Interactive encoding and decoding based on syndrome accumulation over binary LDPC ensembles: Universality and rate-adaptivity

Abstract

In this paper we investigate the performance of linear interactive encoding and decoding based on syndrome accumulation(SA-IED) over binary LDPC ensembles. Assume that the source alphabet is GF(2), and the side information alphabet is finite. It is shown that we can construct universal SA-IED schemes, which are asymptotically optimal for any stationary ergodic source-side information pair. Our analysis further shows that the word error probability will approach 0 sub-exponentially with respect to the block length, while at the same time, the rate approaches H(X|Y) as the average variable node degree of the LDPC ensemble approaches ∞. Further, if the source and side information are correlated through a binary symmetrical memoryless channel, but the cross-over probability of the channel is not known to either the encoder or the decoder, our result on the performance of SA-IED can be further improved for LDPC ensembles with finite average variable node degree. Simulation results on binary source-side information pairs confirm the theoretical analysis above, and further show that SA-IED schemes using LDPC codes coupled with linear time belief propagation decoding consistently outperform Slepian-Wolf coding schemes based on LDPC codes.