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Analysis and optimization of differential PCM systems operating on noisy communication channels Chang, Ke-yen

Abstract

A closed-form analytical expression for the output signal-to-noise ratio (SNR₀) of differential PCM systems operating on noisy communication channels is obtained. A procedure is then proposed for maximizing SNR₀ by joint optimization of the quantizer, predictor, sampling rate, and bandwidth. Several examples are considered, including one- and two-sample feedback systems excited by speech and video signals. Various techniques for reducing channel errors are then discussed. The predictor used in the DPCM system is linear and time invariant, but otherwise arbitrary. As with PCM, contributions to output signal distortion can be expressed as a sum of three distinct terms resulting, respectively, from quantization errors, channel transmission errors, and mutual errors arising from interaction between quantization and channel errors. Constraints on the predictor coefficients for channel errors not to build up unlimitedly are presented. When a conventional optimum linear predictor is used, transmission errors are shown to be no more serious for DPCM than for PCM. The values of SNR₀ obtainable from DPCM are also compared with the theoretical bound obtained from the rate-distortion function. For a well-designed DPCM system, the value of SNR₀ is shown to be considerably higher than that for a well-designed PCM system operating on the same digital channel, even if the channel is noisy. In considering examples, particular attention is devoted to determining maximum values for SNR₀ and to examining the dependence of SNR₀ on predictor coefficient values, number of quantization levels, message statistics, and channel error probability. Implications of this dependence on system design are noted. Among the various techniques investigated for combating channel noise are channel encoding, periodic resetting, and pseudo-random resetting. These techniques are further evaluated subjectively with two video images. DPCM systems with coarse quantization are studied. The fedback quantization noise is considered in optimizing the predictor. Simple equations for the optimum predictor coefficients and the resulting SNR₀ are derived.

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