Second-Order Asymptotics for the Gaussian MAC on the Relative Interior of the Sum-Rate Face
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 < ε < 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.
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BibTeX
@misc{tan2026secondorder,
title = {{Second-Order Asymptotics for the Gaussian MAC on the Relative Interior of the Sum-Rate Face}},
author = {Vincent Y. F. Tan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18013},
eprint = {2609.18013},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18013},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Second-Order Asymptotics for the Gaussian MAC on the Relative Interior of the Sum-Rate Face
AU - Vincent Y. F. Tan
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18013
UR - https://arxiv.org/abs/2609.18013
AB - 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 < ε < 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.
ER -