Non-Asymptotic Converse Bounds Via Auxiliary Channels

TL;DR

This paper introduces a general method for deriving non-asymptotic converse bounds on channel capacity using auxiliary channels, with specific results for various symmetric channels and improved bounds for channels with feedback.

Contribution

It proposes a novel, general derivation technique for non-asymptotic converse bounds applicable to weakly symmetric channels, including specialized results for QEC, BSC, and feedback scenarios.

Findings

Bounds are comparable to state-of-the-art for QEC and BSC.

Tighter bounds achieved for QEC with stop feedback.

Method is applicable to a broad class of symmetric channels.

Abstract

This paper presents a new derivation method of converse bounds on the non-asymptotic achievable rate of discrete weakly symmetric memoryless channels. It is based on the finite blocklength statistics of the channel, where with the use of an auxiliary channel the converse bound is produced. This method is general and initially is presented for an arbitrary weakly symmetric channel. Afterwards, the main result is specialized for the $q$-ary erasure channel (QEC), binary symmetric channel (BSC), and QEC with stop feedback. Numerical evaluations show identical or comparable bounds to the state-of-the-art in the cases of QEC and BSC, and a tighter bound for the QEC with stop feedback.