The present study is a sequel to the authors' 1972 paper [1] where the output signal-to-noise ratio SNRois obtained for nonadaptive differential pulse-code modulation (DPCM) systems with an arbitrary linear predictor operating on noisy digital channels. Important stability constraints for an arbitrary linear predictor are obtained. A complete analytical study of previous line-line-and-sample feedback systems is presented. The SNRoimprovement over previoussample feedback is found to increase from approximately 2.6 dB for error-free channels to 4.1 dB for noisy channels. Optimization of the predictor for noisy channel usage is shown to greatly reduce the sensitivity of SNRoto variations in message and channel parameters, while use of the resulting predictor on error-free channels yields SNRovalues which are almost as good as those obtained when the predictor is optimized for error-free channels. Reduction of the effects of digital channel errors on SNRousing various methods, including periodic or pseudorandom resetting are considered briefly. Hardcopy results from computer-simulated DPCM monochrome image transmission systems corroborate our analytical results.

A closed-form analytical expression is obtained for the output signal-to-noise ratio (SNR0) of differential PCM systems operating on noisy digital channels. A procedure is then proposed for maximizing SNR0by 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 SNR0for 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 SNR0and to examining the dependence of SNR0on predictor coefficient values, number of quantization levels, sampling rate, message statistics, and channel error probability. Implications of this dependence on system design are noted.

The method of using auxiliary random noise to unbias the output of the multilevel digital correlator is investigated. It is shown that any random noise satisfying certain conditions may be used. The uniformly distributed noise that has been used previously in the polarity-coincidence correlator is a special case. Discretely distributed auxiliary noise, although not satisfying the conditions, has the same effect as quantizing the input signals more finely. The mean-square error of this modified digital correlator is analyzed.