Multiuser channel capacity region characterized by new finite geometric framework
A Multiuser Channel Capacity Region
Information Theory
Summary
Communication through channels with multiple users is complex because users interfere with each other. This paper presents a new way to describe the limits on how much data can be sent reliably using three key ideas: breaking messages into parts based on subsets of users, synchronizing decoding steps with information reduction techniques, and decoding in a specific order. This framework avoids complicated extra variables and clarifies the structure of these limits, especially for interference channels. It also shows that for certain Gaussian channels, simple Gaussian signaling achieves the best possible data rates.
What this means in practice
- •For network schedulers: Optimize scheduling and resource allocation in multiuser wireless networks using the finite characterization of capacity regions.
- •For signal processing engineers: Design multiuser decoding algorithms for Gaussian channels leveraging the paper’s finite-super-symbol and mutual-information framework.
Authors
John M. Cioffi
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 $\mathcal{I}_{\min}$. 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.