On the Reliability Function of Variable-Rate Slepian-Wolf Coding

TL;DR

This paper characterizes the reliability function of variable-rate Slepian-Wolf coding, showing it can outperform fixed-rate codes in rate-error tradeoff and maintain a bounded correct decoding probability below the Slepian-Wolf limit.

Contribution

It provides a complete characterization of the reliability function for variable-rate Slepian-Wolf coding near the limit, highlighting its advantages over fixed-rate codes.

Findings

Bounds coincide near the Slepian-Wolf limit, enabling full reliability characterization.

Variable-rate codes outperform fixed-rate codes in rate-error tradeoff.

Decoding probability remains bounded away from zero below the Slepian-Wolf limit.

Abstract

The reliability function of variable-rate Slepian-Wolf coding is linked to the reliability function of channel coding with constant composition codes, through which computable lower and upper bounds are derived. The bounds coincide at rates close to the Slepian-Wolf limit, yielding a complete characterization of the reliability function in that rate regime. It is shown that variable-rate Slepian-Wolf codes can significantly outperform fixed-rate Slepian-Wolf codes in terms of rate-error tradeoff. The reliability function of variable-rate Slepian-Wolf coding with rate below the Slepian-Wolf limit is determined. In sharp contrast with fixed-rate Slepian-Wolf codes for which the correct decoding probability decays to zero exponentially fast if the rate is below the Slepian-Wolf limit, the correct decoding probability of variable-rate Slepian-Wolf codes can be bounded away from zero.