Error Exponents for Randomised List Decoding

TL;DR

This paper analyzes the error exponents of randomized list decoding, providing bounds for mismatched and matched metrics, and explores how list size affects decoding performance in different regimes.

Contribution

It introduces new bounds for random-coding error exponents in randomized list decoding, including ensemble-tight bounds and asymptotic analysis for growing list sizes.

Findings

For fixed list size, the error exponent matches that of ordinary decoding.

For exponentially growing list sizes, a tight lower bound on the error exponent is established at high rates.

Randomized list decoding does not improve error exponents over ordinary decoding for fixed list sizes.

Abstract

This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given for mismatched, and then particularised to matched and universal decoding metrics. Two regimes are studied: for fixed list size, we derive an ensemble-tight random-coding error exponent, and show that, for the matched metric, it does not improve the error exponent of ordinary decoding. For list sizes growing exponentially with the block-length, we provide a non-trivial lower bound to the error exponent that is tight at high rates under the matched metric.