Sequential decoding for lossless streaming source coding with side information

TL;DR

This paper introduces a sequential decoding scheme for lossless streaming source coding with side information, achieving exponential error decay and bounded computation, applicable also to joint source-channel coding with simulations.

Contribution

It proposes a novel Stack Algorithm-based sequential coding scheme with a variable bias, providing delay-universal lossless coding with side information and extending to joint source-channel coding.

Findings

Error probability decays exponentially with delay

The mean of the computation variable is bounded

Simulation results demonstrate effectiveness

Abstract

The problem of lossless fixed-rate streaming coding of discrete memoryless sources with side information at the decoder is studied. A random time-varying tree-code is used to sequentially bin strings and a Stack Algorithm with a variable bias uses the side information to give a delay-universal coding system for lossless source coding with side information. The scheme is shown to give exponentially decaying probability of error with delay, with exponent equal to Gallager's random coding exponent for sources with side information. The mean of the random variable of computation for the stack decoder is bounded, and conditions on the bias are given to guarantee a finite $\rho^{th}$ moment for $0 \leq \rho \leq 1$. Further, the problem is also studied in the case where there is a discrete memoryless channel between encoder and decoder. The same scheme is slightly modified to give a joint-source channel encoder and Stack Algorithm-based sequential decoder using side information. Again, by a suitable choice of bias, the probability of error decays exponentially with delay and the random variable of computation has a finite mean. Simulation results for several examples are given.