Achievable Error Exponents for Channel with Side Information - Erasure and List Decoding

TL;DR

This paper develops universal error exponents for channels with side information, incorporating erasure and list decoding, and extends existing decoding rules to unify these approaches with concrete bounds.

Contribution

It introduces a unified decoding framework for erasure and list decoding with error exponent analysis on channels with side information, extending prior methods.

Findings

Provides universally achievable error exponents for erasure decoding.

Extends decoding rules to variable size list decoding.

Offers exponential bounds on list error probability and incorrect message count.

Abstract

We consider a decoder with an erasure option and a variable size list decoder for channels with non-casual side information at the transmitter. First, universally achievable error exponents are offered for decoding with an erasure option using a parameterized decoder in the spirit of Csisz\'{a}r and K\"{o}rner's decoder. Then, the proposed decoding rule is generalized by extending the range of its parameters to allow variable size list decoding. This extension gives a unified treatment for erasure/list decoding. Exponential bounds on the probability of list error and the average number of incorrect messages on the list are given. Relations to Forney's and Csisz\'{a}r and K\"{o}rner's decoders for discrete memoryless channel are discussed. These results are obtained by exploring a random binning code with conditionally constant composition codewords proposed by Moulin and Wang, but with a different decoding rule.