e r t a i n t i e s i n the head gap and p r e a m p l i f i e r response may p a r t l y e x p l a i n the poor f i t of the mathematical models. S i m i l a r discrepancy i s evident i n the work of Middleton and Wisely [230] whose model i n c l u d e s a d e s c r i p -t i o n of the M-H loop and allows more r e a l i s t i c treatment of the demagnetiza-t i o n process. 3.4.4 Deduced d i s t r i b u t i o n f o r head-tape se p a r a t i o n Notwithstanding d i s c r e p a n c i e s between measured and p r e d i c t e d behaviour, an estimate of the p r o b a b i l i t y d i s t r i b u t i o n f o r head-tape separa-t i o n i s derived. The po i n t s i n F i g . 3.9 are obtained by s u b s t i t u t i n g from F i g s . 3.6 and 3.7 i n t o (3.2). While the r e s u l t s from F i g . 3.6 are remarkably - 62 -0.2 0.3 0-4 0.5 0.6 RECORD LEVEL i m (At) Figure 3.8 Comparison of measured channel response w i t h response p r e d i c t e d  by (3.1). Head-tape s e p a r a t i o n , a=0.54 um, a+d=0.6/tan.15/i,) , where  d i s e f f e c t i v e r e cording depth and i m>2/0.15 r ris the record l e v e l o U J CO LU i Ul t— CJ • X 5 U CD Q . CD .1.0 10-1 10-2 10- 3 10-4 10-5 10"6 0 A - t o X V * A x 82Kc/nV + 245 " o 408 -A 571 -(FROM FIG. 36) T 10dB FADE-j (PROM FIG. 3-7) • 20dB FADE J A + *8 u - J 1.0 1.5 2.0 HEAD-TAPE SEPARATION (^ m) Figure 3.9 P r o b a b i l i t y of head-tape separation being exceeded vs. head-tape s e p a r a t i o n . Derived from f i g s . 3.6, 3.7, and 3.8. - 63 -c o n s i s t e n t , those from F i g . 3.7 show l a r g e r d e v i a t i o n s , p a r t i c u l a r l y as the record l e v e l approaches the abrupt c u t - o f f below 0.2A (see F i g . 3.8). The d i s t r i b u t i o n of head-tape s e p a r a t i o n i s d i s t i n c t l y non-Gaussian. I t i s p o s s i b l e that v a r i a t i o n s i n separation a r i s e from two d i s t i n c t causes; tape surface roughness a f f e c t i n g the c e n t r a l part of the d i s t r i b u t i o n (a^O.5um), and the occurrence of l a r g e p a r t i c l e s embedded i n the tape causing much l a r g e r separations. The c e n t r a l part of the d i s t r i b u t i o n y i e l d s a standard d e v i a t i o n of about 0.05 um f o r v a r i a t i o n s i n e f f e c t i v e s e p a r a t i o n . Sebestyn [8] and Wildmann [231] quote ranges of 0.03 - 0.15 pm and 0.08 - 0.13 pm r e s p e c t i v e l y f o r r.m.s. tape surface roughness. Baker [121] i m p l i e s a head-tape s e p a r a t i o n having an underlying d i s t r i b u t i o n w i t h c h a r a c t e r i s t i c s s i m i l a r to F i g . 3.9. 3.5 OTHER CONSIDERATIONS 3.5.1 Timebase s t a b i l i t y The timebase s t a b i l i t y of recorders used f o r commercial t e l e v i s i o n i s n e c e s s a r i l y high. S t a b i l i t y i s quoted i n Appendix 2 as being b e t t e r than 0.5% of p i c t u r e width over a time constant of 7.5 ms; an im p l i e d time s t a b i l i t y of 3 x 1 0 - 5 . The quoted gross s t a b i l i t y maintains the playback s i g n a l timing to w i t h i n 5 ps of the a p p l i e d 60 Hz synchronizing s i g n a l . Simple v e r i f i c a t i o n of the above s t a b i l i t i e s was made by recording a 1.5 MHz c r y s t a l source. The playback s i g n a l was demodulated against the same source and frequency s t a b i l i t y assessed from the i n t e r v a l s between successive phase c a n c e l l a t i o n s . The short term frequency s t a b i l i t y was thus estimated at 1.7 x 10 r.m.s. w i t h the frequency changes o c c u r r i n g v i s i b l y s lowly (perhaps 2 to 3 Hz). The quoted and measured s t a b i l i t i e s appear adequate f o r conventional c l o c k recovery c i r c u i t s . Although phase j i t t e r w i t h respect to the 60 Hz - 64 -synchronizing s i g n a l i s much greater than the a n t i c i p a t e d c l o c k i n t e r v a l , t h i s j i t t e r occurs s l o w l y and should be e a s i l y followed by a l o c a l l y generated c l o c k . A f t e r data d e t e c t i o n timing v a r i a t i o n s may be removed as necessary. The phase of the 1.5 MHz playback s i g n a l was noted to be completely i n c o n s i s t e n t across the tape edges. The c o n c l u s i o n may be drawn that the tape/transport i s subject to d i m e n s i o n a l / p o s i t i o n a l i n s t a b i l i t y greater than 13 ym. 3.5.2 Tape-edge crossover In the a-format, shown i n F i g . 1.2, tape i s wrapped around a c y l i n d r i c a l drum i n a s i n g l e h e l i c a l t u r n . The record/playback head r o t a t e s w i t h i n the drum t r a v e r s i n g the adjacent tape-edges at the tape e n t r y / e x i t p o i n t . The tape-edges are separated by about 100 ym, however, the e f f e c t s of the tape-edge crossover extend through more than 15% of the head r o t a t i o n . Figure 3.10 shows playback responses around the crossover f o r harmonics of a 1.5 MHz recorded square wave. The observed frequency depend-ence i s l e s s than expected from a simple v a r i a t i o n of head-tape separation. Separation undoubtedly increases around the tape edges where the e f f e c t i v e r e s i l i e n c e of the tape surface i s reduced, but i t i s a l s o l i k e l y that the separation becomes nonuniform across the t r a c k w i d t h . Nonuniform s e p a r a t i o n would tend to cause s i g n a l l e v e l reductions l e s s dependent on frequency and might be i d e n t i f i a b l e by a sharper, s l i g h t l y asymmetric v a r i a t i o n of channel gain w i t h t r a c k i n g o f f s e t . There i s marginal evidence of such v a r i a t i o n . In terms of maximising a r e a l d e n s i t y the tape surface c l o s e to the edges represents a region of degraded performance. The degradation a r i s e s from the d i f f i c u l t y of m a intaining the appropriate head-tape i n t e r f a c e - 65 -- 66 -as w e l l as from p h y s i c a l damage and the a c c r e t i o n of d i s t . S i g n a l and r e c e i v e r designs f u l l y u i t l i z i n g the tape surface must be t o l e r a n t to channel degradation around the tape edges. 3.5.3 Tracking High a r e a l d e n s i t i e s r e q u i r e narrow t r a c k s ; the a b i l i t y on playback to a c c u r a t e l y f o l l o w the recorded t r a c k i s t h e r e f o r e of paramount importance. On most commercial video recorders, t r a c k i n g r e l i e s on t i g h t mechanical tolerances combined w i t h manual adjustment of head r o t a t i o n phase w i t h r e -pect to a l o n g i t u d i n a l synchronizing t r a c k . The t r a c k i n g c o n t r o l was f r e -quently adjusted during the measurements d e t a i l e d i n Chapters I I I , V, VI and V I I . The adjustments stemmed more from the control's eminent c u l p a b i l i t y w i t h regard to sudden changes i n performance and from i t s obvious a c c e s s i b i l i t y than from any l a c k of s t a b i l i t y . 3.5.4. C o m p a t i b i l i t y C o m p a t i b i l i t y i n the exchange of tapes between t r a n s p o r t s n e c e s s i -tates the adoption of standard formats such as e x i s t f o r lower d e n s i t y l o n g i t u d i n a l machines. The absence of such formats p a r t l y r e f l e c t s the dramatic t e c h n o l o g i c a l advances o c c u r r i n g i n the f i e l d of h i g h - d e n s i t y magnetic r e c o r d i n g . I t i s i n t e r e s t i n g to note that although formats i n the consumer video f i e l d were becoming standardized [ 1 ] , more recent developments have again l e d to four mutually incompatible formats [232]. While d i s c u s s i o n of standard formats i s outside the scope of t h i s t h e s i s , the designer of a prototype high d e n s i t y r e cording system should at l e a s t ensure c o m p a t i b i l i t y between nominally i d e n t i c a l t r a n s p o r t s . Such co m p a t a b i l i t y i s by no means a foregone c o n c l u s i o n as evidenced by the pre-sence of the t r a c k i n g c o n t r o l on consumer video recorders. Although improved - 67 -mechanical tolerances and s e r v o - p o s i t i o n e d heads [4, 50, 51] have eased the d i f f i c u l t i e s of t r a c k i n g , v a r i a t i o n s i n the head-tape i n t e r f a c e , r e c o r d / playback c i r c u i t r y , and tape c h a r a c t e r i s t i c s can a l s o create c o m p a t i b i l i t y problems. V a r i a t i o n s i n mean playback l e v e l over the permutations of three nominally i d e n t i c a l heads (P, G, and B) are i n d i c a t e d i n Table 3-.1- The l e v e l s were assessed by r e c o r d i n g a 1 MHz square wave and observing the f i r s t through t h i r t e e n t h playback harmonics. The range encountered i n Table 3.1 confirms the requirement f o r r e c e i v e r s t o l e r a n t to channel gain v a r i a t i o n . Playback Head Record Head \ G P B (Average) G -2.0 0.8 0.8 -0.1 P -2.2 2.8 1.6 0.7 B -4.1 1.5 0.5 -0.7 (Average) -2.8 1.7 1.0 dB 1 Mean playback l e v e l f o r the nine choices of re heads. Figure 3.11 i l l u s t r a t e s the s p e c t r a l v a r i a t i o n of each combination of heads r e l a t i v e to i t s mean response. The r.m.s. d e v i a t i o n (based on the f i r s t through eleventh harmonics) i s j u s t over 1 dB. An e q u a l i z a t i o n e r r o r of approximately -20 dB might t h e r e f o r e be a n t i c i p a t e d f o r a p a r t i c u l a r channel w i t h f i x e d e q u a l i z a t i o n on the mean response. I t i s i n t e r e s t i n g to speculate on the o r i g i n s of these v a r i a t i o n s . S e c t i o n 3.4.3 describes the e f f e c t of changing head-tape s e p a r a t i o n . During the record process increased s e p a r a t i o n causes reduced l e v e l but a p o s i t i v e - 68 -PLAYBACK RESPONSE B G \ 1 s t letter identifies recording head 2 (dB)| 1 0 • - I --2 -34 letter identifies playback head PG / p P i / ^ GB V -\ ' \ A ' B P . ^ ' - < V PB~*" GG""* P P * " GP G B / ' \ - \ ' / PB — / V / ,X V BP - % \ / V \ GG standard deviation = 113 dB (1 - 11 MHz) \ \ \ \ \ \ \ \ BG ' X B B Corrected for mean playback level (each curve). Corrected for mean frequency response (over all choices of heads). 5 F R E Q U E N C Y 10 ( M H z ) Fdtgure. 3.11 Channel response f o r various choices of record and playback "•"heads. Based on spot frequency measurements at 1,3,5 ,7 ,9 ,11,13 MHz . Record l e v e l , i m=0.53. A',- tape'-#l - 69 -f i r s t order v a r i a t i o n w i t h frequency. During playback,increased s e p a r a t i o n causes a s i g n i f i c a n t decrease i n l e v e l and a l a r g e r negative f i r s t order v a r i a t i o n . The above e f f e c t s are d i s c e r n i b l e > i n Table 3.1 and F i g . 3.11 w i t h head G having l a r g e r s e p a r a t i o n , and P and B having smaller separations. Tests were performed w i t h tapes #1, #2, #3 which magnetically are nominally i d e n t i c a l . Results g e n e r a l l y agreed to w i t h i n y dB v e r i f y i n g the high l e v e l of consistency of a v a i l a b l e video tapes. - 70 -IV SIGNAL AND RECEIVER DESIGN CONSIDERATIONS The preceding chapter d e a l t w i t h the c h a r a c t e r i z a t i o n of the magnetic r e c o r d i n g channel. The c h a r a c t e r i z a t i o n was l a r g e l y confined to two- l e v e l balanced b i n a r y s i g n a l l i n g . The co n s i d e r a t i o n s l e a d i n g to t h i s s i g n a l l i n g r e s t r i c t i o n are discussed i n the f i r s t s e c t i o n of t h i s chapter. Based on the s i g n a l l i n g r e s t r i c t i o n and the channel c h a r a c t e r i z a t i o n , a gene r a l i z e d d i s c u s s i o n of r e c e i v e r design appears i n the second s e c t i o n . The t h i r d s e c t i o n . d e s c r i b e s -the • components of a prototype system i n t e n d -ed to demonstrate the f e a s i b i l i t y of the suggested design f e a t u r e s . Some of the s p e c i f i c d i f f i c u l t i e s encountered during i n i t i a l t e s t s of the prototype system are mentioned i n the f i n a l s e c t i o n . 4.1 SIGNAL DESIGN Optimal s i g n a l l i n g on a no n l i n e a r d i s p e r s i v e channel presents a formidable problem. The source data sequence must be embodied i n a s e r i e s of waveforms so as to minimise the o v e r a l l e r r o r r a t e emerging from an optimum (maximum-likelihood) r e c e i v e r . On a l i n e a r channel, r u l e s e x i s t to i n d i c a t e the s p e c t r a l energy of optimum d i f f e r e n c e waveforms [124, Chpt. 5] whi l e dynamic programming techniques can i d e n t i f y c r i t i c a l minimum di s t a n c e sequences [125]. On the magnetic r e c o r d i n g channel the e f f e c t s of n o n l i n e a r i t y and channel fading compound the problem. Nor i s the assumed maximum l i k e l i -hood (ML) r e c e i v e r a p r a c t i c a l p r o p o s i t i o n i n such a s i t u a t i o n . R e a l i s t i c a l l y the choice of s i g n a l l i n g waveforms can only be made w i t h an i n t u i t i v e approach based on c a r e f u l observation and experimentation. The most important r e s t r i c t i o n on the choice of s i g n a l l i n g wave-forms a r i s e s from the severe channel n o n l i n e a r i t y . From crude models of the w r i t e process, which d e f i n e a r e c o r d i n g radius p r o p o r t i o n a l to s i g n a l l e v e l , i t i s apparent that a high l e v e l s i g n a l w i l l erase a preceding low l e v e l s i g n a l . Such g r o s s l y n o n l i n e a r behaviour suggests the use of s i g n a l l i n g waveforms which give r i s e to a constant r e c o r d i n g r a d i u s . Balanced two-l e v e l r e c ording and a.c.-bias recording both s a t i s f y t h i s c r i t e r i o n . The use of a.c.-bias recording r e s u l t s i s not only a constant w r i t e r a d i u s but a l s o a s i n g l e valued B-H curve ( a n h y s t e r e t i c ) . By s u i t a b l y reducing s i g n a l l e v e l s t h i r d harmonic d i s t o r t i o n (THD) can be c o n t r o l l e d ; a 10 dB r e d u c t i o n i n s i g n a l l e v e l reduces THD to 3% [9]. A channel can t h e r e -fore be arranged which i s approximately l i n e a r given reasonable c o n s t r a i n t s on the peak s i g n a l amplitudes. A l i n e a r channel allows the a p p l i c a t i o n of such techniques as pulse compression r e c o r d i n g [211], v e s t i g i a l / s i n g l e -sideband [124], p a r t i a l response or duo-binary [134, 175], and m u l t i l e v e l pulse amplitude modulation [124, 126, 127, 141]. Pulse compression r e c o r d i n g was mentioned i n § 2.3.3 p r i m a r i l y as a means of a v o i d i n g dropout e r r o r s . The r e q u i r e d l e v e l s of l i n e a r i t y and p o s s i b l y timebase s t a b i l i t y would seem to preclude pulse compression recording f o r high d e n s i t y systems. S i n g l e sideband (SSB) or v e s t i g i a l sideband techniques a l l o w a c e r t a i n amount of freedom along the frequency a x i s through the choice of c a r r i e r frequency; the a d d i t i o n a l problem a r i s e s of s y n c h r o n i z i n g to t h i s c a r r i e r . This problem together the l o s s e s i n v o l v e d i n l i n e a r i z i n g the channel lead to the c o n c l u s i o n that SSB o f f e r s no advantages over pulse amplitude modulation (PAM). The d.c. n u l l which can be avoided by the use of SSB can a l t e r n a t i v e l y be handled through the use of d.c. f r e e codes (§2.3.3) or by the i n t r o d u c t i o n of small amounts of d e c i s i o n feedback (§7.1.2). - 72 -P a r t i a l response s i g n a l l i n g [135] may be considered w i t h i n the more general c l a s s of d e c i s i o n feedback e q u l i z a t i o n (DFE). Systems w i t h s p e c t r a l shaping p r i o r to the record process must operate on a l i n e a r i z e d channel w i t h a p p r o p r i a t e l y reduced record l e v e l . DFE schemes which avoid t h i s d i f f i c u l t y are more a p p r o p r i a t e l y discussed i n the f o l l o w i n g s e c t i o n on r e c e i v e r design. M u l t i l e v e l PAM o f f e r s a r e a l i s t i c p o s s i b i l i t y , p a r t i c u l a r l y on wide t r a c k systems w i t h high s i g n a l - t o - n o i s e r a t i o (SNR). I t should be noted that the a.c.-bias l o s s of around 10 dB ( r e q u i r e d to l i n e a r i z e the channel) i s i n a d d i t i o n to approximately 6 dB f o r each doubling of the number of record l e v e l s . F o u r - l e v e l s i g n a l l i n g , f o r example, must be compared w i t h the a l t e r n a t i v e of h a l v i n g the t r a c k width (maintaining two-l e v e l recording) i n order to double the recording d e n s i t y . H a l v i n g the t r a c k width l o s e s -3 dB s i g n a l against tape noise or 6 dB i f r e c e i v e r noise predominates. The a v a i l a b l e narrowband SNR w i t h optimised d i r e c t r e c o r d i n g has been measured (§3.3) to exceed 30 dB over 0.3 to 7 MHz (0.02-0.4 Mcycles/m). This SNR would apparently be adequate to support a f o u r - l e v e l system at 27 Mbit/s, (1.5 Mbit/m). U n f o r t u n a t e l y , magnetic recording channels are plagued by continuous v a r i a t i o n s i n channel gain. These v a r i a t i o n s have been measured at 8% r.m.s. with time constants of the order of 100 symbols. Despite the high data r a t e such a system would r e q u i r e r a p i d and e f f e c t i v e - 3 automatic gain c o n t r o l i n order to achieve e r r o r r a t e s much below 10 (see F i g . 3 - 6 ) . In a d d i t i o n , both record and playback c i r c u i t r i e s i n v o l v e c o n s i d e r -able complexity i n comparison to b i n a r y s i g n a l l i n g . - 73 -Balanced t w o - l e v e l recording s i m i l a r l y maintains a constant w r i t e radius i n the manner of a.c.-bias r e c o r d i n g . Under pressure f o r s p e c t r a l e f f i c i e n c y , the various options (frequency/phase modulation, pulse p o s i t i o n modulation, pulse d u r a t i o n modulation) tend to degenerate i n t o v a r i o u s l y constrained non-return-to-zero (NRZ) b i n a r y formats. D i r e c t r e cording of balanced b i n a r y s i g n a l s on the prototype system would appear to have a v a i l -able a narrowband SNR exceeding 25 dB over approximately 10 MHz (0.55 Mbit/m). Given the l e v e l of l i n e a r i t y suggested i n §3.2, the channel should e a s i l y accommodate 20 Mbit/s (1.1 Mbit/m) NRZ s i g n a l l i n g . With due regard f o r the simpler record and playback c i r c u i t s , the d e c i s i o n was made to implement d i r e c t r e cording of NRZ waveforms at the above r a t e . Such a system does not preclude subsequent examination of more complex precoding techniques such as M i l l e r [205] or 3PM [206]. 