The Gaussian Multiple Access Diamond Channel

TL;DR

This paper investigates the capacity of a specific relay network model called the Gaussian multiple access diamond channel, providing new bounds and conditions under which the capacity can be exactly determined.

Contribution

It introduces a tighter upper bound and an achievable lower bound for the channel capacity, along with conditions for their equality, advancing understanding of this network's capacity.

Findings

Proposed a single-letter upper bound tighter than the cut-set bound.

Developed an achievable scheme using correlated codes with superposition.

Identified conditions where the bounds meet, determining the channel capacity.

Abstract

In this paper, we study the capacity of the diamond channel. We focus on the special case where the channel between the source node and the two relay nodes are two separate links with finite capacities and the link from the two relay nodes to the destination node is a Gaussian multiple access channel. We call this model the Gaussian multiple access diamond channel. We first propose an upper bound on the capacity. This upper bound is a single-letterization of an $n$-letter upper bound proposed by Traskov and Kramer, and is tighter than the cut-set bound. As for the lower bound, we propose an achievability scheme based on sending correlated codes through the multiple access channel with superposition structure. We then specialize this achievable rate to the Gaussian multiple access diamond channel. Noting the similarity between the upper and lower bounds, we provide sufficient and necessary conditions that a Gaussian multiple access diamond channel has to satisfy such that the proposed upper and lower bounds meet. Thus, for a Gaussian multiple access diamond channel that satisfies these conditions, we have found its capacity.