Optimal and sub-optimal decoding for vector quantization over noisy channels with memory

This paper considers optimal decoding for vector quantization over a noisy channel with memory. The optimal decoder is soft in the sense that the unquantized channel outputs are utilized directly for decoding, and no decisions are taken. Since the complexity of optimal decoding is high, we also present an approach to sub-optimal decoding, of lower complexity, being based on Hashimoto's generalization of the Viterbi algorithm. We furthermore study optimal encoding and combined source-channel coding. Numerical simulations demonstrate that both optimal and sub-optimal soft decoding give prominent gain over decision-based decoding.