4.2 RECEIVER DESIGN 4.2.1 Receiver s t r u c t u r e s A v a r i e t y of r e c e i v e r s t r u c t u r e s are o u t l i n e d i n §2.3. The s e l e c -t i o n of b i n a r y NRZ s i g n a l l i n g s i m p l i f i e s some of the processes w i t h i n the r e c e i v e r and e q u a l i z a t i o n g e n e r a l l y becomes l e s s c r i t i c a l , compared, f o r example, w i t h m u l t i l e v e l PAM. With the assumption of adequate channel l i n e a r i t y , NRZ s i g n a l l i n g on the magnetic r e c o r d i n g channel f a l l s i n t o the c l a s s of l i n e a r modulation/transmission schemes. Receiver designs f o r such schemes are g e n e r a l l y w e l l understood and may be categorized i n t o l i n e a r or n o n l i n e a r and adaptive or nonadaptive designs. The r e c o r d i n g channel e x h i b i t s both a d.c. s p e c t r a l n u l l and sharply reducing SNR at higher frequencies; d e f i c i e n c i e s which suggest the - 74 -use of no n l i n e a r r e c e i v e r s . In p a r t i c u l a r the use of c l a s s IV p a r t i a l response [135] has been proposed [233]. Receivers f o r such s i g n a l s , however, r e q u i r e accurate knowledge of the channel gain. The design of automatic gain c o n t r o l (a.g.c.) or an estimator of channel gain i s not simple [188]. In the absense of a.g.c. complete data l o s s occurs f o r fades exceeding 6 dB. -Lt Figure 3.6 suggests an e r r o r r a t e around 10 f o r p a r t i a l response without a.g.c. Whether more moderate s p e c t r a l shaping w i t h D F E r e c e p t i o n can provide u s e f u l r e s u l t s i s the t o p i c of Chapter V I I . The use of ML r e c e p t i o n on magnetic tape systems would g e n e r a l l y be precluded by economic c o n s i d e r a t i o n s . L i n e a r r e c e i v e r s are r e l a t i v e l y i n s e n s i t i v e to channel gain v a r i a -t i o n s (from §3.4 ass o c i a t e d s p e c t r a l changes are presumed s m a l l ) . L i n e a r r e c e i v e r s do not, however, avoid the problem of the d.c. n u l l . Adequate SNR e x i s t s down to about 150 KHz; the absence of frequencies below t h i s would give r i s e to -18 dB of r e s i d u a l intersymbol i n t e r f e r e n c e (ISI) on a 20 Mbit/s s i g n a l . While -18 dB. i s by no means n e g l i g i b l e i t was f e l t that u s e f u l t e s t s could be performed w i t h data sequences s u f f i c i e n t l y short (<130 b i t s ) that a l l harmonics exceed 150 KHz. The r e s u l t s of such t e s t s , although avoiding the problem of the d.c. n u l l , r e l a t e to a more ge n e r a l i z e d s i t u a t i o n than would be the case i f s p e c i f i c a c t i o n were taken to i n c l u d e and compensate the e f f e c t s of the n u l l . At the same time the p o s s i b i l i t i e s of i n v e s t i g a t i n g d.c. f r e e codes or applying DFE to the n u l l are by no means•precluded. With regard to data r a t e or l i n e a r d e n s i t y , i t i s g e n e r a l l y acknowledged [4] that the equalized s i g n a l should exceed tape and p r e a m p l i f i e r noise by about 30 dB. Such apparently excessive SNR i s re q u i r e d to provide adequate margin against non-Gaussian noise and fadi n g . Based on §3.2 and §3.3, e f f e c t i v e s i g n a l - t o - n o i s e r a t i o s are compared i n F i g . 4.1 as a f u n c t i o n - 75 -E F F E C T I V E S I G N A L A D D I T I V E N O I S E 3 0 (dB) 2 0 1 0 \ — • 1 > 1-0 1-5 R E C O R D I N G D E N S I T Y ( M b i t / m ) H — > 2 0 2 5 3 0 D A T A R A T E ( M b i t / s ) Figure 4.1 Calculated effective SNR vs. linear recording density - 76 -of frequency. Although s p e c t r a l shaping ( c l a s s IV p a r t i a l response) can give n o t i c e a b l e improvement of SNR, f l a t e q u a l i z a t i o n i s only s l i g h t l y i n f e r i o r where the SNR approaches 30 dB ( F l a t e q u a l i z a t i o n approximates optimum l i n e a r r e c e p t i o n on sharply bandlimited channels at high SNR). The d e c i s i o n was made to implement a l i n e a r r e c e i v e r at 20 Mbit/s (1.1 Mbit/m). This d e c i s i o n r e f l e c t s c o n s i d e r a t i o n s of both implementation and performance; i n p a r t i c u l a r , the severe gain s e n s i t i v i t y of no n l i n e a r r e c e i v e r s i s avoided w h i l e subsequent i n t r o d u c t i o n of coding or d e c i s i o n feedback i s not precluded. The optimum l i n e a r r e c e i v e r [124] can be considered as a matched f i l t e r followed by a t r a n s v e r s a l f i l t e r . This s e p a r a t i o n i s purely academic; the s p e c t r a l shaping of the matched f i l t e r may be almost completely c a n c e l l e d by the subsequent t r a n s v e r s a l f i l t e r . The matched f i l t e r i s i n f a c t redun-dant - except where s p e c t r a l i n f o r m a t i o n extends (and i s th e r e f o r e d u p l i c a t e d ) outside the Nyquist bandwidth. The e s s e n t i a l f u n c t i o n of the matched f i l t e r l i e s i n i t s weighting and phase c o r r e c t i o n of d u p l i c a t e d s p e c t r a l i n f o r m a t i o n p r i o r to f o l d i n g i n t o the Nyquist bandwidth (sampling). Commonly, s i g n a l - t o -noise r a t i o i s found to decrease r a p i d l y and monotonically across the Nyquist bandedge. For t h i s reason a standard low-pass f i l t e r w i t h appropriate r o l l -o f f performs almost as w e l l as a matched f i l t e r , i s simpler to implement, and i n many cases- eases the design of the subsequent t r a n s v e r s a l f i l t e r . The e q u a l i z a t i o n process on t h i s prototype system i n c l u d e s a 'pre-f i l t e r ' f ollowed by a conventional seven-tap t r a n s v e r s a l f i l t e r . The p r e f i l t e r comprises a d i s c r e t e component f i l t e r ( e q u a l i z i n g down to 160 KHz) and a f i x e d d e l a y - l i n e f i l t e r , i n conjunction w i t h the p r e a m p l i f i e r and channel responses, a l s o provides the necessary r o l l - o f f across the Nyquist bandedge. The p r e f i l t e r removes much of the burden of e q u a l i z a t i o n from the subsequent t r a n s v e r s a l f i l t e r ; the d.c. n u l l , f o r example, i s not e a s i l y c o r r e c t e d w i t h a f i n i t e -impulse-response f i l t e r . P r i c e et a l . [187] a l s o describe an e q u a l i z a t i o n s t r u c t u r e very s i m i l a r to the above. E q u a l i z a t i o n could be attempted e n t i r e l y w i t h d i s c r e t e component f i l t e r s . Although such an approach i s common p r a c t i c e , the t r a n s v e r s a l f i l t e r o f f e r s s e v e r a l advantages: (a) apart from v a r i a t i o n i n the number of taps, the e q u a l i z e r s t r u c t u r e i s f i x e d . Systems employing t r a n s v e r s a l f i l t e r s may thus be more reasonably compared than those employing d i s c r e t e components. (b) the t r a n s v e r s a l f i l t e r i s o r i e n t e d toward a time domain view. This view i s more appropriate to the nature of intersymbol i n t e r f e r e n c e and the sampling operation. Transversal f i l t e r i n g i s i n t u i t i v e l y understandable and ( c e r t a i n l y f o r an open eye) manual adjustment of tap c o e f f i c i e n t s f o l l o w s e a s i l y . (c) the t r a n s v e r s a l f i l t e r i s amenable to a n a l y s i s and tap c o e f f i c i e n t s are r e a d i l y c a l c u l a b l e . In a d d i t i o n , simple algorithms [124] are a v a i l a b l e which a l l o w automatic adjustment of tap gain c o e f f i c i e n t s . (d) i f sampling precedes t r a n s v e r s a l f i l t e r i n g , the t r a n s v e r s a l f i l t e r can be replaced d i r e c t l y by a d i g i t a l f i l t e r . Such techniques are not im-p r a c t i c a b l e , p a r t i c u l a r l y at low t r a n s f e r r a t e s . The t o p i c s of adaptive f i l t e r i n g and automatic gain c o n t r o l are discussed i n §4.2.3. - 78 -4.2.2 Clock recovery The r e c e i v e r r e q u i r e s a knowledge of cl o c k phase. The r e q u i r e d accuracy of cl o c k phase i s a f u n c t i o n of the degree of confinement of the s i g n a l w i t h i n the Nyquist bandwidth. As a r u l e of thumb, i n a c c u r a c i e s of more than ±10% of the c l o c k p e r i o d are g e n e r a l l y i n t o l e r a b l e . Estimates of clo c k phase are not e a s i l y made and s u f f i c i e n t accuracy can only achieved over periods of many b i t s . R o t a t i n g head machines are c h a r a c t e r i z e d by t h e i r good timebase s t a b i l i t y (§ 3.5.1) and timing estimates can be b u i l t up over s e v e r a l hundred b i t s . Clock phase may be obtained v i a e i t h e r a d e c i s i o n - d i r e c t e d estimate or independently from the playback s i g n a l . Although a d e c i s i o n - d i r e c t e d estimate i s g e n e r a l l y more accurate, s a t i s f a c t o r y a c q u i s i t i o n and s t a b i l i t y may not be presumed. In the absence of decision-based i n f o r m a t i o n accurate estimates of c l o c k phase can s t i l l be obtained [152, 153]. Unfort u n a t e l y such estimates f a i l as the s i g n a l becomes constrained to the Nyquist band-width. P r a c t i c a l s o l u t i o n s such as z e r o - c r o s s i n g d e t e c t i o n nevertheless provide estimates of cl o c k phase w i t h no c l a i m to o p t i m a l i t y . The c l o c k phase estimator i n the prototype system i n c l u d e s a z e r o - c r o s s i n g detector and phase-lock loop. I t s design i s discussed i n § 4.3.2. 4.2.3 Adaptive f i l t e r i n g Although a manually a d j u s t a b l e t r a n s v e r s a l f i l t e r was constructed and used f o r i n i t i a l t e s t s on the prototype system, adjustment was tedious ... and not e a s i l y repeatable. The adjustment p o l i c y c o n s i s t e d of maximising the eye opening and/or minimising e r r o r r a t e . The development of automatic or adaptive e q u a l i z a t i o n was deemed worthwhile. The adaptive adjustment - 79 -a l g o r i t h m then provides a f i x e d b a s i s f o r comparison and g r e a t l y f a c i l i t a t e s the measurement of system performance i n response to a v a r i e t y of parameters. Several adjustment algorithms and o p t i m i s a t i o n c r i t e r i a are a v a i l -able [124]. Given the d i f f i c u l t y of minimising b i t e r r o r p r o b a b i l i t y d i r e c t l y , e i t h e r the minimum mean square e r r o r (MMSE) or the z e r o - f o r c i n g (ZF) c r i t e r i o n can be adopted. The former i s more robust and provides b e t t e r performance w i t h short t r a n s v e r s a l f i l t e r s , but the l a t t e r does o f f e r a p a r t i c u l a r l y simple adjustment algorithm. Z e r o - f o r c i n g was adopted. Appendix 3 describes the a l g o r i t h m and c a l c u l a t e s design parameters; an assessment of t r u n c a t i o n e r r o r i s a l s o included f o r the f i n i t e l e n g t h t r a n s v e r s a l f i l t e r under the ZF c r i t e r i o n . Implementation i s described i n §4.3.5 and §4.3.7. 4.3 PROTOTYPE HIGH-DENSITY MAGNETIC RECORDING SYSTEM Based on the preceding d i s c u s s i o n of s i g n a l l i n g , r e c e i v e r s t r u c t u r e , c l o c k recovery, and adaption, F i g . 4.2 d e p i c t s the r e s u l t i n g prototype system. This s e c t i o n contains a b r i e f d e s c r i p t i o n of each of the system elements i n d i c a t e d i n F i g . 4.2,except the tape-crossover e d i t o r which i s described i n §3.1.3. 4.3.1. Record a m p l i f i e r The record a m p l i f i e r i s d e t a i l e d i n F i g . 4.3 and has s i m i l a r design c o n s i d e r a t i o n s to those mentioned i n §3.1.2. In order to improve the swi t c h i n g c h a r a c t e r i s t i c s f u r t h e r the a m p l i f i e r i s fed w i t h complementary d r i v e and the record l e v e l i s determined by the emitter current source. Intersymbol i n t e r f e r e n c e i s b a r e l y p e r c e p t i b l e ( ~ 1%) at the peak of r o t a r y transformer voltage waveform. - 80 -PLAYBACK a.g.c. PREAMPLIFIER AMPLIFIER ROTARY TRANSFORMER RECORD/ PLAYBACK HEAD T A P E CROSSOVER] EDITOR TAP ADJUSTMENT ALGORITHM DATA IN DATA OUT ' CLOCK RECOVERY LSB RECORD AMPLIFIER i out in 4 - LEVEL QUANTIZER Figure 4.2 The prototype system complementary ..in., •«..... ^ H t p drive i to -. J 820 5 rotary £820 transformer 150 150 •40 1-8KS z± ±r o.oijj F i g . 4-3 Reco rd Ampl i f i e r 22 4-7 K J j O p Jp-01p -1 from rotary transformer X 4-7 T__Jo.oiP +5 22 733 10. emitter shunt 150 0-47JJ to a.g.c. - A A A , j | -> 150 Q-47p a m P -F ig . 4-4 P l ayback Preampl i f ie r - 82 -4.3.2 Playback p r e a m p l i f i e r The playback p r e a m p l i f i e r shown i n F i g . 4.4 was designed i n accord-ance w i t h the c o n s i d e r a t i o n s of §3.1.3. A standard v i d e o - a m p l i f i e r i n t e g r a t e d -c i r c u i t was used i n balanced c o n f i g u r a t i o n and provides a noise f i g u r e of 9 dB. Although p r e a m p l i f i e r noise exceeds tape noise by about 6 dB on the equalized channel the e f f e c t s of tape noise tend to predominate because of non-Gaussian nature (§6.1.2). P r e a m p l i f i e r noise nevertheless aggravates the e f f e c t s of fading and considerable reductions i n p r e a m p l i f i e r noise l e v e l could be made. The design of low noise playback p r e a m p l i f i e r s was considered outside the scope of t h i s t h e s i s . The components R and C i n F i g . 4.4 determine the Q and n a t u r a l ... frequency, f Q , of the head/preamplifier response. Unless otherwise i n d i c a t e d R=1.5K and C=5^^ which place f Q at 13.5 MHz and Q at approximately 3. Se c t i o n 5.3.2 i n v e s t i g a t e s performance as a f u n c t i o n of head/preamplifier coupling. 4.3.3 Automatic gain c o n t r o l The automatic gain c o n t r o l (a.g.c.) a m p l i f i e r provides approximately 20 dB of c o n t r o l . The a m p l i f i e r (see F i g . 4.5) accepts a balanced output from the p r e a m p l i f i e r and s u p p l i e s a single-ended low-impedence s i g n a l to the p r e - f i l t e r . Two potentiometers a l l o w adjustment of s i g n a l gain as w e l l as c o n t r o l voltage gain (or loop g a i n ) . The input a t t e n u a t i o n ( F i g . 4.5) i s requ i r e d to reduce intermodulation d i s t o r t i o n . This problem i s p a r t i c u l a r l y troublesome p r i o r to e q u a l i z a t i o n where the s i g n a l s p e c t r a l d e n s i t y v a r i e s widely across the u s e f u l range of frequency. The c o n t r o l voltage a r i s e s from the tap adjustment algorithm. The c e n t r a l tap of the t r a n s v e r s a l f i l t e r i s i n f a c t h e l d constant (at i t s maximum value) and the c o n t r o l voltage - 83 -Fig. 4.5 Automatic gain control amplifier •5 to transversal filter Fig. 4-6 Prefilter - 84 -corresponding to t h i s tap i s i n s t e a d a p p l i e d to the a.g.c. a m p l i f i e r . The response times as s o c i a t e d w i t h the adjustment alg o r i t h m are of the order of one m i l l i s e c o n d . The advantages of a r a p i d response a.g.c. were not i n v e s t i -gated experimentally. 4.3.4 P r e f i l t e r The p r e f i l t e r provides f u r t h e r s i g n a l gain and a p r e l i m i n a r y gross e q u a l i z a t i o n . The s i g n a l f o l l o w s two paths ( F i g . 4.6) the upper path provides SL.f. compensation v i a the d i s c r e t e component (RC) i n t e g r a t o r . This upper path a l s o i n c l u d e s an> i n v e r t e r and a means of s e t t i n g A.f. gain. The lower s i g n a l path i s a d i s c r e t e time d i f f e r e n t i a t o r which provides h.f. compensa-t i o n (with s i m i l a r phase s h i f t to the upper path). In accordance w i t h the d i s c u s s i o n i n §4.2.1 on matched f i l t e r i n g , the n a t u r a l r o l l - o f f across the Nyquist bandedge i s augmented by the choice of 64 usee delay. The frequency response t h e r e f o r e drops r a p i d l y between 10 and 15 MHz. The s i g n a l s from the two paths are combined r e s i s t i v e l y f o r a p p l i c a t i o n to the subsequent adaptive t r a n s v e r s a l f i l t e r . 4.3.5 T r a n s v e r s a l f i l t e r The seven-tap t r a n s v e r s a l f i l t e r i s shown i n F i g . 4.7. S i x 50 ns delay l i n e s are composed of standard 50 0, c o a x i a l cable. The v a r i a b l e gain device i s the same as s e l e c t e d f o r the a.g.c. a m p l i f i e r . The more conventional four quadrant m u l t i p l i e r s are avoided because of t h e i r low gain. The device used is? o s t e n s i b l y an analog channel s e l e c t o r or a gain c o n t r o l l e d a m p l i f i e r , but has s i m i l a r s t r u c t u r e to a four quadrant m u l t i p l i e r . Although l i n e a r gain c o n t r o l i s s a c r i f i c e d , the devices e x h i b i t high o v e r a l l gain. - 85 -Figure 4.7 Transversal f i l t e r Figure 4,8, Decision device (quantizer).. - 86 " The seven outputs are added r e s i s t i y e l y as are the complementary outputs. A video a m p l i f i e r provides the f i n a l d i f f e r e n t i a l combination and d r i v e s two emitter f o l l o w e r s l e a d i n g to the quantizer and to the zero c r o s s -i n g detector ( F i g . 4.2). 4.3.6 D e c i s i o n device The s i g n a l emanating from the t r a n s v e r s a l f i l t e r passes to the d e c i s i o n device. The s i g n a l i s quantized i n t o four p o s s i b l e l e v e l s by the arrangement shown i n F i g . 4.8. The heart of the c i r c u i t i s a high-speed e m i t t e r - c o u p l e d - l o g i c (ECL) comparator/latch. Complementary inputs are a v a i l a b l e at the d e c i s i o n device a l l o w i n g the a p p l i c a t i o n of d e c i s i o n feed-back at t h i s p o i n t (Chapter V I I ) . For t h i s reason d.c. coupling i s maintained i n t o the comparator/latch. A f t e r passing through an ECL/TTL l e v e l convertor, the output from the lower ( F i g . 