Asymmetric PSK Constellation Design to Minimize Distortion in PCM Data Transmission

An analog signal sent over a digital communication infrastructure must undergo sampling, quantization and compression. Although most practical source coders are multiresolution in character (i.e., overall quality of the decoded information are not contributed evenly from different portions of the source data), this factor is rarely taken into account in traditional digital wireless communication systems design. For instance, in pulse-coded modulation (PCM) of speech signals, the importance of the most significant bit far outweighs that of the least significant bit. Multiresolution modulation schemes that consist of nonuniformly spaced symbols allow for unequal error protection (UEP) of transmitted bits within a symbol according to their importance. In this article, we investigate the problem of matching asymmetrical phase shift keying (PSK) modulations with multiresolution temporal waveform coding scheme to minimize the effect of transmission errors in 1D and 2D analog signals. In particular, we capitalize on the concept of generalized hierarchical PSK constellations and propose a simplified PSK constellation which is capable of providing more than two levels of unequal error protection. Numerical results reveal that both mean and variance of signal distortion can be reduced considerably, especially in bad channel conditions, by mapping the PCM bits to a suitable asymmetric PSK constellation. This embedding gain may be translated into energy or spectral efficiency improvement over the baseline uniform PSK case for a specified distortion level.