Vector quantization over Gaussian channels with memory

We consider the problem of transmission of a vector quantized Markov source over channels with memory. A maximum a posteriori (MAP) symbol-by-symbol algorithm is used to obtain a soft decision VQ decoder which approximates the minimum mean-squared error estimate of the source vectors. This algorithm also accounts for the residual redundancy left at the vector quantizer output. The results obtained using this approach are compared to the results obtained by using a hard decision VQ decoder. Also, this decoder is used in conjunction with a channel optimized vector quantizer (COVQ), which is designed using a nonrecursive symbol by symbol detector instead of the optimal MAP symbol by symbol detector, thus reducing the dimensionality considerably. We also introduce simplified design procedure, obtained by determining the channel transition matrix of an equivalent discrete memoryless channel, and then applying well known COVQ procedures for discrete memoryless channels. We find that the soft decision decoder considerably improves reconstruction fidelity at low channel SNR's, and that COVQ further improves the performance.