4.8) comparator should be a good copy of the recorded data. The output from the upper comparator corresponds to a l e a s t s i g n i f i c a n t b i t from the q u a n t i z a t i o n . Together w i t h the hypothesized data, t h i s output d r i v e s the tap adjustment algorithm. In order to minimise the period of data u n c e r t a i n t y and to maximise the c l o c k i n g window f o r suceed-ing stages, short ( ~ 5 ns) c l o c k pulses enable the ECL l a t c h e s . These pulses are generated by a t r i p l e ECL l i n e r e c e i v e r . 4.3.7 Tap adjustment/gain c o n t r o l An o u t l i n e of the c i r c u i t which embodies the tap adjustment a l g o r i t h m (Appendix 3) i s shown i n F i g . 4.9. For reasons of p r a c t i c a l i t y the q u a n t i z e r output streams are sampled only every t h i r t e e n t h b i t . The functions (on nine p a r a l l e l channels) are then accumulated over 2U samples (4 ms). The 8 - b i t tap r e g i s t e r i s thus e i t h e r incremented or decremented - 87 -FROM e c l / t t l leve l conver tor QUANTIZER I CLOCK D 0 D c Q hal t ad jus tment -13 7ALS193 sgnfen) a ./7/-.LS86 reset 74LS175 -* D -»C Q CD14CK0 74LS74 reset CDUCKO 8 - b i t sh i f t reg ister 747/. 74LS86 A • • f x 9 c h a n n e l s • • • 74LS164 1 sgn(ek) I sgn(ek) ak_4 C 0 CD14CK0 TAP REGISTER down up 8 -b i t counter • • » SET CONTENTS 2x 74LS193 D / A _5 6-8 K MC1408 8-2 K ZX TO I TRANSVERSAL FILTER iCDK04 9 down up 8 - b i t counter SET CONTENTS 2x7AL5193 D / A 6-8 K MCK08 8-2K Figure 4.9 Automatic tap adjustment (see a l s o Appendix 3) - 88 -as the accumulator f a l l short of or exceeds 2 1 U . In t h i s manner the c o r r e l a -t i o n between the e r r o r s i g n b i t and the data- i s g r a d u a l l y reduced. The contents of the tap r e g i s t e r are i n t e r p r e t e d by an 8 - b i t d i g i t a l to analog convertor. The output i s a low l e v e l current source which i s capable of d r i v i n g the gain c o n t r o l l e d devices d i r e c t l y . A diode and small s e r i e s r e s i s t o r ( F i g . 4.7) provide necessary voltage s h i f t . Tap gain may be n u l l e d at the centre of the tap r e g i s t e r range by adjustment of the preset, r e s i s t o r which provides output current o f f s e t . The seven most s i g n i f i c a n t b i t s of the tap r e g i s t e r may be loaded from manually set switches. 4.3.8. Clock recovery The process of c l o c k recovery i n v o l v e s the i d e n t i f i c a t i o n of zero-crossings i n the equalized playback s i g n a l , the l o c a l generation of c l o c k waveform, and the establishment of the c o r r e c t r e l a t i o n s h i p between t h i s l o c a l c l o c k and the observed z e r o - c r o s s i n g s . These three aspects are c a t e -gorized below and may a l s o be i d e n t i f i e d i n F i g . 4.10. a) Zero-crossing detector The z e r o - c r o s s i n g detector and a s s o c i a t e d phase comparator are shown i n F i g . 4.10. A r e l a t i v e l y high l e v e l s i g n a l (1 v o l t peak) i s d e l i v e r e d to a p a i r of ECL comparators i n tandem. The r e s u l t i n g h a r d - l i m i t e d s i g n a l then i s s p l i t i n t o d i r e c t and delayed paths and recombined i n an exclusive-OR. Each t r a n s i t i o n or z e r o - c r o s s i n g thus gives r i s e to an 25 ns pulse which i s a p p l i e d to the phase comparator. b) L o c a l o s c i l l a t o r L o c a l o s c i l l a t o r s t a b i l i t y should be commensurate w i t h timebase s t a b i l i t y of the record/playback system. C r y s t a l o s c i l l a t o r s o f f e r e x c e l l e n t - 89 -o from <-5o transversal filter , 0 0 p x - ± - MC10107 " ± " CLOCK! DISTRIBUTION BUFFER ZERO-CROSSING DETECTOR PHASE ADJUST 10n r -IH C50 MC 10114 'tab VOLTAGE CONTROLLED OSCILLATOR -5 -5 560 OOMPARATOR^juJ[}uLr "39 lOn I—I 5 6 0 "4 > P LOOP FILTER Figure 4.10 Clock recovery s t a b i l i t y but allow l i m i t e d c o n t r o l of frequency. Conventional tuned c i r c u i t s are e a s i l y c o n t r o l l e d w i t h a voltage v a r i a b l e capacitance. How-ever considerable care must be taken to ensure a n a t u r a l s t a b i l i t y b e t t e r than 10 . The o s c i l l a t o r i s based on an MC1648 chip as seen i n F i g . 4.10. The o s c i l l a t o r module i s w e l l i s o l a t e d e l e c t r i c a l l y , c o n t a i n i n g i t s own voltage s t a b i l i z a t i o n , and i s a l s o temperature s t a b i l i z e d . Voltage c o n t r o l i s most conveniently afforded by a v a r i a b l e capacitance diode on a l o o s e l y coupled winding. A frequency swing of ±30 KHz on a 20 MHz centre frequency i s a v a i l a b l e . The l o c a l o s c i l l a t o r s i g n a l i s b u f f e r e d w i t h i n the module and i s passed (as a low l e v e l 50 Q s i g n a l ) to the c l o c k d i s t r i b u t i o n c i r c u i t s . c) Phase-locked loop The voltage c o n t r o l l e d o s c i l l a t o r i s d r i v e n by the output of a phase comparator i n such a manner as to maintain s y c h r o n i z a t i o n between the o s c i l l a t o r and the mean ze r o - c r o s s i n g p o s i t i o n . The phase comparator, F i g . 4.10, i s a double-balanced Schottky mixer fed by ECL l o g i c . The output i s fed d i r e c t l y to the loop f i l t e r / a m p l i f i e r which appears approximately as a 50 0, l o a d . The loop f i l t e r , F i g . 4.10, ensures high H.f. gain which minimises phase e r r o r due to frequency o f f s e t s or slow p e r t u r b a t i o n s i n frequency. A h.f. path must a l s o be provided which enables the loop to f o l l o w more r a p i d phase changes. Both h.f. and Z.f. gains are adjusted manually to minimise e r r o r r a t e or v i s i b l e degradations i n time s t a b i l i t y of the eye p a t t e r n . Both gains are optimised on very broad plateaux where i t i s assumed that c l o c k phase inaccuracy has become subordinate to other system degradations (§4.4). - 91 -The d e c i s i o n device c l o c k phase may be adjusted manually, F i g . 4.10, to the nearest 1 ns over a range of 32 ns. Clock phase adjustment i s implemented by switched lengths of 50 fi delay l i n e . 4.4 DIFFICULTIES ENCOUNTERED Sec t i o n 4.3 d e t a i l s the f i n a l form of the prototype system. E a r l i e r versions of the prototype encountered c e r t a i n d i f f i c u l t i e s which prompted design changes. In p a r t i c u l a r the t o p i c s of c l o c k recovery, e l e c t r i c a l i n t e r -ference, d i s t o r t i o n , and adaptive e q u a l i z a t i o n are discussed below. I n i t i a l t e s t s of the c l o c k recovery c i r c u i t s were made using a s i n g l e - p o l e loop f i l t e r w i t h r e l a t i v e l y low bandwidth ( ~ 10 KHz). Poor performance and frequent c l o c k s l i p p a g e occurred. At lower loop gain exces-s i v e phase d r i f t was evident and at higher gains excessive loop noise and i n s t a b i l i t y became evident. A two-pole f i l t e r was implemented, high gain being provided at £.f. to minimise phase d r i f t . From the observed h.f. components i n the loop noise a f i l t e r based on the small s i g n a l design of [153] was introduced. This f i l t e r was i n f a c t at 60 KHz s i n g l e - p o l e low-pass f i l t e r placed i n p a r a l l e l w i t h the low frequency path. Occasional c l o c k slippage occurred however t h i s tendency reduced as the loop f i l t e r band-width was increased to around 120 KHz. In p r a c t i c e , F i g ^ 4.10, e x p l i c i t loop f i l t e r i n g was omitted; an open loop bandwidth of s e v e r a l hundred KHz being determined by the f o l l o w e r / l e v e l s h i f t e r w i t h i n the voltage c o n t r o l l e d o s c i l l a t o r . Loop gains are determined as i n §4.3.8. Clock s l i p p a g e occurs i n f r e q u e n t l y ( l e s s than once per hour of recording) and i s g e n e r a l l y repeat-able and ass o c i a t e d w i t h a dropout. E l e c t r i c a l i n t e r f e r e n c e arose from various sources but was gr a d u a l l y reduced to acceptable l e v e l s . Most troublesome were impulsive noises generated at l i n e r a t e (60 Hz) and noise from l o g i c c i r c u i t s (the e r r o r detector i n p a r t i c u l a r ) . In general terms the presence of e l e c t r i c a l i n t e r f e r e n c e prompted the use of an extensive ground plane under the working s u r f a c e , balanced c o n f i g u r a t i o n through the p r e a m p l i f i e r to the a.g.c. a m p l i f i e r , and a t t e n t i o n to decoupling and s i g n a l r e t u r n s . Impulsive noise at l i n e r a t e appeared on the d.c. supply l i n e s but was reduced by c a p a c i t i v e f i l t e r i n g . S i m i l a r i n t e r f e r e n c e was picked up by the p r e a m p l i f i e r , which i s p h y s i c a l l y c l o s e to the playback head. The sources of t h i s i n t e r f e r e n c e were found to be t r a n s i e n t s i n the capstan d r i v e c i r c u i t r y and l i n e frequency harmonics picked up from the r e l a y based c o n t r o l c i r c u i t s on the t r a n s p o r t (which are fed d i r e c t l y from the 120 v o l t supply l i n e ) . The use of f i l t e r i n g and a balanced 120 v o l t balanced supply suppressed both these sources. Noise a r i s i n g from l o g i c c i r c u i t s , most troublesome above 10 MHz, was g r e a t l y reduced by a t t e n t i o n to decoupling and to d r i v e l e v e l s to e x t e r n a l counters. However, i n t e r f e r e n c e l e v e l s remained approximately 33 dB below the equalized s i g n a l , the l a r g e s t component being at c l o c k frequency. Two high Q notch f i l t e r s were introduced between the t r a n s v e r s a l f i l t e r and the d e c i s i o n device. These f i l t e r s were aimed at the c l o c k component and at a region around 14 MHz where s i g n i f i c a n t breakthrough occurred from the Schottky l o g i c w i t h i n the e r r o r d e tector. With Q's of approximately 30 the i n t r o d u c t i o n of notch f i l t e r s d i d not n o t i c e a b l y perturb the o v e r a l l e q u a l i z a t i o n and i n t e r f e r e n c e was thus reduced below -40 dB. I n t e r f e r e n c e from other l a b o r a t o r y equipment was e i t h e r suppressed at source or avoided by appropriate scheduling of t e s t s . - 93 -With the i n t r o d u c t i o n of the a.g.c. a m p l i f i e r , i n t e r m o d u l a t i o n d i s t o r t i o n became very apparent. Although a m p l i f i e r s were operating at .'. l e a s t 6 dB below t h e i r quoted dynamic range, i n t e r m o d u l a t i o n d i s t o r t i o n was nevertheless apparent i n the a.g.c. a m p l i f i e r and to a l e s s e r extent i n the t r a n s v e r s a l f i l t e r . S i g n a l l e v e l s were v a r i o u s l y adjusted to overcome the problem. D i f f i c u l t i e s encountered w i t h the adaptive t r a n s v e r s a l f i l t e r have been mentioned i n Appendix 3. I t was found necessary to increase accumulator s i z e (the p e r i o d of estimation) by n e a r l y two orders of magnitude. For p r a c t i c a l reasons i t was a l s o found necessary to reduce the e s t i m a t i o n sampling r a t e by a f a c t o r of t h i r t e e n . The p o s s i b i l i t y of t e s t i n g a r a p i d l y adaptive playback r e c e i v e r was th e r e f o r e removed. A c q u i s i t i o n by the adaptive t r a n s -v e r s a l f i l t e r o c c a s i o n a l l y took s e v e r a l seconds, p a r t i c u l a r l y at high record l e v e l s . Although an extended a c q u i s i t i o n p e r i o d must be avoided on a p r a c t i c a l record/playback systems, the fe a t u r e d i d not inconvenience the measurements presented i n the f o l l o w i n g chapter. - 94 -V PERFORMANCE MEASUREMENTS The measurements d e t a i l e d i n t h i s chapter p e r t a i n to the prototype system o u t l i n e d i n Chapter IV. Although i t i s u s e f u l to be able to i n d i c a t e maximum data r a t e or packing d e n s i t y f o r given performance, data r a t e r e -presents one of the l e a s t f l e x i b l e system parameters, p a r t i c u l a r l y w i t h regard to e q u a l i z a t i o n . Throughout t h i s and succeeding chapters the data t r a n s f e r r a t e i s maintained at 20 Mbit/s (1.1 Mbit/m). The o b j e c t i v e i s thus to optimise system performance as a f u n c t i o n of the remaining parameters such as record l e v e l , and to determine and e x p l a i n the e f f e c t s of v a r y i n g these parameters. Although a number of analog measures are of i n t e r e s t , the most f a m i l i a r measure of performance i s the b i t e r r o r r a t e . Both analog and d i g i t a l performance measures are dependent upon the t e s t data or t e s t se-quences used. D e t a i l s of the performance measurements are thus preceded;-by a d i s c u s s i o n of t e s t sequence s e l e c t i o n and of generation/detection. 5.1 TEST PATTERNS Performance may be defined f o r c e r t a i n worst-case sequences or averaged over the supposed ensemble of p o s s i b l e data sequences. While the former leads to admirable design c r i t e r i a , i t can condemn systems s u s c e p t i b l e to infrequent worst-case sequences but which otherwise e x h i b i t high c a p a c i t y . The Shannon ca p a c i t y of a d i g i t a l channel w i t h s o - c a l l e d 'pattern-dependent' e r r o r s i s , i n f a c t , greater than that of a channel w i t h random e r r o r s . Never-t h e l e s s , pattern-dependent e r r o r s are abhorred [205]: r e a l data i s r i c h i n non-random sequences, some of which may represent worst case sequences; the - 95 -e f f e c t i v e n e s s of r e - w r i t e and re-read e r r o r - c o r r e c t i o n s t a t e g i e s i s reduced by severe p a t t e r n dependency; and the presence of p a t t e r n dependency i s o f t e n an i n d i c a t o r of poor e q u a l i z a t i o n or system design. Randomization [46] of the incoming data provides a simple and e f f e c t i v e counter to the above c r i t i c i s m s . The s u s c e p t i b i l i t y of systems to s p e c i f i c sequences i s adequately r e f l e c t e d i n the average e r r o r r a t e . The t e s t sequence i s thus chosen to mimic random binary data. The b i t s should thus appear equiprobable and independent' i n some sense. The sequence should be e a s i l y generated and e r r o r s e a s i l y detected. 5.1.1 Pseudo-random sequences Pseudo-random sequences may be generated i n a s h i f t r e g i s t e r where a l o g i c a l f u n c t i o n of the r e g i s t e r contents i s fed back to the input. Most f a m i l i a r are maximal-length sequences which a r i s e i n b i n a r y r e g i s t e r s w i t h exclusive-OR feedback connections [227], With an m-bit r e g i s t e r the sequence has a length of 2 m - l b i t s and thus inc l u d e s a l l but one m-bit sub-sequences. Such sequences a l s o e x h i b i t a constant d i s c r e t e s p e c t r a l energy d i s t r i b u t i o n except f o r the d.c. component. Maximal-length, pseudo-random sequences provide almost i d e a l t e s t sequences. The non-random nature of such sequences can, however, become apparent upon systems whose memory exceeds the r e g i s t e r l e n g t h , m. In the t o p i c a l s i t u a t i o n of a channel w i t h a narrow d.c. n u l l , the intersymbol i n t e r f e r e n c e (ISI) f o r random data comprises many sm a l l independent terms and has a c l o s e l y Gaussian amplitude d i s t r i b u t i o n . For a pseudo-random t e s t sequence the d i s t r i b u t i o n may be se v e r e l y skewed and non-Gaussian. This f a c t may be explained h e u r i s t i c a l l y by the tendency of zeros to propagate - 96 -through the exclusive-OR feedback f u n c t i o n . However, the e f f e c t i s w e l l recognized [234,235] and manifest as a f a l s e s y n c h r o n i z a t i o n problem i n spread-spectrum communications [236]• C e r t a i n feedback connections give r i s e to c l o s e l y Gaussian low frequency components [235]. Generators w i t h two feedback taps are to be p a r t i c u l a r l y avoided [234] on t e s t s i n v o l v i n g the d.c. n u l l . With due regard f o r o c c a s i o n a l m a n i f e s t a t i o n s of non-randomness, pseudo-random sequences provide e x c e l l e n t t e s t sequences. They are e a s i l y generated and crude e r r o r d e t e c t i o n may be performed simply by applying the generator polynomial i n the form of a p a r i t y check. Also t h e i r a p p l i c a t i o n i n n o n l i n e a r channel c h a r a c t e r i z a t i o n has been proposed by Wood and Donaldson [io7], v: " /.; 5.1.2 Sequence generation and e r r o r d e t e c t i o n Since sequence generation and e r r o r d e t e c t i o n f a c i l i t i e s are not requ i r e d simultaneously, the c i r c u i t i n d i c a t e d i n F i g . 5.1 can economically incorporate both f a c i l i t i e s . A high-speed, p a r i t y - c h e c k device computes . the feedback f u n c t i o n . When b i s t a b l e Ql i s high t h i s f u n c t i o n i s a p p l i e d to the s h i f t - r e g i s t e r input and a pseudo-random sequence thus generated. Schottky TTL l o g i c i s used throughout to minimize loop delay, however the c i r c u i t does not f u n c t i o n r e l i a b l y above 22 MHz. D i f f e r e n t i a l precoding i s not used and the sequence d r i v e s the record a m p l i f i e r d i r e c t l y v i a balanced Schottky TTL output. Asynchronous e r r o r d e t e c t i o n may be performed by feeding the recovered t e s t sequence back through the s h i f t r e g i s t e r and checking that - 97 -PLAYBACK,— C DATA (D " I D Q RESET R C Q F7474 74S00 (1), 74S86 74500 •AO 74162 74163 2 x 74163 3 * 74S164 24 - bit SHIFT REGISTER TAP SELECT ^ t 74S280 7400 m-1 SYNCH. PULSE reset D Q 7A574 C Q PSEUDO-> feedback RANDOM > SEQUENCE ERRORS » (low) Figure 5.1 Sequence generator / e r r o r detector FROM ERROR — * 74164 74 74 DETECTOR TOTAL 560 ERRORS I—*w\ , > 56< <*2) 560 A A / v ;56 ISOLATED ERRORS xlock 74LS193 Figure 5.2 I d e n t i f i c a t i o n of i s o l a t e d and bur s t e r r o r s - 98 -the feedback f u n c t i o n so generated matches the incoming b i t . Asynchronous d e t e c t i o n i s , however, i n s e n s i t i v e to c l o c k s l i p p a g e and overcounts by a l a r g e f a c t o r which f o r h i g h e r r o r r a t e s or f o r bursty e r r o r s i s not e a s i l y determined. Synchronous e r r o r d e t e c t i o n , which r e f e r s to a b i t - b y - b i t comparison of the recovered sequence against the c o r r e c t l y synchronized t e s t sequence, i s ther e f o r e p r e f e r r e d and achieved as f o l l o w s . At the commence-ment of each head scan, the tape crossover e d i t o r r e l e ases the r e s e t on Q l . The c i r c u i t continues to detect e r r o r s asynchronously u n t i l a s e r i e s of 40 s u c c e s s f u l p a r i t y checks occur; at which time Ql i s set and the c i r c u i t r e -arranges to form a sequence generator. The recovered sequence may now be compared b i t - b y - b i t against the l o c a l l y generated sequence. As an a i d to observation of e i t h e r recorded or recovered s i g n a l s a synchronizing pulse i s a v a i l a b l e from the c i r c u i t . The pulse i s generated upon the occurrence of m-1 consecutive z e r o s , a s i t u a t i o n o c c u r r i n g only once f o r each r e p e t i t i o n of a ( 2 m - l ) - b i t sequence. 