Almost-Noiseless Joint Source-Channel Coding-Decoding of Sources with Memory

The design of joint source-channel encoders and decoders to obtain low block error rate is considered in this paper. Linear encoders based on various low-density structures, and in particular the new class of Lotus codes are considered along with belief propagation decoders. We extend the schemes we recently introduced to design universal linear data compressors for sources with memory to the case of transmission through a noisy channel. The resulting encoders and decoders have linear complexity in the length of the source block and are particularly effective in the moderate blocklength regime relative to the conventional separate source-channel encoding approach. The availability of a modicum of feedback can be very beneficial to simplify the complexity and blocklength required to achieve a predetermined reliability level. Several new feedback schemes tailored to belief propagation decoding are proposed.