A Unified Perspective on Parity- and Syndrome-Based Binary Data Compression Using Off-the-Shelf Turbo Codecs

We consider the problem of compressing memoryless binary data with or without side information at the decoder. We review the parity- and the syndrome-based approaches and discuss their theoretical limits, assuming that there exists a virtual binary symmetric channel between the source and the side information, and that the source is not necessarily uniformly distributed. We take a factor-graph-based approach in order to devise how to take full advantage of the ready-available iterative decoding procedures when turbo codes are employed, in both a parity- or a syndrome-based fashion. We end up obtaining a unified decoder formulation that holds both for error-free and for error-prone encoder-to-decoder transmission over generic channels. To support the theoretical results, the different compression systems analyzed in the paper are also experimentally tested. They are compared against several different approaches proposed in literature and shown to be competitive in a variety of cases.