5.1.3 Burst e r r o r s I t i s observed i n Chapter I I I that the magnetic recording channel s u f f e r s from fades or dropouts. E r r o r s t h e r e f o r e occur i n d i s t i n c t i v e b u r s t s , an important c o n s i d e r a t i o n i n design f o r e r r o r c o n t r o l . The behaviour of d i g i t a l channels may be u s e f u l l y described by P(m,n) s t a t i s t i c s (§6.2.2). The s t a t i s t i c s , however, r e q u i r e considerable e f f o r t to assemble. For the purposes of t h i s chapter and Chapter V I I a simpler but e f f e c t i v e measure of channel burstyness i s re q u i r e d as provided by the c i r c u i t of F i g . 5.2. I s o l a t e d e r r o r s are thus defined as being separated by at l e a s t e i g h t b i t s from any other e r r o r . A l l other e r r o r s are considered to have occurred i n - 99 -b u r s t s . This method provides a s e n s i t i v e measure of burstyness, avoiding the a r b i t r a r y i n t e r p o s i t i o n of bl o c k boundaries i m p l i e d by P(m,n) s t a t i s t i c s . . Consider the operation of the c i r c u i t as the underlying p r o b a b i l i t y of e r r o r changes. I f random data i s being r e c e i v e d during an e r r o r burst more than 99.99% of the e r r o r s w i l l be c l a s s i f i e d as bursty. On the other hand, at an e r r o r r a t e of 10 5 , 99.99% w i l l be c l a s s i f i e d as i s o l a t e d . 5.2 ANALOG MEASUREMENTS 5.2.1 Frequency domain I t i s i n s t r u c t i v e to observe playback s i g n a l processing i n the frequency domain. The continuous spectrum of random data was simulated by recording a pseudo-random sequence of length 2 2 t f - l . Power s p e c t r a l d e n s i t i e s were observed through a 30 KHz bandwidth and recorded on an X-Y p l o t t e r over a p e r i o d of 100s. In order to c l a r i f y the responses, the head shunt r e a c t -ances (§4.3.2) were removed causing the n a t u r a l frequency of head reasonance to r i s e w e l l above the Nyquist bandedge. Figure 5.3 shows smoothed t r a c i n g s of s p e c t r a l d e n s i t i e s measured at the a.g.c. a m p l i f i e r output. The v a r i a t i o n s i n s p e c t r a l d i s t r i b u t i o n w i t h record l e v e l are c l e a r l y i l l u s t r a t e d . Figures 5.3a and b p e r t a i n to tapes #3 and #4 r e s p e c t i v e l y (Appendix 2 ) , p r e a m p l i f i e r noise i s i n d i c a t e d as a common reference l e v e l . The magnetic c h a r a c t e r i s t i c s of tape #3 are nominally i d e n t i c a l to those of tape #1 c h a r a c t e r i z e d i n Chapter I I I . Tape #4 has higher c o e r c i v i t y which should l e a d to improved high frequency (h.f.) performance. In f a c t F i g . 5.3 i n d i c a t e s the c o n t r a r y , w i t h tape #3 ac h i e v i n g higher responses at a l l frequencies of i n t e r e s t . I t i s p o s s i b l e that the - 100 -^SPECTRAL DENSITY NOISE 0 5 FREQUENCY 10 (MHz) Figure 5.3a fSPECTRAL DENSITY NOISE 0 5 FREQUENCY 10 (MHz) Figure 5.3b Playback signal spectra vs. record level - 10.1 -higher record l e v e l n e c e s s i t a t e d by tape #4 aggravates p o l e - t i p s a t u r a t i o n s u f f i c i e n t l y to reduce h.f. response. The poor SL.f. response of tape #4 can be r e l a t e d to lower r e t e n t i v i t y . Despite lower s i g n a l - t o - n o i s e r a t i o . (SNR), tape #4 has l e s s s p e c t r a l r o l l - o f f (reduced d i s p e r s i o n ) f a c i l i t a t i n g subse-quent e q u a l i z a t i o n . This e q u a l i z a t i o n process i s i l l u s t r a t e d below f o r tape #3. Figure 5.4 i n d i c a t e s the a c t i o n of the p r e - f i l t e r at a record l e v e l , i m=0.53 Amps. The playback s i g n a l i s s p l i t between an i n t e g r a t o r and a d e l a y / d i f f e r e n c e c i r c u i t . The s p e c t r a r e s u l t i n g from these operations are shown as w e l l as the spectrum of t h e i r sum which emerges from the pre-f i l t e r . The p r e - f i l t e r i s seen to extend...the i.f. response and reduce h.f. r o l l - o f f (at 10 MHz). The c o r r e c t i o n of phase by a constant TT/2, perhaps the most important f u n c t i o n , i s not i l l u s t r a t e d . F igure 5.5 shows the e f f e c t of the t r a n s v e r s a l f i l t e r . Considerable h.f. boost i s evident and the r e s u l t i n g response i s c l o s e to being f l a t over the f o l d e d Nyquist spectrum (phase response i s discussed below). A r i p p l e of perhaps 3 dB remains and the d.c. n u l l i s s t i l l evident. The e q u a l i z e d s i g n a l spectrum i s shown against a l i n e a r s c a l e i n F i g s . 5.6 and 5.7. Figure 5.6 shows the degrees of e q u a l i z a t i o n achieved by f i l t e r s of length 1, 3, 5 and 7 taps. F i g . 5.7 shows how the seven-tap f i l t e r adapts to changes i n record l e v e l . Increases i n e q u a l i z a t i o n e r r o r and a d d i t i v e n o i s e l e v e l are apparent as the record l e v e l r i s e s . Although the e q u a l i z e r components appear to perform i n a s a t i s f a c t o r y manner, the e q u a l i z a t i o n e r r o r i s higher than a n t i c i p a t e d . With 2^=0.53 Amps and a seven-tap f i l t e r the e r r o r i s at l e a s t 0.12 r.m.s. r a t h e r than 0.03 - 102 -SPECTRAL DENSITIES Figure 5.4 Signal spectra illustrating the action of the pre-filter o1 — 0 FREQUENCY 5 (MHz) Figure 5.5 Spectra I l l u s t r a t i n g the a c t i o n of the t r a n s v e r s a l  f i l t e r . 1^=0.53 A, tape #3 5 FREQUENCY 1 0 (MHz) Figure 5.6 Spectrum of equalized playback s i g n a l vs. number of t r a n s v e r s a l f i l t e r taps. i w=0.53 A, tape #3 - 104 -RECORD LEVEL i m = 0-35 A l-O+i 0-5+ i m =0-53 A 0 FREQUENCY N O I S E i m = 071 A (MHz ) Figure 5.v7>' Equalized signal and noise spectra vs. record level, tape #3 - 105 -suggested i n Appendix 3. To c l a r i f y the discrepancy attempts were made to assess the channel's phase response. Two methods were t r i e d , both of which required the prototype system to maintain s y n c h r o n i z a t i o n of the c l o c k and pseudo-random t e s t sequence. Method A The s i g n a l and the weighted t e s t sequence ( a v a i l a b l e at the e r r o r detector) are summed and the req u i r e d harmonic picked o f f by the spectrum analyser. The amplitude of t h i s harmonic was then minimised over the t e s t sequence weighting and delay (tapped fromjthe s h i f t r e g i s t e r i n the e r r o r d e t e c t o r ) . The phase of the harmonic was estimated from the three l e a s t harmonic amplitudes found and from t h e i r a s s o c i a t e d delays. Method B A sampling o s c i l l o s c o p e provided a p l o t of the s i g n a l i n the time domain (§5.2.2). The phase response was computed i n the in v e r s e F o u r i e r transform of the c r o s s - c o r r e l a t i o n between the t e s t sequence and the s i g n a l . While method B i s accurate f o r those s p e c t r a l components w i t h l a r g e amplitude, method A i s more d i r e c t and more accurate f o r smaller components. Channel gain i n s t a b i l i t y , i n p a r t i c u l a r , f r u s t r a t e s accurate measurement, and n o n l i n e a r i t y ensures that the measured d i s c r e t e s p e c t r a do not f o l l o w a smooth phase response. Figure 5.8 d i s p l a y s phase measurements w i t h 15 and 31-bit sequences. Before e q u a l i z a t i o n , a t the output of the a.g.c. a m p l i f i e r , the c h a r a c t e r i s t i c h.f. phase advance [97] i s c l e a r l y seen. This phase response i s v e r i f i e d by the complementary response (dashed l i n e ) c a l c u l a t e d from the t r a n s v e r s a l f i l t e r tap gains. As a n t i c i p a t e d , the phase response i s r e l a t i v e l y w e l l behaved and s u c c e s s f u l l y e q u a l i z e d . Non-zero channel phase response probably c o n t r i b u t e s only a small part to the high e q u a l i z a t i o n error,noted above. The r e s i d u a l - 106 -x 31 - bit s e q u e n c e 4- 15-bit s e q u e n c e O 15-bit s e q u e n c e r e v e r s e d A 31 - bit s e q u e n c e f- method (a.) method (b) P p h a s e r e s p o n s e of t r a n s v e r s a l f i l ter I + X + x X*" A A X A ^ X A x + n O O A „ A A->5A 0 ° ^ x ^ A P A before A+" O A A -f- 4- O " A x " • „ g X ^ O A A + ^ C f A A A X o a f t e r "* . o A x A 0 5 f requency 1 0 ( M H z ) . 5 . 8 Phase response before and after equalizationt i m =0-53; -.107 -d.c. n u l l has a s i g n i f i c a n t e f f e c t on the o v e r a l l e q u a l i z a t i o n . The excessive l e v e l of the equalized s i g n a l at 1 MHz r e s u l t s from the t r a n s v e r s a l f i l t e r ' s attempt to compensate the n u l l . The a p p l i c a t i o n of d e c i s i o n feedback to remove the n u l l (§7.3.1) reduces the e q u a l i z a t i o n e r r o r over the remainder of the spectrum by about 30%. The remaining discrepency i s a t t r i b u t e d to the s u b s t a n t i a l d i f f e r -ence between the i d e a l spectrum assumed i n Appendix 3 and the a c t u a l amplitude spectrum emanating from;the p r e - f l i t e r . V a r i a t i o n s of hand/preamplifier coupling as i n d i c a t e d i n §5.3.2 were w e l l compensated by the adaptive f i l t e r i n g . The v a r i a t i o n s l e d to only s l i g h t changes i n s p e c t r a l emphasis around the Nyquist bandedge. Results w i t h tape #4 were e s s e n t i a l l y i d e n t i c a l to those w i t h tapes #1, #2 and #3 when expressed i n terms of s p e c t r a l r o l l - o f f r a t h e r than record l e v e l . 5.2.2 Time domain Time domain responses were obtained by means of a sampling o s c i l l o -scope and X-Y p l o t t e r . Th'e^  e q u a l i z a t i o n process i s depicted i n F i g . 5.9 f o r a 31-bit pseudo-random t e s t sequence. Although the d e c i s i o n device sampling i n s t a n t s are i n d i c a t e d , i t i s d i f f i c u l t to estimate the accuracy of e q u a l i z a -t i o n . Figure 5.10 shows 'eye diagrams' (formed by superimposing the equalized s i g n a l waveforms at the sampling i n s t a n t s ) and i n d i c a t e s the amplitude and ... .. timing margins more c l e a r l y . The use of a f i n i t e 3 1-bit sequence avoids d i f f i c u l t i e s w i t h the d..c. n u l l . In f a c t such a n u l l causes eye c l o s u r e on random data. Measures of performance from F i g . 5.10 th e r e f o r e p e r t a i n to d.c. -free codes or to s i t u a t i o n s where the n u l l i s otherwise c o r r e c t e d . - 108 -Figure 5.9 Responses to a 31-blt pseudo-random sequence illustrating action of prefilter and  transversal f i l t e r ; decision sampling instants indicated. i^O.53 A, tape #3 RECORD LEVEL 0-35 A EYE CLOSURE 22% r.m.s. ERROR 11% RECORD LEVEL 0-53 A EYE CLOSURE 30% r.m.s. ERROR 17% RECORD LEVEL 071 A EYE CLOSURE 49 % r.m.s. ERROR 27% F i g . 5.10 S i g n a l e q u a l i z a t i o n vs. record l e v e l - eye diagrams. tape #3 - 110 -From time domain measurements w i t h the sampling o s c i l l o s c o p e , c r o s s - c o r r e l a t i o n f u n c t i o n s may be computed. Figure 5.11, f o r example, i l l u s t r a t e s the a c t i o n of the ' z e r o - f o r c i n g algorithm' i n reducing I S I from the three c l o s e s t b i t s on e i t h e r s i d e . 5.2.3 S i g n a l - t o - n o i s e r a t i o s The s p e c t r a l d i s t r i b u t i o n s of s i g n a l and noise are i n d i c a t e d i n F i g . 5.7. The bulk of t h i s a d d i t i v e noise a r i s e s from the playback preampli- , f i e r . O v e r a l l SNR on the equalized s i g n a l measured immediately at the input to the f i n a l comparator i s shown i n F i g . 5.12. The v a r i a t i o n s of SNR w i t h record l e v e l are very s i m i l a r bearing i n mind that tape //4 has a c o e r c i v i t y 30% higher than tape #3, and r e q u i r e s correspondingly increased record l e v e l . 5.3 ERROR RATES E r r o r r a t e provides the fundamental performance measure f o r d i g i t a l systems. I s o l a t e d and b u r s t e r r o r s (§5.1.3) are d i s t i n g u i s h e d thus p r o v i d i n g f u r t h e r i n f o r m a t i o n u s e f u l i n e r r o r c o n t r o l . E r r o r s are measured f o r a 31-b i t pseudo-random sequence and head/preamplifier c o u p l i n g , Cs^=5pF, R s ^ = 3.9kft. 5.3.1 E r r o r r a t e vs. record l e v e l and number of e q u a l i z e r taps Figure 5.13 shows e r r o r r a t e s as a f u n c t i o n of the record l e v e l and the number of e q u a l i z e r taps. Each po i n t represents the geometric mean er r o r r a t e over three separate reproductions of each of two 15 minute seg-ments recorded on tape #3 and 'one segment recorded on tape #2. I s o l a t e d e r r o r s are seen to be s e n s i t i v e to both record l e v e l and number of taps. - I l l -.CROSS-CORRELATION ti.o. Figure 5.11 C r o s s - c o r r e l a t i o n of equalized playback s i g n a l against 31- b i t pseudo-random input sequence. i =0.53 A, tape #3 SNR 30+ (dB) 25{ > i i i v i i 204 \ \tape # 4 \ \ tape #3\ v \ | ; , , H > 0-3 06 0-9 RECORD LEVEL (Amps) Figure 5.12 Measured s i g n a l - t o - n o i s e r a t i o s a f t e r e q u a l i z a t i o n - .1.12 -RECORD LEVEL (Amp.-turns) RECORD LEVEL (Amp.- turns) Figure 5.13 Error rate vs. record level and number of equalizer taps  tapes #2,#3 - 113 -The presence of the t r a n s v e r s a l f i l t e r w i t h s e v e r a l taps reduces the i s o l a t e d e r r o r r a t e and a l s o the s e n s i t i v i t y to record l e v e l . The b u r s t e r r o r r a t e , although aggravated by poor e q u a l i z a t i o n , i s g e n e r a l l y i n s e n s i t i v e to the number of t r a n s v e r s a l f i l t e r taps and decreases w i t h i n c r e a s i n g record l e v e l . The o v e r a l l e r r o r r a t e reaches a broad minimum w i t h 4 to 7 taps and i m=0.3 to 0.5A. The measured e r r o r r a t e s f o r tape #2/#3 are s i g n i f i c a n t l y lower than f o r #1 which was used i n the i n i t i a l c h a r a c t e r i z a t i o n i n Chapter I I I . Figure 5.14 shows the same r e s u l t s f o r the higher c o e r c i v i t y tape, #4. S i m i l a r observations may be made although the e r r o r r a t e s are s i g n i f i c a n t l y higher than those encountered on tape //2/#3. 5.3.2 E r r o r r a t e vs. head/preamplifier coupling The playback head may be considered as a s i g n a l source w i t h an i n d u c t i v e impedence. Design f o r maximum s i g n a l - t o - p r e a m p l i f i e r noise r a t i o o f t e n leads to a d i s t i n c t i v e resonance forming between the head inductance and the p r e a m p l i f i e r input capacitance. Such a resonance can not only im-prove s i g n a l t r a n s f e r around the upper bandedge but o f t e n a i d s the e q u a l i z a -t i o n process. The o v e r a l l head/preamplifier responses were measured by p l a c i n g a w i r e causing a known current i n the p r o x i m i t y of the playback head. The responses, p a r t i c u l a r l y f o r l a r g e r shunt admittances, are c l o s e l y approximated by a simple resonance and the corresponding values of n a t u r a l frequency, fQ , and Q are shown i n F i g . 5.15. The range of shunt capacitance and r e s i s t a n c e chosen f o r these t e s t s cover s i t u a t i o n s ranging from a high-Q resonance around the Nyquist bandedge to a low-Q resonance w e l l above the bandedge. - 114 -1-6 x 10" RECORD LEVEL (Amp.-turns) ,1-13 x 10" RECORD LEVEL (Amp.-turns) Figure 5.14 E r r o r r a t e vs. record l e v e l and number of e q u a l i z e r taps.  tape #4 - 115 -15 10 0 o x" / \ 0 0 O R s h = 3-9 KA A j (_l-5 KA SHUNT RESISTANCE 9 FREQUENCY f 0 ( M H z ) Q o A o X O A Q o 0-0 2-2 50 8-3 150 SHUNT CAPACITANCE, C s h (pF) Figure 5.15 Head c o u p l i n g : v a r i a t i o n of n a t u r a l frequency, f 0 ,  and Q w i t h shunt r e s i s t a n c e , R s h , and capacitance ,C s h . -1..116 -Figure 5.16 shows i s o l a t e d and b u r s t e r r o r r a t e s on tape #4 at a record l e v e l of 0.44 A. Each p o i n t represents the geometric mean of three reproductions of each of two 15 minute recorded segments. E q u a l i z a t i o n i n -cluded the seven-tap t r a n s v e r s a l f i l t e r a d a p t i v e l y adjusted by the zero f o r c i n g algorithm. Both i s o l a t e d and b u r s t e r r o r s are r e l a t i v e l y i n s e n s i t i v e to head/preamplifier c o u p l i n g . A high-Q c l o s e to the Nyquist bandedge makes the subsequent e q u a l i z a t i o n more d i f f i c u l t ; t h i s f a c t i s r e f l e c t e d i n the increased i s o l a t e d e r r o r r a t e at R = °° , C = 15r.F. sh sh R 5.3.3 The n e c e s s i t y f o r p r e f i l t e r i n g I t might be convenient i n some s i t u a t i o n s f o r the p r e f i l t e r i n g o peration to be avoided and e q u a l i z a t i o n to be provided by the adaptive t r a n s v e r s a l f i l t e r alone. The recording channel e x h i b i t s a n a t u r a l bandpass c h a r a c t e r i s t i c and a f r a c t i o n a l - t a p t r a n s v e r s a l f i l t e r [142] can be used to enforce s u i t a b l e r o l l - o f f across the Nyquist bandedge. While s u p e r f i c i a l l y a t t r a c t i v e such an approach s u f f e r s s e v e r a l disadvantages. The nature of . the low frequency channel response n e c e s s i t a t e s a very long t r a n s v e r s a l f i l t e r f o r adequate e q u a l i z a t i o n . The use of f r a c t i o n a l taps leads to more complex adjustment algorithms. F i n a l l y the d e c i s i o n - d i r e c t e d adjustment algorithm does not acquire e a s i l y on very poorly e q u a l i z e d (closed-eye) channels. The t e s t s of §5.3.1 and F i g . 