Optimum Weighted PCM for Speech Signals

Weighted digital modulation schemes which provide bit error probabilities matched to the PCM bits with respect to their sensitivity to digital errors are analyzed. The channel is additive, white Gaussian. The PCM system has arbitrary code, companding law and input signal density function. Especially optimum weighted PSK/PCM and QAM/PCM are given for speech signals. The average channel signal to noise ratio is kept constant when schemes are compared. We obtain a channel signal to noise ratio gain in threshold extension of 2 dB for standard 8 bit PCM. The performance of suboptimum schemes, where the number of different bit error probability levels are smaller than the number of PCM bits are also studied. Two levels per 8 bit PCM word yield more than half of the achievable gain (in dB) and 4 levels is almost equal to optimum.