Soft decoding for vector quantization over noisy channels with memory

We provide a general treatment of optimal soft decoding for vector quantization over noisy channels with finite memory. The main result is a recursive implementation of optimal decoding. We also consider an approach to suboptimal decoding, of lower complexity, being based on a generalization of the Viterbi algorithm. Finally, we treat the problem of combined encoder-decoder design. Simulations compare the new decoders to a decision-based approach that uses Viterbi detection plus table lookup decoding. Optimal soft decoding significantly outperforms the benchmark decoder. The introduced suboptimal decoder is able to perform close to the optimal and to outperform the benchmark scheme at a comparable complexity.