Interactive Encoding and Decoding Based on Binary LDPC Codes With Syndrome Accumulation
Jin Meng, En‐hui Yang · IEEE Transactions on Information Theory · 2012
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 isGF(2), and the side information alphabet is finite. It is first demonstrated how to convert any classical universal lossless codeCn(with block lengthnand 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 subexponentially withn, 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 ofCn, which in turn approaches the compression rate ofCnfor 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 degreel̅of 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 crossover 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 whenl̅is 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.