Second-Order Asymptotics for the Gaussian MAC on the Relative Interior of the Sum-Rate Face

2026-09-15

AI Summary

研究解决了两用户高斯多址信道在和速率面相对内部的二阶编码速率区域问题，通过优化功率分配改进了标准内界。

Abstract

We completely characterize the second-order coding rate region of the two-user Gaussian multiple-access channel at points in the relative interior of the sum-rate face, under maximal per-codeword power constraints. For any fixed average error probability $0 < \varepsilon < 1/2$, a nontrivial mixture of power splits reduces the sum-rate dispersion and strictly improves upon standard inner bounds based on a constant power split. Thus, a constant power split, although sufficient to attain the first-order capacity region, is insufficient for second-order optimality in this regime. Our achievability proof builds on the constant composition and coded time-sharing framework of Scarlett, Martinez, and Guillén i Fàbregas, with an optimization over admissible power splits. A matching second-order converse establishes the optimality of the resulting coded time-sharing strategy.

Problem

• Gaussian MAC
• second-order asymptotics
• sum-rate dispersion
• power constraints
• relative interior

Innovation

• second-order coding rate region
• Gaussian multiple-access channel
• power split
• sum-rate dispersion
• coded time-sharing