State-Dependent Gaussian Multiple Access Channels: New Outer Bounds and Capacity Results

TL;DR

This paper derives new outer bounds and capacity results for a two-user state-dependent Gaussian MAC with noncausal state knowledge at one encoder, improving understanding of its capacity region and optimal coding strategies.

Contribution

It introduces improved outer bounds for the capacity region and fully characterizes the region in key cases, using novel proof techniques like optimal transportation and worst-case noise analysis.

Findings

New outer bounds on capacity region are tighter than previous bounds.

Exact capacity region is characterized for certain sum rate cases.

Single-letter solutions suffice for corner points and sum rate capacity.

Abstract

This paper studies a two-user state-dependent Gaussian multiple-access channel (MAC) with state noncausally known at one encoder. Two scenarios are considered: i) each user wishes to communicate an independent message to the common receiver, and ii) the two encoders send a common message to the receiver and the non-cognitive encoder (i.e., the encoder that does not know the state) sends an independent individual message (this model is also known as the MAC with degraded message sets). For both scenarios, new outer bounds on the capacity region are derived, which improve uniformly over the best known outer bounds. In the first scenario, the two corner points of the capacity region as well as the sum rate capacity are established, and it is shown that a single-letter solution is adequate to achieve both the corner points and the sum rate capacity. Furthermore, the full capacity region is characterized in situations in which the sum rate capacity is equal to the capacity of the helper problem. The proof exploits the optimal-transportation idea of Polyanskiy and Wu (which was used previously to establish an outer bound on the capacity region of the interference channel) and the worst-case Gaussian noise result for the case in which the input and the noise are dependent.