5.13 were repeated w i t h the p r e f i l t e r absent and w i t h record l e v e l s im=0.24, 0.35, 0.47 A. A c q u i s i t i o n was not a t t a i n e d f o r fewer than three taps or f o r im=0.47 A and 6 taps. Figure 5.17 shows the r a t e of i s o l a t e d e r r o r s obtained under these c o n d i t i o n s and r e f l e c t s the d i f f i c u l t y of p r o v i d i n g adequate e q u a l i z a t i o n and c o n s i s t e n t a c q u i s i t i o n - 117 -I S O L A T E D E R R O R P R O B A B I L I T Y 0-0 2-2 5-0 csh 8-3 t-15-0 (pF) 10 "t * B U R S T E R R O R P R O B A B I L I T Y Csh 8-3 ( p F ) 15-0 Figure 5.16 Error rates vs. head/preamplifier coupling. iw=0.44 A tape #4 - 118 -I ! 1 V > 0-2 A 0 - 3 5 0 - 4 3 RECORD LEVEL (Amps) Figure 5.1? I s o l a t e d e r r o r r a t e vs. record l e v e l  and number of e q u a l i z e r taps. P r e - f i l t e r absent, tape #3. ERROR —t = , . . 1 - > 0 - 3 5 0 - 5 3 0 7 1 0 - 8 8 1-06 RECORD LEVEL (Amp.-turns) Figure 5.18 Er r o r rates vs. record l e v e l f o r adaptive and non-adaptive e q u a l i z e r s . tape #4. w i t h a s h o r t t r a n s v e r s a l f i l t e r a l o n e . The b u r s t e r r o r r a t e was more c o n -- 7 s i s t e n t a t around 10 5.3.4 The advantages o f a d a p t i v e e q u a l i z a t i o n Even the r e l a t i v e l y s l o w l y a d a p t i v e e q u a l i z a t i o n o f the p r o t o t y p e system demonstrates the u s e f u l n e s s o f a d a p t i v e t e c h n i q u e s , p a r t i c u l a r l y i n the a r e a o f c o m p a t a b i l i t y . F i g u r e 5.18 r e l a t e s t o a 10 minute segment o f 3 1 - b i t pseudo-random p a t t e r n r e c o r d e d on tape #4. The g e o m e t r i c mean e r r o r r a t e s from t h r e e r e p r o d u c t i o n s . a r e i n d i c a t e d a t f i v e r e c o r d l e v e l s . Both i s o l a t e d and b u r s t e r r o r r a t e s remain r e a s o n a b l y low when the t r a n s v e r s a l f i l t e r i s f u l l y a d a p t i v e . I f , however, the e q u a l i z e r i s a l l o w e d t o adapt a t a r e c o r d l e v e l , i =0.71 A, and then f i x e d , the e r r o r r a t e s become e x c e s s i v e a t h i g h and low r e c o r d l e v e l s . T o l e r a n c e t o v a r i a t i o n o f r e c o r d l e v e l s u g g e s t s s i m i l a r t o l e r a n c e to v a r i a t i o n o f mean head-tape s e p a r a t i o n . F i g u r e 5.19 may be compared d i r e c t l y w i t h F i g . 5.16 and i l l u s t r a t e s the e f f e c t s o f f i x i n g the t r a n s v e r s a l f i l t e r f o r a g i v e n h e a d / p r e a m p l i f i e r c o u p l i n g (C g^= -*pF' R s h = ^'^ • A g a i n t h e t o l e r a n c e t o v a r i a t i o n s i n head/ p r e a m p l i f i e r c o u p l i n g i s improved by the use o f a d a p t i v e e q u a l i z a t i o n . 5.4 CONCLUSIONS The p r e l i m i n a r y d i s c u s s i o n o f t e s t sequences s u g g e s t e d t h a t the use o f pseudo-random sequences i s b o t h a p p r o p r i a t e and c o n v e n i e n t . A 31-b i t sequence was s e l e c t e d t o a v o i d the problem o f e q u a l i z a t i o n c l o s e to the d.c. n u l l . The r e s u l t s o f t h i s and the f o l l o w i n g c h a p t e r p e r t a i n to s i t u a t i o n s i n which the code has m i n i m a l d.c. c o n t e n t , and p o s s i b l y t o s i t u a t i o n s where the d.c. n u l l i s a v o i d e d by the use o f d e c i s i o n feedback (Chapter V I I ) . - 1 20 -" I S O L A T E D E R R O R P R O B A B I L I T Y 5X10~3 Figure 5.19 .Error rates vs. head/preamplifier c o u p l i n g . Non-adaptive  t r a n s v e r s a l f i l t e r . iw=0'. 44 A, tape #4. - 121 -S p e c t r a l , measurements i l l u s t r a t e the nature of the s i g n a l emanat-ing from the playback head and of i t s v a r i a t i o n w i t h record l e v e l . The subsequent e q u a l i z a t i o n through the prototype system proceeded as a n t i c i p a t e d and i s i l l u s t r a t e d by analog measurements i n both the frequency and time domains. Measurements of SNR vs. record l e v e l f o r the e qualized channel r e v e a l a d i s t i n c t maximum which may be l o o s l y a s s o c i a t e d w i t h the minimum i n the i s o l a t e d e r r o r r a t e . I s o l a t e d e r r o r r a t e s as defined i n t h i s chapter are at best about one order of magnitude below the b u r s t e r r o r r a t e s . The r a t e of i s o l a t e d e r r o r s r e f l e c t s the accuracy of e q u a l i z a t i o n and i s t h e r e -fore s e n s i t i v e to the number of t r a n s v e r s a l f i l t e r taps and to the head/ p r e a m p l i f i e r c o u p l i n g . Burst e r r o r s , although aggravated by poor e q u a l i z a -t i o n , g e n e r a l l y decrease monotonically w i t h i n c r e a s i n g record l e v e l . The t r a n s v e r s a l f i l t e r gives r i s e to small (a f a c t o r of two) improvements i n o v e r a l l e r r o r r a t e which can be a t t r i b u t e d to the increased record l e v e l s made p o s s i b l e by the improved e q u a l i z a t i o n . Greater improvements might be a n t i c i p a t e d on narrow t r a c k s where poor SNR emphasises random or i s o l a t e d e r r o r s . The n e c e s s i t y i s demonstrated f o r preceding the t r a n s v e r s a l f i l t e r by some f i x e d p r e f i l t e r making i n i t i a l c o r r e c t i o n s to the system response. S i g n i f i c a n t advantages can be a t t r i b u t e d to the use of adaptive e q u a l i z a t i o n . D i f f e r e n c e s between recording machines i n terms of head p r o f i l e , head/preamplifier c o u p l i n g , e t c . create a c o m p a t a b i l i t y problem. Adaptive e q u a l i z a t i o n g r e a t l y reduces s e n s i t i v i t y to such parameter v a r i a -t i o n s , even to the extent of accommodating d i f f e r e n t recording media. In general, tape #1 e x h i b i t e d the highest e r r o r r a t e s (vLO - 6) and _7 tapes #2 and #3 the lowest (vLO ). Tape #4 d i f f e r s i n i t s magnetic c h a r a c t e r i s t i c s (Appendix 3) and r e q u i r e s l e s s e q u a l i z a t i o n . I t s o v e r a l l e r r o r r a t e however exceeded those of tapes #2 and #3. - 122 -VI ERROR CONTROL The magnetic re c o r d i n g channel i s c h a r a c t e r i z e d by extended periods of degraded performance which can defeat some techniques f o r e r r o r c o n t r o l . Design f o r e r r o r c o n t r o l must i n c l u d e i n f o r m a t i o n not only on raw e r r o r r a t e s but a l s o on the manner of occurrence,of e r r o r s . The d i s t r i b u t i o n of s i g n a l .'. l e v e l at the detector i s i n v e s t i g a t e d and a fade d i s t r i b u t i o n d e r i v e d . The higher order d i s t r i b u t i o n s of e r r o r s and erasures are measured. From such s t a t i s t i c s i t i s p o s s i b l e to assess the e f f i c a c y of e r r o r c o n t r o l techniques, i n p a r t i c u l a r , erasure decoding and i n t e r l e a v i n g . 6.1 SIGNAL AMPLITUDE DISTRIBUTIONS 6.1.1 Cumulative d i s t r i b u t i o n of equalized playback s i g n a l Three 15-minute rec o r d i n g s , at i m=0.35A, of a 31-bit pseudo-random sequence were made on each of tapes #1, #2 and #3. On playback, w i t h head coupling Csh=5 pF and Rs^=3.9 k f i , and with the seven-tap z e r o - f o r c i n g t r a n s -v e r s a l f i l t e r , the c i r c u i t of F i g . 6.1 counted the number of times the equal-i z e d playback s i g n a l f e l l short of the threshold v o l t a g e , V s, at the sampling i n s t a n t s . Figure 6.2 shows f o r each tape the r e s u l t i n g cumulative d i s t r i b u t i o n s derived by ta k i n g the geometric mean of the r e s u l t s from the three recordings. Zero count was replaced by ^  g i v i n g the i n d i c a t e d lower l i m i t of measurement. The r e s u l t i n g d i s t r i b u t i o n s are c l e a r l y non-Gaussian. The ass o c i a t e d density functions are anomalously high around V g=0, which suggests a f i n i t e p r o b a b i l i t y f o r fades to zero channel gain. - 123 -HEAD-SCAN EDITOR EQUALIZED PLAYBACK SIGNAL SYNC.^  DATA SEQUENCE RECOVERY •— GENERATOR s COUNTER COMPARATOR / SAMPLER 74 86 Figure 6.1 Measurement of cumulative d i s t r i b u t i o n f o r the eq u a l i z e d playback s i g n a l conditioned on a recorded '1'. CUMULATIVE PROBABILITY DISTRIBUTION A ANALOG MEASUREMENT R'~ AROUND MEDIAN / LQ"1 (tape # 3 ) ' / v tape #1 o tape #2 x tape #3 j 1 0 - 3 o V V O o V o OF MEASUREMENT LOWER LIMIT -0-5 0-0 0-5 1-0 THRESHOLD. V s ( median* 1-0 ) Figure 6.2 Cumulative d i s t r i b u t i o n of playback s i g n a l at sampling instant^;" "conditioned on recorded '1', record l e v e l , i«,=0.35 A, equalized by p r e f i l t e r and by seven-tap z e r o - f o r c i n g t r a n s v e r s a l f i l t e r 6.1.2 Deduced fade d i s t r i b u t i o n While the p r i n c i p a l e f f e c t of v a r i a t i o n i n head-tape s e p a r a t i o n i s to a l t e r the playback s i g n a l l e v e l , changes i n s p e c t r a l response a l s o occur. The e f f e c t s of playback s i g n a l e q u a l i z a t i o n f u r t h e r ensure that fading behaviour cannot be s t r i c t l y m u l t i p l i c a t i v e when observed at the d e c i s i o n device. Nevertheless, the longer time constants and r e l a t i v e l y s m a l l s p e c t r a l changes associated w i t h fades do a f f o r d some j u s t i f i c a t i o n f o r d e r i v i n g a d i s t r i b u t i o n f u n c t i o n f o r m u l t i p l i c a t i v e noise from measurements made at the d e c i s i o n device. The cumulative d i s t r i b u t i o n of playback s i g n a l l e v e l shown i n F i g . 6.2 i s assumed to a r i s e from the combined e f f e c t s of m u l t i p l i c a t i v e n o i s e , I S I , and noise which i s s t r i c t l y a d d i t i v e . Figure 6.3 shows the d i s t r i b u t i o n f u n c t i o n of the l a t t e r (assessed as i n §6.1.1) f o r tape #1 a f t e r bulk a.c. erasure. Although p r e a m p l i f i e r noise exceeds tape noise by about 6 dB f o r the equalized channel, tape noise c l e a r l y dominates the t a i l of the combined a d d i t i v e noise d i s t r i b u t i o n , which i s i t s e l f s i g n i f i c a n t l y non-Gaussian. A fade d i s t r i b u t i o n can be obtained by deconvolving the a d d i t i v e noise from the playback s i g n a l d i s t r i b u t i o n , although problems might be a n t i c i p a t e d w i t h machine p r e c i s i o n during transform computation. The chosen a l t e r n a t i v e method'involved the o p t i m i z a t i o n of an assumed fade density ( d i s -c r e t i z e d w i t h AV S=0.05). This method f a c i l i t a t e d i n t r o d u c t i o n of appropriate c o n s t r a i n t s and allowed the e f f e c t s of in e x a c t e q u a l i z a t i o n to be inc l u d e d . I n i t i a l l y , a l i n e a r e x t r a p o l a t i o n was made of the l o g a r i t h m i c p l o t of the a d d i t i v e noise d i s t r i b u t i o n i n F i g . 6.3, and the e q u a l i z a t i o n e r r o r ( I S I , F i g . 5.10) was introduced as a uniform d i s t r i b u t i o n over 0.8 to 1.2 of the nominal r e c e i v e l e v e l . The assumed fade d e n s i t y was then convolved w i t h the a d d i t i v e noise d i s t r i b u t i o n and the (fade-depth dependent) e q u a l i z a t i o n - 125 -CUMULATIVE PROBABILITY DISTRIBUTION ho — i 1 1 . • 0-4 0-3 0-2 0-1 0-0 THRESHOLD, V s Figure 6.3 Cumulative d i s t r i b u t i o n s f o r -ffre'amplifier  noise and f o r p r e a m p l i f i e r noise + a.c.-bias, tape n o i s e ; e q u a l i z a t i o n as f o r f i g . 6.2, tape #1 CUMULATIVE PROBABILITY 0 3 ^ -6 -8 -10 -12 -14 FADE DEPTH (dB) Figure 6.4 Fade d i s t r i b u t i o n derived from f i g u r e s 6.2 and 6.3; tape #1 e r r o r . The fade d e n s i t y was f i n a l l y adjusted to provide minimum mean square l o g a r i t h m i c e r r o r against the measured s i g n a l d i s t r i b u t i o n i n F i g . 6.2. The fade d i s t r i b u t i o n corresponding to t h i s s i t u a t i o n i s depicted i n F i g . 6.4. The s i m i l a r i t y of t h i s derived fade d i s t r i b u t i o n to the d i s t r i b u t i o n s i n F i g . 3.6 suggests that the fade d i s t r i b u t i o n f o r the channel can be u s e f u l l y and more e a s i l y assessed from d i s c r e t e s p e c t r a l measurements on the unequalized channel as i n §3.4.1. 6.2 HIGHER ORDER ERROR AND ERASURE STATISTICS Multigap e r r o r and erasure s t a t i s t i c s were compiled f o r the magnetic recording channel. Such s t a t i s t i c s do not provide exhaustive i n f o r m a t i o n about the channel but a l l o w performance to be estimated f o r s e v e r a l e r r o r c o n t r o l schemes. Erasures are defined as being more than 10 dB below the median l e v e l sampled by the d e c i s i o n device. 6.2.1 Measurement of multigap d i s t r i b u t i o n s The m-th order multigap or w a i t i n g d i s t r i b u t i o n describes the i n t e r v a l between a given event and the m-th succeeding event i n a sequence of B e r n o u l l i t r i a l s , e. [2371. I t i s convenient to work w i t h the cumulative 1 d i s t r i b u t i o n C(m,n) which i s the p r o b a b i l i t y t h a t , given one event (an e r r o r or e r a s u r e ) , the m-th succeeding event occurs a f t e r the m-th t r i a l ( b i t ) . Since the time constants a s s o c i a t e d w i t h fading on the re c o r d i n g channel are of the order of 100 b i t s , i t i s i m p r a c t i c a l to measure C(m,n) f o r a l l . M N m,n of i n t e r e s t . A c cordingly C(2 , 2 ) f o r M < 9, N < 12 were estimated . using the c i r c u i t of F i g . 6.5. The operation of t h i s c i r c u i t may not be s e l f - e v i d e n t and i s t h e r e f o r e described b r i e f l y i n the f o l l o w i n g paragraph. - 127 -INPUTr^SlTB D Q C MSB! 7W3 . J + 2 set order of gap 2x74S163 V74S00 74 S74 74LS175 7AS74 D Q. 0 0 MHz 20 MHz SETf LOAD 20 MHz 7408. RESET. /740 0 \ 74LS276 AUX-ILIARY ICOUNTERj 560 (1) D c 0 A 6 SELECT 1 of 16 74154 D 0 RESET SET. St D Q 0 20 MHz SET^1_ 3 0 p l 4-4096 3x 74S163 L S B COUNT LENGTH OF GAP M S B | (1) A K J O 12 15 2 1 0 CHANNEL SELECT .(1) -^2 TIMER ("74LS393 )CD4020 ]CD4020 (,2N3646 34 K J K J K J 1 ; V K J BIN BIN BIN BIN WIRE OR [KM •"7400 ^ 740 0 7400 "L TO COUNTER/ DISPLAY FROM K BIT OF GAP LENGTH SELECT CHANNEL FOR DISPLAY BIN 2N3646 5 J O * K •=-256 • 21* 74LS393 CD4020 •5 2N3646 560 (AUXILIARY COUNTER HAS SAME STRUCTURE) Figure 6.5 Measurement of multigap distributions - 128 -The ORDER OF GAP, 2 , i s set p r i o r to the playback run, and CHANNEL 15 s e l e c t e d . To begin each playback run, B and the TIMER are r e s e t . The M c i r c u i t then l a b e l s every 2 - t h event and counts the lengths of the i n t e r v e n -N ing gaps. As t h i s count reaches 2 , 0 < N < 12, the BIN on CHANNEL N i s incremented. I f none of the BIN's overflow, the TIMER e v e n t u a l l y terminates the run by s e t t i n g B. The cumulative gap counts f o r the run are now contained i n the BIN's. With appropriate CHANNEL SELECT the contents of the s e l e c t e d BIN are t r a n s f e r r e d as a 4 MHz c l o c k , v i a the AUXILIARY ''COUNTER to an ex-t e r n a l c o u n t e r / d i s p l a y . Nine such runs are r e q u i r e d to complete a 117 p o i n t M count a r r a y , i n c l u d i n g the 2 - t h order t o t a l e r r o r counts accumulated on -. CHANNEL 0. The r e s u l t s from each run are d i v i d e d by the a s s o c i a t e d t o t a l e r r o r count to give estimated cumulative multigap p r o b a b i l i t y d i s t r i b u t i o n s which may be enhanced by ensuring monotonicity against the order of gap. Multigap p r o b a b i l i t y d i s t r i b u t i o n s were thus derived f o r s i x segments of tape each c o n t a i n i n g 2 3 4 b i t s . A 31-bit pseudo-random p a t t e r n was recorded at 0.35 Amps. The playback s i g n a l e q u a l i z a t i o n i n d i c a t e d i n §6.1.1 was used thoughout. 6.2.2 Derived s t a t i s t i c s , P(>m,n) and E ( e Q , e^) Two p a r t i c u l a r s t a t i s t i c s are u s e f u l i n assessing the performance of e r r o r c o r r e c t i o n techniques. The p r o b a b i l i t y , P(>m,n), of m or more events, e^ . = l, o c c u r r i n g i n a block of .n b i t s allows e v a l u a t i o n of b l o c k codes. In terms of the cumulative gap d i s t r i b u t i o n s , the f o l l o w i n g r e s u l t ( s i m i l a r to Adoul [237]) may be derived. n P(>m,n) = p e I [C(m,r-1)-C(m-1, r-1)] (6.1) r = l - 129 -where pe=E{eQ}: i s the unconditional probability of error or erasure. n nN+n The expectation E{ £ e • £ e g } between errors/erasures i n two r=l r s=nN+l n-bit blocks r e l a t i v e l y displaced by nN bits i s of interest with regard to interleaved or concatenated codes [174, 238]. n nN+n nN E{ I V E e s } = Pe I I [C(m,r)-C(m,r-n)] (6.2) r=l s=nN+l m r=nN-n+l In par t i c u l a r for n=l,"(6.2) becomes the probability of two b i t s , separated by N-l intervening b i t s , both being incorrect (or erased). M N In deriving the above s t a t i s t i c s from the C(2 , 2 ) d i s t r i b u t i o n s , use was made of appropriately constrained, second-order interpolations. The accuracy of the derived s t a t i s t i c s was tested for multigap d i s t r i b u t i o n s generated by a variety of simulated binary channels. As an example, Fig. 6.6 shows three evaluations of E(e 0e^) forbinary signals i n Gaussian noise. For uncorrelated noise the method i s not s i g n i f i c a n t l y biased but exhibits large variance for small N due to the infrequent occurrence of.short gaps. Conversely for correlated noise the variance increases with N; i n addition, the necessary interpolations result i n some bias manifest as a smoothing along the N-axis. The theoretical curve (dashed line) may be obtained v i a the cumulative bivariate normal d i s t r i b u t i o n tabulated i n convenient form by Owen [239]. Figure 6.7 shows E{e Qe N} :for errors on the s i x tape segments for which multigap distributions were compiled. Allowing for the variation i n underlying error rate the segments a l l exhibit s i m i l a r v a r i a t i o n of E{e e„} o N with N. This fact suggests the use of conditional expectations E i e ^ J e ^ l } as a means of description. Figure 6.8 shows E{e Qe^} for erasures and Fig. 6.9 plots the geometric mean conditional expectation for both errors and erasures. From Fig. 6.9 a characteristic length of approximately 200 bi t s - 130 -10't V O X X 5. 