Efficient MMSE Source Decoding Over Noisy Channels

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 the noisy channel degradations. Researchers have recently developed techniques to employ this redundancy to either assist the channel decoder for improved performance or design better source decoders. However, the method used for modeling the redundancy is a first-order Markov model which fails to encapsulate all the remaining redundancies. In this work, we present a family of solutions for the asymptotically optimum MinimumMean Squared Error reconstruction of a source over memoryless noisy channels when the redundancy in the source encoder output stream is exploited in the form of a γ-order Markov model (γ ≥ 1) and a delay of δ, δ > 0, is allowed in the decoding process. We demonstrate that the proposed solutions provide a wealth of trade-offs between computational complexity and the memory requirements. We also present a simplified MMSE decoder which is optimized to minimize the computational complexity. Considering the same problem setup, we present several other Maximum A Posteriori symbol and sequence decoders as well. Numerical results are presented which demonstrate the efficiency of the proposed algorithms.