Interactive Encoding and Decoding Based on Binary LDPC Codes with Syndrome Accumulation

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Interactive encoding and decoding based on binary low-density parity-check codes with syndrome accumulation (SA-LDPC-IED) is proposed and investigated. Assume that the source alphabet is GF(2), and the side information alphabet is finite. It is first demonstrated how to convert any classical universal lossless code Cₙ (with block length n and side information available to both the encoder and decoder) into a universal SA-LDPC-IED scheme. It is then shown that with the word error probability approaching 0 sub-exponentially with n, the compression rate (including both the forward and backward rates) of the resulting SA-LDPC-IED scheme is upper bounded by a functional of that of Cₙ, which in turn approaches the compression rate of Cₙ for each and every individual sequence pair (xⁿ,yⁿ) and the conditional entropy rate H(X |Y) for any stationary, ergodic source and side information (X, Y) as the average variable node degree l of the underlying LDPC code increases without bound. When applied to the class of binary source and side information (X, Y) correlated through a binary symmetrical channel with cross-over probability unknown to both the encoder and decoder, the resulting SA-LDPC-IED scheme can be further simplified, yielding even improved rate performance versus the bit error probability when l is not large. Simulation results (coupled with linear time belief propagation decoding) on binary source-side information pairs confirm the theoretic analysis, and further show that the SA-LDPC-IED scheme consistently outperforms the Slepian-Wolf coding scheme based on the same underlying LDPC code. As a by-product, probability bounds involving LDPC established in the course are also interesting on their own and expected to have implications on the performance of LDPC for channel coding as well.