0 ~9-V. GAUSSIAN NOISE WITH CORRELATION Xg FUNCTION 0-99N, SNR = 73dB THEORY SIMULATIONS WITH 5000 ERRORS ° \ x "9 5 . X V X— v ©—®—a—©— 9~-$~ 9 »• WHITE GAUSSIAN NOISE, SNR=8-2dB 1 10 100 1000 RELATIVE DISPLACEMENT (bits) oo Figure 6.6 Probability of two b i t s both being;incorrect,  E(e„ew), as a function of their r e l a t i v e displacement;  derived from the multigap error s t a t i s t i c s for a sim- ulated binary s i g n a l l i n g ;qhannel with additive Gaussian noise E(e 0 e N ) * n • 2 * v $ X X X X © X x « X v + D + 6 v } tape #1 * } tape #2 ° ) tape #3 8 x 1 10 100 1000 co RELATIVE DISPLACEMENT, (bits) Figure 6.7 Probability of two b i t s both being i n - correct ,E (e„eM ) , as a function of th e i r r e l a t i v e  displacement; derived from the measured multigap error s t a t i s t i c s for the binary magnetic recording •channel AE(e0eN) -5 10 1 -6 10 •id* -8 10 -9 10 -10 10 •'•8 A ] tape #1 D S v I + o | M t a P e # 2 * • } tape # 3 • • 0 1 10 100 1000 oo RELATIVE DISPLACEMENT, N (bits) Figure 6.8 P r o b a b i l i t y of two b i t s both being erased, E ( e 0 e M ) , as a f u n c t i o n of t h e i r r e l a t i v e displacement: 'derived from the measured multigap erasure s t a t i s t i c s  f o r the binary magnetic recording channel ,04 0-1 10 io: 16A--5' 10 io6 id' ERRORS ERASURES EXTRAPOLATIONS USED IN CODE EVALUATIONS 0-01 0-1 .1-0 10 ( m m ) oo 1 10 100 1000 10* ( b i t s ) oo RELATIVE DISPLACEMENT, N Figure 6.9 Geometric, mean c o n d i t i o n a l p r o b a b i l i t i e s ,  E ( e w | e 0 = l ) , from f i g u r e s 6.7 and 6.8 (0.1 mm) may be assigned although e r r o r s / e r a s u r e s do not become completely independent even at separations of 2000 b i t s . Because of the e f f e c t s of no i s e , inexact e q u a l i z a t i o n , and fades which are not s t r i c t l y m u l t i p l i c a t i v e , the c o n d i t i o n a l p r o b a b i l i t i e s do not exceed 0.5 even f o r erasures. The p r o b a b i l i t i e s around N=31 may be exaggerated by the r e p e t i t i v e nature of the t e s t sequence. Figure 6.10 shows the p(>m,n) s t a t i s t i c s f o r m, n as powers of 2. The s t a t i s t i c s are based on the mean multigap e r r o r d i s t r i b u t i o n over the s i x tape segments. 6.3 ERROR CORRECTION 6.3.1 Block codes An (n, k, d) block code encodes k inf o r m a t i o n b i t s i n t o n transmitted tr b i t s w h i le assuniing a minimum d i s t a n c e , d, between codewords. A l i n e a r (n, k, d) code can c o r r e c t up to t e r r o r s ( t i s the l a r g e s t i n t e g e r < d/2). For a block c o n t a i n i n g m>t e r r o r s the nearest codeword contains at l e a s t d er r o r s but fewer :than m+t e r r o r s [240] . Assuming these e r r o r s to be uniformly d i s t r i b u t e d on a systematic code, the o v e r a l l e r r o r r a t e , p^, f o r the informa-t i o n b i t s i s th e r e f o r e bounded by . £ £p(m,n) < P o < I £±£p(m,n) ( 6 . 3 a ) m>t m>t or A A 1 t + 1 - P(>t+l,n)<p < - P(>t+l,n)+ p - - V P(>m,n) (6.3b) n — o n — e n L. — m=l Figure 6.11 shows (6.3) evaluated f o r codes of r a t e approximately 5/6 as a fu n c t i o n of block length. I n v e s t i g a t i o n of erasure and erasure-and-error - 133 -10 10' 10 Pe io7t 10 P(^m.n) 1 10 E R R O R S P E R BLOCK 100 m Figure 6 . 1 0 P r o b a b i l i t y that n consecutive b i t s Include at l e a s t m  e r r o r s , Pfe-m,n); derived from the measured multigap e r r o r s t a t i s t i c s  f o r the bi n a r y magnetic recording channel - 134 -decoding [241] proves s i m i l a r l y unrewarding f o r block codes. Some advantage may accrue from the use of b u r s t e r r o r or burst-and-random e r r o r c o r r e c t i n g codes, although Mabey's r e s u l t s [242] suggest the contrary f o r fading channels i n the context of mobile r a d i o . The codes i l l u s t r a t e d i n F i g . 6.11 and Table 6.1 (§6.3.3) may be found i n MacWilliams and Sloan's t a b l e of best known codes [165]. 6.3.2 I n t e r l e a v e d codes A s i n g l e - e r r o r - c o r r e c t i n g (n, k, d) code i s i n t e r l e a v e d at every N*"*1 transmitted b i t . The p r o b a b i l i t y , P^, of block e r r o r i s lower bounded by the p r o b a b i l i t y of a given p a i r of b i t s f a i l i n g simultaneously and upper bounded by the union over a l l such p a i r s , i . e . , n-1 E ( e Q e N ) £ P b ^ I (n-j) E ( e D e i N ) (6.4) As N increases and the elements of the block code become i n c r e a s i n g l y independent, the upper bound becomes a good approximation, and Po = f I (n-j) E ( e o e j N > (6-5) This expression i n p l o t t e d i n F i g . 6.12 f o r a (31,26) code i s a f u n c t i o n of N, the i n t e r l e a v i n g r a t i o . Over much of the range of N, the o v e r a l l e r r o r r a t e , p Q , i s based on the e x t r a p o l a t i o n s i n d i c a t e d i n F i g . 6.9. U s e f u l reductions i n e r r o r r a t e are apparent and the coding/decoding can be performed e a s i l y . However l a r g e amounts of b u f f e r storage are r e q u i r e d , and decoding delay can become a problem. In these two respects there i s l i t t l e advantage i n progressing to m u l t i p l e - e r r o r - c o r r e c t i n g codes. In a s i m i l a r manner to (6.5), the o v e r a l l e r r o r r a t e f o r a s i n g l e erasure c o r r e c t i n g (n, n-1) block code can be approximated from the j o i n t - 135 -LU I-< cr cr o tr cr L U < cr LU o io6t 10' ro i n t^-<£>- CS 2 ~ S- °°' ^ 2 ^ to" IZ-cs CO 1 0 CM* cs m < 3 ^ _ i O cs UJ CD i=J V V A UPPER BOUND v LOWER BOUND 100 1000 10000 B L O C K L E N G T H , n (bits) Figure 6.11 O v e r a l l e r r o r r a t e , p 0 , on. the bin a r y magnetic re c o r d i n g  channel f o r various codes w i t h rates of approximately 5/6 id6-• o C L 10 - -8 LU 10 " < * -9 cr 10 1 o cr -io w 10 < -11 £ 10 > o (31,26.3) SINGLE ERROR CORRECTING CODE ON BINARY CHANNEL' RAW P e ERROR RATE (6.5,2) SINGLE ERASURE CORRECTING CODE ON TERNARY ERASURE CHANNEL 100 1000 10000 I NTERLEAV ING RATIO. N (bits) Figure.6.12 O v e r a l l e r r o r r a t e s , p 0 , on the magnetic recording  channel f o r i n t e r l e a v e d coding at approximately 5/6-rate - 136 -expectation of erasures, E z ( e 0 e ^ ) , shown i n F i g . 6.9. 1 n _ 1 Po = „ I ( n _J> E z ( e o e j N ) + Pm ( 6- 6> j = l where p^ 1 0 - 1 0 , from F i g . 6.2, represents the p r o b a b i l i t y of e r r o r s r e -maining undetected as -10 dB erasures. The o v e r a l l e r r o r r a t e f o r a 5/6 -ra t e code i s als o shown i n F i g . 6.12. Compared w i t h the (31,26) e r r o r -c o r r e c t i n g code, erasure decoding connot achieve such low e r r o r r a t e s ; at —9 P£=10 however, erasure decoding i n v o l v e s only one t h i r d of the decoding delay. Erasure decoding may be f u r t h e r improved by o p t i m i z a t i o n of the erasure l e v e l and/or by the replacement of undecodable erasures by the normal (zero d e c i s i o n - l e v e l ) comparator output. Some assessment of these improvements may be made by reference to the equalized playback s i g n a l d i s -t r i b u t i o n , F i g . 6.2. The use of a (31,26) i n t e r l e a v e d code could u s e f u l l y a l l o w c o n t r o l over the e f f e c t s of p m i n (6.6). However the a v a i l a b l e s t a t i s t i c s do not permit performance e v a l u a t i o n f o r m u l t i p l e e r r o r / e r a s u r e c o r r e c t i n g i n t e r - , leaved codes except at l a r g e i n t e r l e a v i n g r a t i o (§6.3.3). 6.3.3 Concatenated codes The use of a concatenated code, as envisaged by Chase [171], provides a f l e x i b l e and e f f e c t i v e approach to e r r o r c o n t r o l . The inner b l o c k code may provide some e r r o r c o r r e c t i o n but, on bursty channels, i t s most appro-p r i a t e f u n c t i o n i s to detect e r r o r s and declare a block erasure which may be subsequently c o r r e c t e d by the outer code. E r r o r d e t e c t i o n i s more e a s i l y performed than c o r r e c t i o n . A r e l a t i v e l y long inner code may be considered, w i t h length comparable to the expected b u r s t length. The elements of the - 137 -outer code may be rendered independent by i n t e r l e a v i n g although Reed-Solomon codes [165, 243] e x h i b i t u s e f u l burst e r r o r / e r a s u r e c o r r e c t i o n c a p a b i l i t y . The o v e r a l l b i t e r r o r r a t e , p Q , i s d i r e c t l y a f f e c t e d by the p r o b a b i l i t y , p , of an erroneous b i t being missed by the inner (n,k,d) code [124] Pm * ^ I J H M (6.7) mjd Correspondingly the p r o b a b i l i t y , P z, of an inner b l o c k being erased a f f e c t s the performance of the outer code. P - P ( ^ l , n ) f o r np « P << 1 (6.8) z ' rm z Unfortunately the a v a i l a b l e s t a t i s t i c s do not a l l o w e s t i m a t i o n of the o v e r a l l e r r o r r a t e f o r moderate i n t e r l e a v i n g r a t i o s , although the degree of dependence between blocks may be assessed from ( 6 . 2 ) . For a s y m p t o t i c a l l y large i n t e r l e a v i n g r a t i o s (independent blocks) the f o l l o w i n g o v e r a l l e r r o r r a t e a p p l i e s to a s i n g l e erasure c o r r e c t i n g ( n 1 , n ' - l ) outer code. , n'(n'-l) T ) 2 2 r m . , . w n \ p o a P m + 2 P z n* • I n p ( m ' n ) / p z <6'9a> m = 2 k _ n [ n p - I P(^m,n)+(d-l)P(^d,n)]+(n ,-l)P(^l,n)p (6.9b) m<d Table' 6.1 •. i n d i c a t e s /overalls e r r o r p r o b a b i l i t i e s f o r fhree simple con-catenated codes w i t h r a t e s of approximately 5/6. The performance of i n t e r -leaved codes from §6.3.2 i s a l s o i n d i c a t e d f o r l a r g e i n t e r l e a v i n g r a t i o s . E v a l u a t i o n of the s i n g l e - e r r o r / double-erasure c o r r e c t i n g (31,26) code i s based on the p r o b a b i l i t y of a t r i p l e erasure or of a s i n g l e undetected e r r o r w i t h a s i n g l e erasure. Unavoidable erasures are f i n a l l y replaced by the .. normal (zero d e c i s i o n l e v e l ) comparator output, thus corresponding to a - 138 -CONCATENATED CODES on b i n a r y channel OVERALL ERROR INNER CODE OUTER CODE RATE (128,114) X (16,15) 3.4 x 1 0 ~ U (256,240) X ( 9, 8) 1.8 x I O " 1 1 (512,494) X ( 7, 6) 1.9 x 1 0 _ i i (6,5) on 4-- l e v e l erasure channel 2.2 X 10" 11 (31,26) on bina r y channel 4.5 X 10" 12 (31,26) on 4 - l e v e l erasure channel 1.3 X 10" 13 Table 6.1. O v e r a l l e r r o r rates achieved by various 5/6 rate codes at high i n t e r l e a v i n g r a t i o s . The equalized magnetic recording channel i s quantized i n t o e i t h e r a binary or a f o u r - l e v e l erasure channel. f o u r - l e v e l erasure scheme. 6.4 CONCLUSIONS In t h i s chapter i t has been shown that the cumulative amplitude d i s t r i b u t i o n of the playback s i g n a l at the sampling i n s t a n t s can be r e a d i l y obtained. This d i s t r i b u t i o n d i s p l a y s a c h a r a c t e r i s t i c 'kink' r e f l e c t i n g the occurrence of dropouts on the magnetic recording channel. Removing the e f f e c t s of a d d i t i v e noise and inexact e q u a l i z a t i o n , the r e s u l t i n g fade d i s t r i b u t i o n confirmed the v a l i d i t y of the fade d i s t r i b u t i o n s of Chapter I I I which were based on d i s c r e t e s p e c t r a l measurements. Although the nature of the cumulative d i s t r i b u t i o n suggests the use of erasure decoding, e v a l u a t i o n of e r r o r c o n t r o l techniques r e q u i r e s the a c q u i s i t i o n of more comprehensive e r r o r and erasure s t a t i s t i c s . Multigap e r r o r and -lOdB erasure d i s t r i b u t i o n s were the r e f o r e compiled from which - 139 -f u r t h e r s t a t i s t i c s ( a l l o w i n g the e v a l u a t i o n of i n t e r l e a v e d codes i n p a r t -i c u l a r ) were deri v e d . Block codes remain i n e f f e c t i v e even at lengths ex-ceeding 100 b i t s . I n t e r l e a v e d block codes are s u r p r i s i n g l y e f f e c t i v e but may i n v o l v e excessive decoding delay and storage i n order to r e a l i s e t h e i r f u l l p o t e n t i a l . U s e f u l improvements i n e r r o r r a t e can be achieved through the simple expedient of three or four l e v e l erasure decoding. The implemen-t a t i o n of a (6,5) code w i t h a more reasonable span, nN, of 10,000 b i t s could approach an e r r o r r a t e of 10" 1 0 w i t h a four l e v e l erasure channel; the raw channel e r r o r r a t e being 3 x 10"7. Concatenated codes can improve on the e r r o r r a t e s of erasure decoding and on the code span of i n t e r l e a v e d block codes. Such improvements occur at the expense of coder/decoder s i m p l i c i t y . Supplying erasure i n f o r m a t i o n w i t h a (31,26) code s i g n i f i c a n t l y reduces o v e r a l l e r r o r r a t e but a l s o increases decoder complexity. - 140 -V I I DECISION FEEDBACK EQUALIZATION ON THE MAGNETIC RECORDING CHANNEL The use of d e c i s i o n feedback e q u a l i z a t i o n (DFE) 'allows a d d i t i o n a l freedom f o r s i g n a l and r e c e i v e r design. The magnetic r e c o r d i n g channel e x h i b i t s poor response at both high and low frequencies and i s thus a t t r a c t i v e f o r the a p p l i c a t i o n of DFE. In p a r t i c u l a r the a p p l i c a t i o n s are discussed of p a r t i a l response s i g n a l l i n g as w e l l as a novel scheme f o r e q u a l i z i n g the d.c. n u l l . A simple channel model i s developed to i l l u s t r a t e the e f f e c t s of channel fading on such r e c e i v e r s . The second s e c t i o n presents r e s u l t s taken with DFE r e c e i v e r s on the prototype magnetic r e c o r d i n g system of Chapter IV. 7.1 DECISION FEEDBACK EQUALIZATION 7.1.1 D e c i s i o n feedback / p a r t i a l response The p r i n c i p l e s of DFE and the r e l a t e d technique of p a r t i a l response s i g n a l l i n g were introduced i n §2.3.1. These techniques prove u s e f u l when the s p e c t r a l s i g n a l - t o - n o i s e r a t i o (SNR) i s not f l a t o r , i n p a r t i c u l a r , i n the presence of s i g n a l s p e c t r a l n u l l s . The magnetic r e c o r d i n g channel e x h i b i t s both a d.c. n u l l and r a p i d l y decreasing SNR at high frequency ( h . f . ) . From the c o n s i d e r a t i o n s of §4.1, i t should be noted that the record waveforms are constrained throughout to balanced b i n a r y formats. In t h i s context both DFE and p a r t i a l response s i g n a l l i n g are e x c l u s i v e l y r e c e p t i o n techniques; a l l necessary s i g n a l shaping i s done by the r e c e i v e f i l t e r s i n combination w i t h the n a t u r a l channel response. I f the response seen by the quantizer i n F i g u r e 2.4b i s f l a t e q u a l i z e d then, w i t h one b i t delay, T, as the feedback f i l t e r , the playback response .emerging from the forward f i l t e r must be of the form 2 c'os(wT/2). Compared w i t h a l i n e a r r e c e i v e r , the s e n s i t i v i t y of t h i s DFE r e c e i v e r i s quadrupled at low frequency ( l . f . ) but reduced to zero at the Nyquist - 141 -frequency. This reduced s e n s i t i v i t y to h.f. noise can allow e i t h e r improved performance or increased data r a t e s . The corresponding time-domain response from the forward f i l t e r i s a t h r e e - l e v e l s i g n a l which can,, i n f a c t , be d i r e c t l y quantized and decoded without recourse to d e c i s i o n feedback. Such i s the technique of (class.:!) p a r t i a l response r e c e p t i o n [135] which o f f e r s comparable performance and can be used whenever DFE gives r i s e to a simple m u l t i l e v e l eye. For example, feedback comprising an i n v e r s i o n and two b i t delay corresponds to c l a s s IV p a r t i a l response and provides r e c e p t i o n n u l l s at both d.c. and the Nyquist frequency. Problems associated w i t h the d.c. n u l l are thus avoided and some improvement i n SNR i s p o s s i b l e , F i g . 4.1. Class IV p a r t i a l response has been a p p l i e d t o a high d e n s i t y magnetic d i s c system [187]. Such techniques provide a crude match to the c h a r a c t e r i s t i c s of the magnetic recording channel; DFE schemes designed to more c l o s e l y match the channel g e n e r a l l y preclude the use of p a r t i a l response r e c e p t i o n . 7.1.2 E q u a l i z a t i o n of the d.c. n u l l At low frequencies a conventional gapped-ring magnetodynamic head reproduces the d e r i v a t i v e of the record current waveform. Low frequency e q u a l i z a t i o n may thus be achieved by i n t e g r a t i n g the playback s i g n a l as i n P i g . 4.'6. The time constant of the i n t e g r a t o r must be l i m i t e d to avoid the i n t r o d u c t i o n of excessive l . f . noise or i n t e r f e r e n c e . I n e v i t a b l y a narrow d.c. n u l l remains. I t was recognised by Wood and Donaldson [131] that the nature of t h i s r e s i d u a l n u l l i s appropriate f o r the a p p l i c a t i o n of DFE i n the form of d.c. r e s t o r a t i o n [124]. The f o l l o w i n g h e u r i s t i c arguments describe the technique i l l u s t r a t e d by E i g . 7.1. In the absence of data e r r o r s , l e t the spectrum of a recovered b i t equal that of a normalized recorded b i t i n NRZ format, i . e . A(w) = I m(w) = .