A Multiuser Channel Capacity Region
Abstract
A finite structural characterization of the U-user multiuser channel-capacity region appears here. This region relies upon three concepts: (i) subset-based message atomization, (ii) synchronized receiver chain-rule/Fano reduction, and (iii) successive-decoding achievability via a finite-super-symbol closure. The resulting region is a finite union of order-indexed polytopes parameterized by the synchronized minimum mutual-information vector ℐmin. The framework removes auxiliary-random-variable proliferation and makes explicit the finite geometric structure underlying general multiuser converses, with the interference channel providing the primary illustration. For the linear matrix Gaussian multiuser-channel special case under per-user trace covariance constraints, Gaussian signaling is capacity-region-achieving within this framework. Also shown is that maximum rate sum for any Gaussian multiple-user-channel derives from simple iterative procedures.
Related
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BibTeX
@misc{cioffi2026multiuser,
title = {{A Multiuser Channel Capacity Region}},
author = {John M. Cioffi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17212},
eprint = {2609.17212},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17212},
}
RIS
TY - UNPB
TI - A Multiuser Channel Capacity Region
AU - John M. Cioffi
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17212
UR - https://arxiv.org/abs/2609.17212
AB - A finite structural characterization of the U-user multiuser channel-capacity region appears here. This region relies upon three concepts: (i) subset-based message atomization, (ii) synchronized receiver chain-rule/Fano reduction, and (iii) successive-decoding achievability via a finite-super-symbol closure. The resulting region is a finite union of order-indexed polytopes parameterized by the synchronized minimum mutual-information vector ℐ_min. The framework removes auxiliary-random-variable proliferation and makes explicit the finite geometric structure underlying general multiuser converses, with the interference channel providing the primary illustration. For the linear matrix Gaussian multiuser-channel special case under per-user trace covariance constraints, Gaussian signaling is capacity-region-achieving within this framework. Also shown is that maximum rate sum for any Gaussian multiple-user-channel derives from simple iterative procedures.
ER -