Error-and-Erasure Decoding for Block Codes with Feedback

TL;DR

This paper establishes bounds on the performance of block codes with feedback and errors-and-erasures decoding, revealing the limits and trade-offs in error and erasure exponents for discrete memoryless channels.

Contribution

It introduces new inner and outer bounds on the optimal performance of such codes, including a proof that feedback does not improve the error exponent trade-off for two-message codes.

Findings

Inner bounds using a two-phase encoding scheme

Outer bounds based on a generalized straight-line bound

Feedback does not increase the error exponent trade-off for two-message codes

Abstract

Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with communication and control phases together with the optimal decoding rule for the given encoding scheme, among decoding rules that can be represented in terms of pairwise comparisons between the messages. Then an outer bound is derived using a generalization of the straight-line bound to errors-and-erasures decoders and the optimal error exponent trade off of a feedback encoder with two messages. In addition upper and lower bounds are derived, for the optimal erasure exponent of error free block codes in terms of the rate. Finally we present a proof of the fact that the optimal trade off between error exponents of a two message code does not increase with feedback on DMCs.