- 142 -FEEDBACK FILTER CHANNEL " EQUALIZER E(w);RC J _ PLAYBACK SIGNAL • LR RESPONSE + R V(co) DECISION DEVICE A(u>) (COMPARATOR- — ' > SAMPLER) DATA —"—7^ 1 OUT BIT SYNCHRONIZATION Figure 7.1 I l l u s t r a t i n g the use of DFE to compensate f o r the d.c. n u l l  i n the magnetic recording channel F E E D B A C K F I L T E R FEEDBACK TO j SUMMING DEVICE Figure 7.2 Feedback f i l t e r amalgamating compensation f o r the d.c. n u l l  w i t h c l a s s I p a r t i a l response s i g n a l l i n g - 143 -s i n ( u T / 2 ) / (CJT/2) . I f the playback s i g n a l , E(UJ), m u l t i p l i e d by constant RC, i s a p p l i e d to the channel e q u a l i z e r the r e s u l t i n g v o l t a g e , V(ui), seen by the d e c i s i o n device may be expressed. V(di) = RC E(to) (1+jwRC) - 1 + A(w) ( l + j u R C ) " 1 ^ 7 - 1 ^ With E(o)) from ( 2 . 9 ) or ( 2 . 1 0 ) i t i s found that at low frequencies V(w) becomes constant. The d.c. n u l l i s thus avoided. A d i s c r e t e - t i m e a n a l y s i s [ 1 3 1 ] may be performed which i n d i c a t e s that the technique can be combined with an o v e r a l l e q u a l i z a t i o n scheme. Feedback predominates i n the spectrum, V ( u ) , f o r OJ<I/RC and the feedback power i s approximately •: T/2RC of the t o t a l power seen by the d e c i s i o n device. The time constant, RC, may be chosen independently of the f a c t of e q u a l i z a t i o n to compromise between excessive l . f . noise and i n t e r f e r e n c e at l a r g e RC, and excessive channel gain s e n s i t i v i t y at s m a l l RC (high feedback power). I t i s noted that compensation f o r the d.c. n u l l i s independent of head-tape v e l o c i t y , v, an important c o n s i d e r a t i o n on v a r i a b l e speed machines. Figure 7.2 i n d i c a t e s how feedback f o r compensation of the d.c. n u l l can be amalgamated w i t h the u n i t y feedback corresponding to c l a s s I p a r t i a l response s i g n a l l i n g . The s p e c t r a l s e n s i t i v i t y of such a r e c e i v e r i s p a r t i c u l a r l y appropriate to a high d e n s i t y magnetic recording channel. 7.1.3 S e n s i t i v i t y to channel fades L i n e a r r e c e i v e r s w i t h balanced b i n a r y s i g n a l l i n g are r e l a t i v e l y i n s e n s i t i v e to f l u c t u a t i o n s i n channel gain. The use of DFE, however, i m p l i e s a knowledge of incoming s i g n a l l e v e l s , and the advantageous a p p l i c a t i o n of DFE on the fading channel cannot t h e r e f o r e be presumed. The f o l l o w i n g example, based on the measured c h a r a c t e r i s t i c s of the magnetic - 144 -r e c o r d i n g channel, i l l u s t r a t e s how degradations due to f a d i n g can be reduced by s u i t a b l e choice of feedback l e v e l . A model of the d i s c r e t e - t i m e channel and DFE r e c e i v e r i s shown i n F i g . 7.3. The v o l t a g e , v^., seen by the d e c i s i o n device i s V k = K + fk> ™k n k " f k \ (7.2) where a^=a^ i s the t r a n s m i t t e d / r e c e i v e d data, f represents the feedback, m^  and n^ are r e s p e c t i v e l y the m u l t i p l i c a t i v e and a d d i t i v e n o i s e s , and m^ i s a l o c a l estimate of m^ . As i n d i c a t e d i n F i g . 7.3, the combination of the forward r e c e i v e f i l t e r ( F i g . 2.4b) and the re c o r d i n g channel n e c e s s a r i l y complements the feedback f i l t e r . J u s t i f i c a t i o n of t h i s model i n v o l v e s arguments s i m i l a r to those a r i s i n g i n §6.1 where an attempt i s made to de r i v e the fade d i s t r i b u t i o n from measurements taken at the d e c i s i o n device. By c o n d i t i o n i n g (7.2) on a =+1, the p r o b a b i l i t y of e r r o r , p , may be w r i t t e n P e = Pr{ (i:+ f k ) (n^ - \ ) + ( n k + \ ) < 0 } (7.3) I f the es t i m a t o r , m^ , i s constant, the three bracketed expressions w i t h i n (7.3) are independent and p^ may be evaluated from the amplitude p r o b a b i l i t y d e n s i t y f u n c t i o n s of f ^ , m^ , and n^. The density f u n c t i o n of f ^ may be c a l c u l a t e d or approximated from the feedback f i l t e r t r a n s f e r f u n c t i o n , h ( k ) . The d i s t r i b u t i o n s of m^ and n^ f o r z e r o - f o r c i n g l i n e a r e q u a l i z a t i o n are shown i n F i g s . 6.4 and 6.3 r e s p e c t i v e l y . Both d i s t r i b u t i o n s are, however, dependent upon the choice of h ( k ) , a f a c t which makes u s e f u l comparisons between r e c e i v e r s d i f f i c u l t . Nevertheless, the measured d i s t r i b u t i o n s w i t h (7.3) can be used to i l l u s t r a t e , i n F i g . 7.4, the advantages of applying reduced feedback, m k < l » o n the f a d i n g channel w i t h p a r t i a l response r e c e p t i o n , - 145 -a k = ±1 RECORDED SEQUENCE MAGNETIC RECORDING CHANNEL AND FORWARD RECEIVE FILTER m, n, MULTIPLICATIVE ADDITIVE NOISE NOISE ESTIMATE OF CHANNEL GAIN A m k FEEDBACK DECISION DEVICE RECOVERED SEQUENCE Figure 7.3 D i s c r e t e time model of the magnetic recording channel with DFE reception A -3 1 0 10*' 10 -6 1 0 t ERROR RATE 1-0 0 - 0 0 - 5 FEEDBACK MULTIPLIER A m. Figure 7.4 Calculated effect of applying reduced feedback level  with partial response (ternary eye) signalling; based on measured additive noise and fade distributions - 147 -S i m i l a r behaviour i s found when the feedback f i l t e r i s used to compensate the d.c. n u l l ; i n t h i s case, however, the e r r o r rates are dominated by the p r o b a b i l i t y of fades to zero channel g a i n , an e f f e c t a l s o evident as the f l a t ' v a l l e y f l o o r ' of F i g . 7.4. I f an e f f e c t i v e e s t i m a t o r , m^ ., or an e f f e c t i v e automatic gain c o n t r o l (a.g.c.) i s a v a i l a b l e , then (7.3) may be rearranged p e = P r d ^ + n k + f k (n^ - i y < 0 } (7.4) With the assumption that m^  - m^  i s independent of m^ , an estimate of e r r o r p r o b a b i l i t y may be made. Again, f o r any reasonable e s t i m a t o r , E{(m k-m k) 2}< varCrn^}, the r e s u l t s are dominated by the p r o b a b i l i t y of fades to zero channel g a i n , Pr{m k=0}. The e r r o r rates measured"in the f o l l o w i n g s e c t i o n do not e x h i b i t t h i s i n d i f f e r e n c e to the es t i m a t o r , m^ : a f a c t which must r e f l e c t some of the shortcomings of the s t a t i c model. The i n c l u s i o n of dynamic e f f e c t s such as e r r o r propagation, the dependency of channel response upon fade depth, and the e f f e c t on fades of the subsequent e q u a l i z a t i o n process, would un-doubtedly improve the model. However, i t i s not c l e a r that s u i t a b l y g e n e r a l i z e d measurements of m u l t i p l i c a t i v e and a d d i t i v e noise d i s t r i b u t i o n s could be made which would a l l o w the e f f e c t s of various s p e c t r a l shapings (various h(k) ) upon these d i s t r i b u t i o n s to be deduced. In c o n c l u s i o n , however, the a p p l i c a t i o n of a.g.c. appears to be of dubious advantage; e s p e c i a l l y s i n c e the same l i m i t i n g performance i s achieved by the use of a constant estimator (m^O.3 i n F i g . 7.4). - 148 -7.2 RESULTS ON PROTOTYPE MAGNETIC RECORDING SYSTEM The f o l l o w i n g r e s u l t s p e r t a i n to the a p p l i c a t i o n of DFE to the prototype magnetic re c o r d i n g system described i n Chapter IV. Random data at 20 Mbit/s was simulated by a 2 2 t + - l b i t pseudorandom sequence. A record l e v e l of 0.5 A on tape #3 was used throughout. The playback head c o u p l i n g included R =3.9 Kfi and C =5 pF. The seven-tap t r a n s v e r s a l f i l t e r was sh sh allowed to adapt f r e e l y i n the presence of the feedback. 7.2.1 E q u a l i z a t i o n of the d.c. n u l l The d.c. n u l l i s compensated by the a p p l i c a t i o n of DFE as i n d i c a t e d i n §7.1.2. Figure 7.5 shows measured e r r o r r a t e s , w i t h and without feedback, as a f u n c t i o n of the width of the r e s i d u a l n u l l l e f t by the forward f i l t e r ( p r e f i l t e r ) . The p r o p o r t i o n of i s o l a t e d e r r o r s i s a l s o d i s t i n g u i s h e d p r o v i d i n g a measure of channel 'burstyness'. Each point represents the geometric mean of three reproductions of a s i n g l e segment of tape c o n t a i n i n g 2 3 1 + b i t s . Without feedback the e r r o r r a t e reaches a minimum when the -3dB point f o r the forward i n t e g r a t o r i s at approximately 20KHz; below t h i s frequency excessive noise and i n t e r f e r e n c e are introduced, above t h i s frequency the e f f e c t s of the e q u a l i z a t i o n e r r o r become apparent. The use of feedback permits an order of magnitude red u c t i o n i n e r r o r r a t e ; best r e s u l t s are obtained w i t h the i n t e g r a t o r s ' -3dB points at approximately 200KHz. As suggested by §7.1.3 i t i s advantageous to use reduced l e v e l s of feedback, i . e . some f i x e d m j c < L ^ n f a c t , the above r e s u l t s were obtained w i t h an e f f e c t i v e m u l t i p l i e r , 1^=0.83, on the feedback loop i n d i c a t e d i n F i g . 7.1. Figure 7.6 shows the e f f e c t ( at f r a c t i o n a l bandwidth, T/TTRC=0.02 ) of reducing the feedback m u l t i p l i e r , m^ , from u n i t y to zero. The r a t e of i s o l a t e d e r r o r s decreases as feedback increases and the e q u a l i z a t i o n . - 149 -* ERROR o-ooi ooo2 oool 001 &02 F R A C T I O N A L W I D T H O F R E S I D U A L ' D.C. N U L L , T/nRC Figure 7.5 E r r o r r a t e vs. bandwidth of d.c. n u l l , w i t h and without DFE, . 1.^ =0 ,.5 A, . ...tfl^ =0.83 ERROR A RATE Figure 7.6 E f f e c t of reducing feedback l e v e l , improves. The o v e r a l l e r r o r r a t e appears to reach a minimum f o r m^. s l i g h t l y below u n i t y . The e f f e c t s of the uncompensated d.c. n u l l are more severe than a n t i c i p a t e d i n §7.1.3. While some of t h i s discrepency can be a t t r i b u t e d to the s i m p l i s t i c channel modelling, i t has a l s o been noted t h a t , when extended l . f . e q u a l i z a t i o n i s attempted, a l a r g e p r o p o r t i o n of e r r o r s can be associated w i t h l i n e frequency harmonics. The presence of such harmonics and the apparent aggravation of adaptive e q u a l i z a t i o n i n a c c u r a c i e s by the uncompensated n u l l represent a d d i t i o n a l c o n t r i b u t i o n s to the discrepency between measured and a n t i c i p a t e d r e s u l t s . 7.2.2 M o d i f i c a t i o n of h.f. response Attempts to introduce c l a s s IV p a r t i a l response s i g n a l l i n g by o m i t t i n g the p r e f i l t e r i n F i g . 4.2, i n t r o d u c i n g feedback from the b i t -detected 2T e a r l i e r , and r e l y i n g on the adaptive e q u a l i z e r to force the necessary response, proved u n s u c c e s s f u l . The adaptive e q u a l i z e r tap gains f a i l e d to converge, a f a c t which perhaps i n d i c a t e s . t h e r e l a t i v e l y poor match between the d e s i r e d c l a s s IV response and the a c t u a l channel response. Attempts to s i m i l a r l y introduce c l a s s I p a r t i a l response s i g n a l l i n g together w i t h compensation of the d.c. n u l l (using the feedback c i r c u i t of F i g . 7.2) a l s o proved unsuccessful. Tap convergence d i d not occur r e l i a b l y and was very s e n s i t i v e to c l o c k phase. The use of reduced feedback (with the playback response correspondingly adjusted by the adaptive e q u a l i z e r ) proved more s u c c e s s f u l . Noise and e q u a l i z a t i o n e r r o r s on the eye diagram appeared p a r t i c u l a r l y small when 30% of the preceding b i t and 80% of the l . f . e q u a l i z a t i o n were fed back. Figure 7.7 shows the e f f e c t on e r r o r r a t e of v a r y i n g the l e v e l fed back from the previous b i t w i t h c l o c k phase having - 151 -ERROR RATE TOTAL ERRORS .d6i 16" ,o cr ISOLATED ERRORS ~i 1 1 1 1 1 1 — 0-0 0-1 0-2 0-3 0-4 0-5 0-6 FEEDBACK MULTIPLIER n\ Figure 7-7 E r r o r r a t e vs. l e v e l of feedback from immediately preceding b i t ; l . f . feedback a p p l i e d w i t h T/TTRC=0.02, mk=0.8, i m=0.50 .d5t ERROR RATE TOTAL ERRORS^ 7 ' .d' ISOLATED ERRORS — i 1 1 1 1 1 j > 0 0 0-2 0-4 WIDTH OF ERASURE REGION Figure 7.8 E f f e c t upon d.c. n u l l compensation of in t r o d u c i n g erasure region as i n f i g . 7.9a T/irRC=0.02, rn^O.8, yO.50 A been adjusted to provide the best eye f o r each l e v e l of feedback. In t h i s case the apparent improvement i n eye opening i s misleading and only marginal improvements i n e r r o r r a t e appear p o s s i b l e on the present system. 7.2.3 Attempts to compensate f o r channel fading Although' some slow a.g.c. i s e s s e n t i a l .to•compensate f o r changes i n head's s o r f o r component aging ; .etc-:. _j n i t •'is.v.-.tib.t.'clear that the a p p l i c a t i o n of more r a p i d a.g.c. to the magnetic r e c o r d i n g channel o f f e r s any u s e f u l improvements i n the context of DFE. The prototype system a.g.c. d r i v e n by the t r a n s v e r s a l f i l t e r tap adjustment a l g o r i t h m i s r e l a t i v e l y slow w i t h a time constant of s e v e r a l m i l l i s e c o n d s . No c o n s i s t e n t changes i n e r r o r r a t e occurred when the adjustment a l g o r i t h m was a r r e s t e d during playback. Rapid and accurate estimates of channel gain are f r u s t r a t e d by the presence of a d d i t i v e n o i s e , by the a d d i t i o n a l channel d i s p e r s i o n a s s o c i a t e d w i t h fades, and by the subsequent d i s p e r s i o n of simple fades by the playback s i g n a l e q u a l i z a t i o n . The most i n t r a c t a b l e problem, however, r e l a t e s to the d i f f i c u l t y of d i s t i n g u i s h i n g between channel fades and long runs of i d e n t i c a l b i t s to which the channel response i s very s m a l l . A crude but almost instantaneous measure of channel gain i s i m p l i c i t i n erasure decoding described i n Chapter VI. Figure 7.9a i n d i c a t e s a simple means of using such an estimate. Erased b i t s do not c o n t r i b u t e to the feedback s i g n a l and i d e a l l y , during a fade, no feedback i s a p p l i e d . This technique i s appropriate when DFE i s used to e q u a l i z e the d.c. n u l l s i n c e excessive feedback during a fade leads to c a t a s t r o p h i c e r r o r propagation, whereas, i n the absence of feedback, reasonable performance i s maintained. Figure 7.8 shows the e r r o r rates achieved f o r an implementation of F i g . 7.9a as a f u n c t i o n of the width of the erasure r e g i o n . Each point represents the - 153 -CLOCK (BIT SYNCHRONIZATION) COMPARATOR SAMPLER PLAYBACK SIGNAL FROM TRANSVERSAL FILTER OUT. OUTPUT DATA h— IN SEQUENCE CLOCK CLOCK R J — A A ^ F i g u r e 7.9a FEEDBACK TO SUMMING DEVICE MONOSTABLE 40T I normally y|C/2 closed T 2R A A r C/2 DATA ERASURES FROM DECISION DEVICE F i g u r e 7.9b Attempts t o compensate f o r channel f a d i n g by the use of erasure decoding - 154 -geometric mean of three reproductions of a segment of tape #3 c o n t a i n i n g 2iH b i t s . The technique does not appear to o f f e r any advantage on the prototype system. Those d.c. or l . f . components which are present during a fade tend to be aggravated by the technique i l l u s t r a t e d i n Fig.7.9a g i v i n g r i s e to a form of e r r o r propagation. An a l t e r n a t i v e technique a v o i d i n g t h i s problem i s i n d i c a t e d i n Fig.7.9b. In t h i s case a s i n g l e erasure causes feedback to be stopped f o r approximately 40 b i t s . Implementation of t h i s second t e c h -nique caused the e r r o r r a t e to increase by almost a f a c t o r of t e n , the bulk of these e r r o r s being i s o l a t e d e r r o r s . I t i s c l e a r from the above r e s u l t s t h a t , w h i l e e r r o r s a r e . . associated w i t h the fading process, they a l s o occur during periods when the DFE i s p r o v i d i n g a u s e f u l c o n t r i b u t i o n to s i g n a l e q u a l i z a t i o n . The r e s u l t s suggest that even s o p h i s t i c a t e d e s t i m a t i o n techniques may give l i t t l e im-provement over simpler f i x e d - l e v e l feedback schemes w i t h s l o w l y adaptive a.g.c. - 1 5 5 -V I I I CONCLUSIONS This t h e s i s i s concerned p r i m a r i l y w i t h the improvement of bulk data packing d e n s i t i e s on magnetic tape. The concept of the 'magnetic re c o r d i n g channel' t r a n s l a t e s the t h e s i s o b j e c t i v e s i n t o a concern f o r the maximiza-t i o n of channel data r a t e and mi n i m i z a t i o n of e r r o r r a t e . A r e l a t i v e l y com-prehensive review provides background and i n d i c a t e s the present s t a t e of understanding f o r both magnetic recording and conventional communication channels. A h e l i c a l - s c a n video-tape t r a n s p o r t was s e l e c t e d as the v e h i c l e f o r implementation and t e s t i n g of s i g n a l and playback r e c e i v e r designs. The magnetic re c o r d i n g channel was c h a r a c t e r i s e d by the use of balanced two-l e v e l s i g n a l s , but the relevance of the c h a r a c t e r i z a t i o n extends to l i n e a r i z e d a n h y s t e r e t i c r e c o r d i n g i n general. The c h a r a c t e r i z a t i o n revealed a channel which i s approximately l i n e a r but perturbed by a d d i t i v e and m u l t i p l i c a t i v e noises as w e l l as by some no n l i n e a r behaviour. t I n v e s t i g a t i o n of d i r e c t r e -cording w i t h a r b i t r a r y waveforms i s v i r t u a l l y precluded by the s e v e r i t y of the channel n o n l i n e a r i t y . Although a method of c h a r a c t e r i z i n g the gen e r a l i z e d n o n l i n e a r d i s p e r s i v e data channel was developed, the r e s u l t i n g d e s c r i p t i o n gives l i m i t e d i n s i g h t i n t o the problems of s i g n a l and r e c e i v e r design f o r such a channel. However, the method was s u c c e s s f u l l y a p p l i e d to q u a n t i f y the n o n l i n e a r p e r t u r b a t i o n s evident on a magnetic recording channel employing conventional non-return-to-zero (NRZ) s i g n a l l i n g . The h e l i