Second-Order Rate Region of Constant-Composition Codes for the Multiple-Access Channel

TL;DR

This paper derives second-order asymptotic rate bounds for the discrete memoryless and Gaussian multiple-access channels using constant-composition coding, revealing potential advantages over i.i.d. coding.

Contribution

It introduces a new inner bound on second-order rates for constant-composition codes, extending previous i.i.d. bounds and applying to Gaussian channels.

Findings

Inner bound includes i.i.d. coding bounds, with possible strict inclusion.

Extension of bounds to Gaussian channels via input quantization.

Provides a detailed characterization of second-order rate regions.

Abstract

This paper studies the second-order asymptotics of coding rates for the discrete memoryless multiple-access channel with a fixed target error probability. Using constant-composition random coding, coded time-sharing, and a variant of Hoeffding's combinatorial central limit theorem, an inner bound on the set of locally achievable second-order coding rates is given for each point on the boundary of the capacity region. It is shown that the inner bound for constant-composition random coding includes that recovered by i.i.d. random coding, and that the inclusion may be strict. The inner bound is extended to the Gaussian multiple-access channel via an increasingly fine quantization of the inputs.