Improved joint source-channel decoding for variable-length encoded data using soft decisions and MMSE estimation

Abstract

Summary form only given. We develop improved joint source-channel (JSC) methods for decoding variable length encoded data based on residual source redundancy. Until very recently, all JSC methods based on residual redundancy assumed fixed length codewords. Recently, a practically realizable system which performed best over a significant range of channel conditions consisting of inner binary convolutional (BC) (bit-level) decoding, followed by outer (symbol-level) approximate maximum a posteriori (MAP) JSC decoding was suggested. Here we suggest two ways of improving on this method. First, a straightforward improvement is realized by using soft/probabilistic bit decisions output by the BC decoder, rather than hard decisions. Second, the JSC decoder can itself generate soft/probabilistic output, at the symbol level. The exact VLC minimum mean-squared error (MMSE) decoder has large complexity, similar to the exact MAP method, because the number of states increases with time. Thus we suggest an approximate MMSE method. In this approximate scheme, we first form a reduced directed graph, using the same MAP state reduction procedure as used for approximate MAP JSC decoding. Next, we rearrange the remaining states to form an (equivalent) directed graph. We then apply the forward/backward algorithm and a state merging procedure to this reduced graph to get approximate a posteriori probabilities, used for MMSE estimation.