c a l - s c a n recorder provided a channel w i t h moderate (-20 dB) l e v e l s of a d d i t i v e noise as w e l l as no n l i n e a r behaviour. More ser i o u s degradations r e s u l t e d from m u l t i p l i c a t i v e n o i s e (fading) manifest as extended - 156 -(100 b i t s ) periods of reduced playback l e v e l (dropouts). Fading was a s c r i b e d to f l u c t u a t i o n s i n head-tape contact, and the development of models f o r the record and playback processes enabled the d e r i v a t i o n of a d i s t r i b u t i o n f o r head-tape separation. Although the measured channel c h a r a c t e r i s t i c s by no means preclude m u l t i l e v e l s i g n a l l i n g schemes, the s e n s i t i v i t y of such schemes to channel fadi n g and the l o s s of s i g n a l - t o - n o i s e r a t i o (SNR) i n v o l v e d i n channel l i n e a r i z a t i o n make d i r e c t - recorded t w o - l e v e l s i g n a l l i n g schemes more a t t r a c -t i v e . A c cordingly a prototype h i g h - d e n s i t y recording system based on NRZ s i g n a l l i n g was assembled. The r e c e i v e r s t r u c t u r e comprised a f i x e d p r e f i l t e r followed by a seven-tap adaptive t r a n s v e r s a l f i l t e r . Measurement of s p e c t r a and waveforms confirm and i l l u s t r a t e the c o r r e c t operation of the prototype system components. E r r o r r a t e s , cater-"-'.'" gorized as 'burst' or ' i s o l a t e d ' , provide b a s i c measures of system performance. I t was found that burst e r r o r s g e n e r a l l y decrease monotonically w i t h record l e v e l but are r e l a t i v e l y i n s e n s i t i v e to e q u a l i z a t i o n inaccuracy. I s o l a t e d e r r o r s , however, increase r a p i d l y ( e v e n t u a l l y predominating) as the SNR degrades at h i g h record l e v e l s . I s o l a t e d e r r o r s were noted to be s e n s i t i v e to the e f f e c t s of head/preamplifier coupling and to the number of t r a n s v e r s a l f i l t e r taps. The p r e f i l t e r alone provides reasonable channel e q u a l i z a t i o n ; the subsequent t r a n s v e r s a l f i l t e r allows only s m a l l (a f a c t o r of 2) reductions i n e r r o r r a t e , l a r g e l y by f a c i l i t a t i n g the use of higher record l e v e l s . The advantage of adaptive f i l t e r i n g however i s apparent as a r e d u c t i o n i n system s e n s i t i v i t y to parameters such as record l e v e l . Dropouts c o n s t i t u t e the p r i n c i p a l degradation f o r the magnetic r e c o r d -ing channel. This f a c t i s r e f l e c t e d i n the l i m i t e d reductions i n e r r o r r a t e - 157 -a t t r i b u t a b l e to improved e q u a l i z a t i o n . Dropouts r e s u l t i n g i n extended e r r o r bursts can a l s o f r u s t r a t e some e r r o r c o n t r o l techniques, a d i f f i c u l t y which can be avoided by the use of i n t e r l e a v i n g . However, based on measurement of higher order e r r o r s t a t i s t i c s , the r e q u i r e d code spans (47,000 b i t s , f o r example) are almost c e r t a i n l y p r o h i b i t i v e . Erasure decoding i s p a r t i c u l a r l y appropriate f o r a fading channel and allows more moderate code spans (14,000 - 7 —9 b i t s ) . E r r o r r a t e s are t y p i c a l l y reduced from 3 x 10 to below 10 by the use of such codes with rates of approximately 5/6. The a p p l i c a t i o n of d e c i s i o n feedback e q u a l i z a t i o n (DFE) or p a r t i a l response r e c e p t i o n i s suggested by the presence of a d.c. n u l l and an acute high frequency r o l l - o f f i n the magnetic recording channel. Such r e c e i v e r s , however, are s e n s i t i v e to channel fades. From measurements on the prototype system i t appears that DFE compensation at higher frequencies o f f e r s l i t t l e advantage. The a p p l i c a t i o n of DFE as a novel method of compensation f o r the d.c. n u l l i s , however, shown to provide a u s e f u l means of av o i d i n g high e r r o r rates-due to the l a c k of d.c. response or of avoiding the use of s e v e r e l y - c o n s t r a i n e d , d.c.-free codes. Attempts to reduce the e f f e c t s of channel fading on DFE r e c e i v e r s proved unsuccessful. The tape t r a n s p o r t u t i l i z e d throughout t h i s work i s , by very recent standards, a r e l a t i v e l y wide-track machine. Narrower tracks give r i s e to increased a d d i t i v e n o i s e , s l i g h t l y increased m u l t i p l i c a t i v e n o i s e , and to i n t e r t r a c k i n t e r f e r e n c e which can be s i g n i f i c a n t . The advantages of accurate e q u a l i z a t i o n become more apparent under such c o n d i t i o n s . While e x h i b i t i n g higher e r r o r r a t e s the d i g i t a l channel would be l e s s bursty suggesting the use of lower—rate e r r o r - c o r r e c t i n g codes w i t h reduced span; the advantages - 158 -of erasure decoding would be l e s s pronounced. P a r t i a l response and DFE .-become more a t t r a c t i v e as a d d i t i v e noise becomes predominant. Since narrow t r a c k machines are e s s e n t i a l to the development of high bulk packing d e n s i t i e s , i t i s suggested that f u t u r e work concentrate on the a p p l i c a t i o n of simple forms of l i n e a r or DFE r e c e i v e r s to narrow-t r a c k machines. Performance ev a l u a t i o n s may i n c l u d e the e f f e c t s of i n t e r -t rack i n t e r f e r e n c e which predominates at low frequencies. High raw e r r o r rates are to be a n t i c i p a t e d from narrow-track systems and considerable e f f o r t could be expended on the design of e f f i c i e n t and e f f e c t i v e e r r o r c o n t r o l schemes. - 159 -APPENDIX 1 EVALUATION OF THE RATIO OF SIGNAL TO TAPE-NOISE SPECTRAL DENSITIES Tape noise a r i s i n g from the p a r t i c u l a t e nature of the recording medium provides fundamental l i m i t a t i o n s on the cap a c i t y of magnetic r e c o r d -i n g systems. This e v a l u a t i o n of SNR i s s i m i l a r to that of M a l l i n s o n but avoids c e r t a i n dimensional i n c o n s i s t e n c i e s [109, Eqns. ( 9 ) , (13), (14)] and permits comparison of s i g n a l and tape noise s p e c t r a as w e l l as o v e r a l l SNR. Assume that the magnetic medium i s composed of sm a l l p a r t i c l e s w i t h magnetic moment, ±u(Ampere-metre2). The p a r t i c l e s are o r i e n t e d along the d i r e c t i o n , x, of head-tape v e l o c i t y , v, but are otherwise randomly d i s t r i b u t e d (with d e n s i t y n) throughout the medium. Dimensions and axes are defined as f o l l o w s and w i t h reference to F i g . 2.1: a (head-tape separa-t i o n ) , d (recording depth), and d' (depth of medium) a l l l i e along the y - a x i s , w (trackwidth) l i e s along the x - a x i s . Although energy s p e c t r a l d e n s i t y i s oft e n expressed i n volt 2-sec.-? , i n t h i s case the transform i s made along the x- a x i s i n t o the s p a t i a l frequency domain, k, and u n i t s of Ampere 2-metre 2 prove more convenient. "Power" s p e c t r a l d e n s i t y must be i n t e r p r e t e d as energy s p e c t r a l d e n s i t y per u n i t x - a x i s , w i t h u n i t s of Ampere 2-metre. From §2.1.4, the response of an i d e a l i z e d head w i t h small gap. to an elementary magnetized p a r t i c l e i s , k>0 E(k)=juk exp(-yk) (Amp. -m) ( A l . l ) - 160 -where the conjugate nature of the response f o r negative wavenumbers, k<0, i s presumed.. P a r t i c l e s w i t h f i n i t e • l e n g t h , I, provide t h e i r own s p e c t r a l response (2/k&)sin(k&/2), as an a d d i t i o n a l f a c t o r i n ( A l . l ) . For |k|£<l t h i s f a c t o r may be ignored. The energy s p e c t r a l d e n s i t y corresponding to the s i n g l e p a r t i c l e above may be taken as | E ( k ) | 2 . I f the p a r t i c l e s i n the demagnetized tape assume t h e i r sense of magnetization randomly and independently, the noise 'power' s p e c t r a l d e n s i t y , S n ( k ) , i s given by i n t e g r a t i o n of | E ( k ) | 2 over the y and z axes and by i n t e g r a t i o n over u n i t x -axis 1 S n(k) = •w ra+d' (• •l-o J a ' n.(uke y k ) 2 d x d y d z 0 y wnu 2k (1-e ^  ^) e (Amp.2-m) > (A1.2) D e r i v a t i o n of the s i g n a l 'power' s p e c t r a l d e n s i t y may be approached i n a s i m i l a r manner. The recorded s i g n a l , however, i s c h a r a c t e r i z e d by c o r r e l a t i o n between the magnetic moments of adjacent p a r t i c l e s along the y and z axes. The c o r r e l a t i o n , f 2 ( x ) , i s assumed uniform over the y and z axes p e r m i t t i n g d e f i n i t i o n of a mean d e n s i t y , n u f ( x ) , f o r the magnetic moment of p a r t i c l e s . The f u n c t i o n f ( x ) i s the recorded magnetization w i t h a bandwidth of K rad/m. The sampling theorem permits r e d u c t i o n of f ( x ) to a set of independent samples, f ^ ' h ( x - i ^ ) , and leads to the d e f i n i t i o n of an elementary filament w i t h magnetization nuh(x)Sy6z. The response of the playback head to such a fil a m e n t i s E(k)= ny6ySz • H(k) k exp(-ky) (Amp-m) (A1.3) The magnetization i s uniform over the y and z dimensions. The recorded s i g n a l i s represented byK/ir independent samples per metre. Hence the - 161 -s i g n a l 'power' s p e c t r a l d e n s i t y i s S s(k) k f 2 •W t IT 0 • a+d ^ 2 E(k)dydz d = w 2 n 2 u 2 f 2 | ( l - e " d k ) 2 e " 2 a k | H ( k ) l 2 (A1.4) the narrowband SNR i s s 8 0O 2K wnf 2 ( l ~ e ) -2d'k H(k) S N(k) irk 1 - e and the o v e r a l l SNR on a f l a t e q u a l i z e d scheme i s SNR= K r K i dk /{••• s N(k)/s s(k)dk} 0 J o = — Kwn f 2 U 7f K ( l - e - 2 d ' k ) kdk 0 ( l - e " d k ) 2 |H(k)| 2 ^ -1 > (A1.5) (A1.6) I f the recorded magnetization, f ( x ) , has uniform s p e c t r a l d e n s i t y w i t h bandwidth K rad/m, h(x) may be taken as ( s i n Kx)/Kx. Equation (A1.6) then becomes i d e n t i c a l to [109, Eqn. (15)], and leads to the same approxima-t i o n f o r wideband systems, 2dK>l. SNR = 4 iron f 2 / K 2 (A1.7) For NRZ s i g n a l l i n g , f 2 , which represents the r.m.s. l e v e l of magnetization, i s c l o s e to u n i t y . The s p e c t r a l r o l l o f f i m p l i c i t i n the use of a re c t a n g u l a r s i g n a l l i n g waveform, h ( x ) , causes a r e d u c t i o n of about 4 dB i n the approximate SNR, (A1.7), f o r f l a t e q u a l i z a t i o n . Record process l o s s e s , appearing as a h y p o t h e t i c a l spacing l o s s , a w , can be s i m i l a r l y i n c l u d e d , g i v i n g : SNR N R Z - |-wnb2 exp(-2ira w/b) (A1.8) 162 where b is the recorded b i t length. This fi n a l expression is similar to those quoted in [4, 110]. - 163 -APPENDIX >2> DETAILS OF VIDEO TAPE TRANSPORT AND OF VIDEO TAPES IVC 825A v i d e o tape r e c o r d e r t r a n s p o r t : l o n g i t u d i n a l tape speed l o n g i t u d i n a l tape speed s t a b i l i t y v i d e o r e c o r d i n g format: h e l i c a l s c a n , oc-wrap, s i n g l e head t r a c k w i d t h guard band scan a n g l e t r a c k l e n g t h r e l a t i v e head-tape speed v i d e o head: gap(nominal) p o l e f a c e o v e r a l l dimension c o u p l i n g m a t e r i a l l i f e v i d e o performance: bandwidth > -4 dB rpk.-pk. s i g n a l / r.m.s. n o i s e h o r i z o n t a l j i t t e r (7.5 ms time c o n s t , on h o r i z . synch.) m o d u l a t i o n c e n t r e f r e q u e n c y , peak d e v i a t i o n 0.0.76 m/.s-<0.25% r.m.s, 152 pm 89 um 4.75° 0.31 m 18.4 i/s 1.3 um 2 mm 4 mm 13 t u r n s f e r r i t e > 1000 hours @ 4.2 43 MHz dB 0.5% p i c t u r e w i d t h p u l s e f r e q u e n c y 6 . 0 , ± 0 . 6 MHz Tapes: tape #1: :; m a n u f a c t u r e r ' s number dimensions) s u b s t r a t e c o a t i n g c o a t i n g t h i c k n e s s c o e r c i v i t y r e t e n t i v i t y ' 3M-462 28'. _um x 25.4 mm x 660; m p o l y e s t e r l o n g i t u d i n a l l y o r i e n t e d Co-^Fe 0 500 Oe 1350 Gauss dropouts (<-18 dB, >10 _us, @ 6 MHz ) tapes #2,#3: m a n u f a c t u r e r i s number <20 per min. 3M-461 ( as #1 but p o l y e s t e r s u b s t r a t e p r e - s t r a i n e d ) tape #4: ma n u f a c t u r e r ' s number c o e r c i v i t y r e t e n t i v i t y ( e t c . as #3 ) 3M-455 ' J 650 Oe 1200 Gauss - 164 -APPENDIX 3 ZERO-FORCING ADAPTIVE TRANSVERSAL FILTERING Z e r o - f o r c i n g (ZF) i s an e q u a l i z a t i o n technique d i r e c t e d at the e l i m i n a t i o n of intersymbol i n t e r f e r e n c e ( I S I ) . In co n t r a s t to minimum mean square e q u a l i z a t i o n , ZF ignores the presence of a d d i t i v e n o i s e . However, at high s i g n a l - t o - n o i s e r a t i o (SNR) the tap gains f o r long t r a n s v e r s a l f i l t e r s become the same w i t h e i t h e r technique. At low SNR, ZF g e n e r a l l y gives i n f e r i o r r e s u l t s but does a l l o w the use of p a r t i c u l a r l y simple adap-t i o n algorithms. Design f o r one such a l g o r i t h m i s discussed i n the f i r s t p a rt of t h i s appendix, w h i l e the i n a c c u r a c i e s a r i s i n g from the f i n i t e t r a n s v e r s a l f i l t e r length are assessed i n the f i n a l paragraph. Let e ^ v ^ - a ^ be the r e s i d u a l e r r o r on the e q u a l i z e d , sampled playback s i g n a l ; ^=±1 i s the hypothesized r e c e i v e d b i t . To e l i m i n a t e I S I the automatic e q u a l i z e r must force E{e,a 1 .} to zero at a l l j f o r which k k—3 s i g n i f i c a n t I S I occurs. Lucky [244] describes the e f f e c t i v e n e s s of an ... algor i t h m which forces E{sgn(e 1 )a, .} to zero by incrementing or decrementing k k—j the j - t h tap g a i n , c., i n response to sgn(s,)a, .. This a l g o r i t h m i s 3 k k 2 adopted i n the prototype system although, f o r convenience of implementation, the tap gains are incremented as n sgn(Ac ) = -sgn £ s g n ( E k N > a k N * (A3.1) J k=0 J where ( s t a r t i n g w i t h a r b i t r a r y k=0) inf o r m a t i o n has been accumulated by sampling every N-th b i t over a block of nN b i t s . Assume that c_. i s the value of the j - t h tap gain r e q u i r e d to e l i m i n a t e I S I , and c^+ i A c ^ i s the current value of t h i s tap gain. In the - 165 -presence of Gaussian n o i s e , variance a 2 , and f o r s m a l l ±Ac^/6a iAc.= 1 iAc.i P r { s g n ( £ k ) a =1} = 1-Q i—f- ) = (A3.2) where Q(') i s the a n t i - c u m u l a t i v e , zero-mean, u n i t - v a r i a n c e normal d i s t r i b u -t i o n . The sum of n such terms, as i n (A3.1), can be approximated by a Gaussian d i s t r i b u t i o n w i t h mean 2niAc_./fz~n a and variance n; the assumptions are l a r g e N (independence of terms), s m a l l iAc^/a ( s m a l l e r r o r i n tap gain s e t t i n g ) , and l a r g e n ( f o r c e n t r a l l i m i t theorem). The p r o b a b i l i t y of a negative tap gain increment i s t h e r e f o r e i— i A c j vn P r {sgnACj=-l} = 1-Q ( 2 ^ i A c ^ / v ^ c r ) j+ —- -— (A3.3) By analogy with the continuous d i s t r i b u t i o n generated by a massless e l a s t i c a l l y -bound p a r t i c l e with Gaussian perturbation [124], the expected magnitude of residual I S I for each tap, for the above algorithm i n the steady state i s E{ |e| } = Johcjl^ (A3.4) I t i s d e s i r a b l e to keep t o t a l d i s t o r t i o n due to tap i n a c c u r a c i e s below -30dB or roughly -40 dB per tap. The tap gain increments, Ac_., are approximately 1%. A v a r i e t y of sources c o n t r i b u t e to the noise v a r i a n c e , a: -27 dB of a d d i t i v e n o i s e , -22 dB of m u l t i p l i c a t i v e n o i s e , -18 dB of no n l i n e a r d i s t o r t i o n , -30 dB from t r u n c a t i o n of the t r a n s v e r s a l f i l t e r l e n g t h , and, of course -30 dB from tap gain i n a c c u r a c i e s . The standard d e v i a t i o n i s thus a=0.16, g i v i n g r i s e to an accumulator s i z e from (A3.4) of n=64. The f i n a l implementation contained an accumulator of s i z e 2048, . some t h i r t y times l a r g e r than a n t i c i p a t e d . The s e n s i t i v i t y of n i n (A3.4) to E{|e|} and 0 i s apparent; s e n s i t i v i t i e s to the assumed tap-gain independence - 166 -and Gaussian noise d i s t r i b u t i o n are l e s s obvious. The t r a n s v e r s a l f i l t e r i s c a l l e d upon to c o r r e c t severe s p e c t r a l r o l l o f f 20 dB across the Nyquist bandwidth) and the adjustment al g o r i t h m thus causes the tap gain s e t t i n g s to be s t r o n g l y interdependent aggravating s e t t l i n g i n a c c u r a n c i e s . The noise described by the variance a 2 i s non-Gaussian and contains l a r g e b i n a r y components. The presence of a s i n g l e such component, ±b, leads to an a d d i t i o n a l f a c t o r exp(-b 2/2a 2) i n the l a t t e r term of (A3.2); the e f f e c t s of t h i s f a c t o r may be followed through to (A3.4). These two c o n s i d e r a t i o n s probabably e x p l a i n the l a r g e accumulator s i z e which was found necessary i n order to l i m i t the steady-state 'wander' on tap gain s e t t i n g s to two or three increments. The f i n i t e l e ngth of the t r a n s v e r s a l f i l t e r causes i n e x a c t equal-i z a t i o n . These t r u n c a t i o n e r r o r s are depicted i n F i g . A3.1 as a f u n c t i o n of the slope across the Nyquist bandwidth. A s p e c t r a l response, exp(f-a|o)|) , i s assumed which i s appropriate to the form of the s i g n a l presented to the t r a n s v e r s a l f i l t e r . Non-zero phase response g e n e r a l l y increases the l e v e l of t r u n c a t i o n d i s t o r t i o n , and F i g . A3.1 may be i n t e r p r e t e d as a lower bound. Eye c l o s u r e w i t h seven taps occurs f o r a s p e c t r a l slope of 57 dB i n comparison to 16 dB f o r the unequalized response. - 167 -SLOPE ACROSS NYQUIST BANDWIDTH, e" a T T / T Figure A3.1 E q u a l i z a t i o n e r r o r r e s u l t i n g from the use of a 7-tap z e r o - f o r c i n g t r a n s v e r s a l f i l t e r upon a s i g n a l of the r • .-a I CO I form, ' . - 168 -REFERENCES [1] J.C. MALLINSON, " T u t o r i a l Review of Magnetic Recording", Proc. IEEE, v o l . 64, no.2, pp.196-208, Feb. 1976. 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