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On the undetected error probability of BCH codes Chong, William
Abstract
The undetected error probability, Pu(ε), for a variety of Bose-Chaudhuri-Hocquenghem (BCH) codes, used solely for error detection on a binary symmetric channel (BSC) with cross-over probability, is studied. The undetected error probability can be evaluated if the weight distribution of the code or its dual is available. Unfortunately, no general expression for the weight distribution of BCH codes which correct more than 3 errors is known. A few BCH codes for which it is computationally feasible to determine the weight clisiribution are studied. A proper code is one for which Pu(ε) increases monotonically with for 0 ≤ε≤0.5 Algorithms for determining the properness of linear block codes based on Fourier’s and Sturm’s Theorems for finding the number of real roots of a polynomial in a given interval are investigated. They are useful in cases where the weight distribution is known. Kasami et al have studied linear programming methods for obtaining upper and lower bounds on the weight distributions of 4- and 5-error-correcting BCH codes. Here, two methods which can be used to improve these bounds are presented. The first method uses the minimum distance of a dual BCH code. The second method requires, in addition, the number of codewords at the minimum distance. Comparisons between the improved bounds and the Kasami bounds are given for several BCH codes.
Item Metadata
Title |
On the undetected error probability of BCH codes
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1992
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Description |
The undetected error probability, Pu(ε), for a variety of Bose-Chaudhuri-Hocquenghem (BCH) codes, used solely for error detection on a binary symmetric channel
(BSC) with cross-over probability, is studied. The undetected error probability can be
evaluated if the weight distribution of the code or its dual is available. Unfortunately, no
general expression for the weight distribution of BCH codes which correct more than 3
errors is known. A few BCH codes for which it is computationally feasible to determine
the weight clisiribution are studied.
A proper code is one for which Pu(ε) increases monotonically with for 0 ≤ε≤0.5
Algorithms for determining the properness of linear block codes based on Fourier’s and
Sturm’s Theorems for finding the number of real roots of a polynomial in a given interval
are investigated. They are useful in cases where the weight distribution is known.
Kasami et al have studied linear programming methods for obtaining upper and lower
bounds on the weight distributions of 4- and 5-error-correcting BCH codes. Here, two
methods which can be used to improve these bounds are presented. The first method uses
the minimum distance of a dual BCH code. The second method requires, in addition,
the number of codewords at the minimum distance. Comparisons between the improved
bounds and the Kasami bounds are given for several BCH codes.
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Extent |
1079156 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2008-12-23
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0065187
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1992-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.