Abstract
A closed-form analytical expression is obtained for the output signal-to-noise ratio (SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> ) of differential PCM systems operating on noisy digital channels. A procedure is then proposed for maximizing SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> by joint optimization of the quantizer, predictor, and sampling rate. Several examples are considered, including one- and two-sample feedback systems excited by speech and video (Gaussian) signals. 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 separate terms resulting, respectively, from quantization errors, channel transmission errors, and mutual errors arising from interaction between quantization and channel errors. When a conventional optimum linear predictor is used, transmission errors are shown to be no more serious for DPCM than for PCM. The results show that SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> for a well-designed DPCM system is considerably higher than 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 SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> and to examining the dependence of SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> on predictor coefficient values, number of quantization levels, sampling rate, message statistics, and channel error probability. Implications of this dependence on system design are noted.
Published Version
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