Ensemble-Tight Second-Order Asymptotics and Exponents for Guessing-Based Decoding with Abandonment

TL;DR

This paper analyzes guessing-based decoding with abandonment for discrete memoryless channels, deriving tight asymptotics and exponents, and showing its efficiency surpasses traditional methods under certain conditions.

Contribution

It provides the first ensemble-tight second-order asymptotics and exponents for guessing-based decoders with abandonment, advancing understanding of their performance limits.

Findings

Guessing-based decoding is more efficient than testing-based decoding when channel capacity exceeds half the input entropy.

The paper characterizes the optimal second-order region in terms of code and abandonment rates.

Error and strong converse exponents are expressed through channel coding and abandonment exponents.

Abstract

This paper considers guessing-based decoders with abandonment for discrete memoryless channels in which all codewords have the same composition. This class of decoders rank-orders all input sequences in the codebook's composition class from ``closest'' to ``farthest'' from the channel output and then queries them sequentially in that order for codebook membership. Decoding terminates when a codeword is encountered or when a predetermined number of guesses is reached, and decoding is abandoned. We derive ensemble-tight first-order asymptotics for the code rate and abandonment rate, which shows that guessing-based decoding is more efficient than conventional testing-based decoding whenever the capacity of the channel exceeds half the entropy of the capacity-achieving input distribution. The main focus of this paper is on refined asymptotics, specifically, second-order asymptotics, error exponents, and strong converse exponents. The optimal second-order region is characterized in terms of the minimum of the second-order code and abandonment rates. The error (resp.\ strong converse) exponent is characterized in terms of the minimum (resp.\ maximum) of the usual channel coding exponent and an abandonment exponent, which turns out to be a special case of the exponent of conditional almost-lossless source coding.