Refinement of the Sphere-Packing Bound: Asymmetric Channels

TL;DR

This paper refines the sphere-packing bound for asymmetric channels, improving the pre-factor in the exponential decay rate of error probability for constant composition codes.

Contribution

It provides a tighter pre-factor in the sphere-packing bound for asymmetric discrete memoryless channels, enhancing understanding of error decay rates.

Findings

Pre-factor order is Ω(N^{-1/2(1+ε+ρ_R^*)}) for any ε>0

Improves the exponential bound for constant composition codes

Applicable to asymmetric discrete memoryless channels

Abstract

We provide a refinement of the sphere-packing bound for constant composition codes over asymmetric discrete memoryless channels that improves the pre-factor in front of the exponential term. The order of our pre-factor is $\Omega(N^{-1/2(1+\epsilon + \rho_{R}^{\ast})})$ for any $\epsilon >0$, where $\rho_{R}^{\ast}$ is the maximum absolute-value subdifferential of the sphere-packing exponent at rate $R$ and $N$ is the blocklength.