Efficient source decoding over memoryless noisy channels using higher order Markov models

Exploiting the residual redundancy in a source coder output stream during the decoding process has been proven to be a bandwidth-efficient way to combat noisy channel degradations. This redundancy can be employed to either assist the channel decoder for improved performance or design better source decoders. In this work, a family of solutions for the asymptotically optimum minimum mean-squared. error (MMSE) reconstruction of a source over memoryless noisy channels is presented when the redundancy in the source encoder output stream is exploited in the form of a gamma-order Markov model (gamma greater than or equal to 1) and a delay of delta, delta > 0, is allowed in the decoding process. It is demonstrated that the proposed solutions provide a wealth of tradeoffs between computational complexity and the memory requirements. A simplified MMSE decoder which is optimized to minimize the computational complexity is also presented. Considering the same problem setup, several other maximum a posteriori probability (MAP) symbol and sequence decoders are presented as well. Numerical results are presented which demonstrate the efficiency of the proposed algorithms.