Digital communications systems commonly use compression (source coding) and error control (channel coding) to allow efficient and robust transmission of data over noisy channels. When compression is imperfect, some residual redundancy remains in the transmitted data and can be exploited at the decoder to improve the decoder's probability-of-error performance. A new approach to joint source-channel maximum a posteriori probability (MAP) decoding applicable to systems employing variable-length source codes (VLCs) was previously developed by the authors-the resulting joint decoder's structure is similar to that of the conventional Viterbi decoder. This paper extends the authors' previous work to address the problem of error propagation, an inherent problem with using VLCs. Options considered include list decoding, trellis-pruning, and composite schemes. Simulation results presented show that the proposed techniques can result in significant improvement in decoding performance.

One-step majority-logic decoding is one of the simplest algorithms for decoding cyclic block codes. However, it is an effective decoding scheme for very few codes. This paper presents a generalization based on the "common-symbol decoding problem." Suppose one is given M (possibly corrupted) codewords from M (possibly different) codes over the same field; suppose further that the codewords share a single symbol in common. The common-symbol decoding problem is that of estimating the symbol in the common position. This is equivalent to one-step majority logic decoding when each of the "constituent" codes is a simple parity check. This paper formulates conditions under which this decoding is possible and presents a simple algorithm that accomplishes the same. When applied to decoding cyclic block codes, this technique yields a decoder structure ideal for parallel implementation. Furthermore, this approach frequently results in a decoder capable of correcting more errors than one-step majority-logic decoding. To demonstrate the simplicity of the resulting decoders, an example is presented.>