Soft-decoding combined trellis-coded quantization/modulation

The well-known Bahl-Cocke-Jelinek-Raviv (BCJR) symbol-by-symbol MAP algorithm (1974) is modified as a soft-decoder for combined TCQ/TCM. The optimal TCQ encoder is derived for the soft-decoding BCJR algorithm. The TCQ encoder and the soft-decoder are optimized iteratively for minimum distortion. Significant performance improvement is achieved for both memoryless Gaussian and uniform source, especially for very noisy channel.