Second-Order Asymptotics for the Discrete Memoryless MAC with Degraded Message Sets

TL;DR

This paper analyzes the second-order asymptotics of the discrete memoryless multiple-access channel with degraded message sets, providing convergence rates of rate pairs near capacity boundary for fixed error probabilities.

Contribution

It characterizes the convergence speed of rate pairs approaching the capacity boundary in the discrete memoryless MAC with degraded message sets, extending previous Gaussian results.

Findings

Derived second-order asymptotic bounds for the MAC with degraded message sets.

Established convergence rates of rate pairs near the capacity boundary.

Complemented existing Gaussian channel results with discrete memoryless case.

Abstract

This paper studies the second-order asymptotics of the discrete memoryless multiple-access channel with degraded message sets. For a fixed average error probability $\epsilon\in(0,1)$ and an arbitrary point on the boundary of the capacity region, we characterize the speed of convergence of rate pairs that converge to that point for codes that have asymptotic error probability no larger than $\epsilon$, thus complementing an analogous result given previously for the Gaussian setting.