Upper bounds on the channel distortion of combined TCQ/CPM systems

Joint source and channel (JSC) coding using combined trellis coded quantization (TCQ) and continuous phase modulation (CPM) is studied. The channel is assumed to be the additive white Gaussian noise (AWGN) channel. Analytical bounds on the channel distortion for jointly designed TCQ/CPM systems with maximum likelihood sequence detection (MLSD) are developed. For a memoryless uniform source, our upper bounds for the investigated TCQ/CPM systems are shown to be asymptotically tight for increasing channel signal-to-noise ratio (SNR) values. It is concluded that the minimum Euclidean distance of the CPM system alone is not enough to evaluate the performance of the combined TCQ/CPM systems. The number of the error events having the minimum Euclidean distance and the total distortion caused by those error events also affect the asymptotic performance of the investigated systems. This work provides an analysis tool to estimate the performance for a given combined TCQ/CPM system. The analysis method is very general, it may be applied to any trellis based JSC coding schemes.