Exponent Function for One Helper Source Coding Problem at Rates outside the Rate Region

TL;DR

This paper establishes a strong exponential decay rate for the error probability in the one helper source coding problem outside the rate region, strengthening the known strong converse theorem.

Contribution

It provides a new explicit lower bound on the error exponent, demonstrating the exponential decay of error probability outside the rate region.

Findings

Error probability tends to one exponentially outside the rate region.

Derived an explicit lower bound for the error exponent.

Strengthened the strong converse theorem for the problem.

Abstract

We consider the one helper source coding problem posed and investigated by Ahlswede, K\"orner and Wyner. In this system, the error probability of decoding goes to one as the source block length $n$ goes to infinity. This implies that we have a strong converse theorem for the one helper source coding problem. In this paper we provide a much stronger version of this strong converse theorem for the one helper source coding problem. We prove that the error probability of decoding tends to one exponentially and derive an explicit lower bound of this exponent function.