Optimum PCM Codes for DPSK

The effect of digital errors in PCM systems for speech signals depends on the PCM code used. The standard binary folded PCM code is superior to the natural binary code but it is not optimum. This paper considers PCM codes especially designed to be insensitive to the double error patterns produced by DPSK. It is concluded that the dynamic range with especially designed PCM codes is considerably extended compared to standard binary folded PCM. Special simplified interleaving schemes and optimum PCM codes for coherent PSK are also considered. The dynamic behavior of various PCM codes is calculated and compared, e.g., asymptotically optimum PCM codes for DPSK, binary folded PCM with and without interleaving, asymptotically optimum PCM codes for coherent PSK, etc. We conclude that the best scheme for DPSK is simplified interleaving and an optimum PCM code for PSK. This paper also gives analytical formulas for double error -factors for standard PCM systems.