Capacity of Burst Noise-Erasure Channels With and Without Feedback and Input Cost

TL;DR

This paper analyzes burst noise-erasure channels with errors and erasures, deriving capacity formulas with and without feedback, and exploring how feedback can increase capacity-cost functions under certain conditions.

Contribution

It provides a closed-form non-feedback capacity formula, characterizes feedback capacity, and demonstrates feedback's potential to increase capacity-cost functions for Markov noise-erasure channels.

Findings

Uniform input maximizes mutual information under certain conditions.

Feedback does not increase capacity for the basic channel.

Feedback can increase capacity-cost functions in channels with Markov noise-erasure processes.

Abstract

A class of burst noise-erasure channels which incorporate both errors and erasures during transmission is studied. The channel, whose output is explicitly expressed in terms of its input and a stationary ergodic noise-erasure process, is shown to have a so-called "quasi-symmetry" property under certain invertibility conditions. As a result, it is proved that a uniformly distributed input process maximizes the channel's block mutual information, resulting in a closed-form formula for its non-feedback capacity in terms of the noise-erasure entropy rate and the entropy rate of an auxiliary erasure process. The feedback channel capacity is also characterized, showing that feedback does not increase capacity and generalizing prior related results. The capacity-cost function of the channel with and without feedback is also investigated. A sequence of finite-letter upper bounds for the capacity-cost function without feedback is derived. Finite-letter lower bonds for the capacity-cost function with feedback are obtained using a specific encoding rule. Based on these bounds, it is demonstrated both numerically and analytically that feedback can increase the capacity-cost function for a class of channels with Markov noise-erasure processes.