On Bounds for $E$-capacity of DMC

TL;DR

This paper derives bounds on the E-capacity of discrete memoryless channels using types and graph decomposition, comparing decoding rules and consolidating previous results.

Contribution

It introduces bounds for E-capacity of DMCs using novel combinatorial methods and compares their attainability across different decoding rules.

Findings

Random coding bound is attainable by all three decoding rules.

Expurgated bound is achievable only by maximum-likelihood decoding.

Sphere packing bound is derived using simple combinatorial reasoning.

Abstract

Random coding, expurgated and sphere packing bounds are derived by method of types and method of graph decomposition for $E$-capacity of discrete memoryless channel (DMC). Three decoding rules are considered, the random coding bound is attainable by each of the three rules, but the expurgated bound is achievable only by maximum-likelihood decoding. Sphere packing bound is obtained by very simple combinatorial reasonings of the method of types. The paper joins and reviews the results of previous hard achievable publications.