On the Sum Rate of a 2 x 2 Interference Network

TL;DR

This paper analyzes the sum rate capacity of a 2x2 interference network, identifying the minimal set of messages needed to maximize sum rate under various interference conditions.

Contribution

It introduces an achievable sum rate region for the 2x2 interference network and determines the minimal message set required for optimal sum rate.

Findings

Two messages suffice for sum rate maximization in many cases.

The achievable rate region is similar to the Han-Kobayashi region.

Optimal message sets vary with interference conditions.

Abstract

In an M x N interference network, there are M transmitters and N receivers with each transmitter having independent messages for each of the 2^N -1 possible non-empty subsets of the receivers. We consider the 2 x 2 interference network with 6 possible messages, of which the 2 x 2 interference channel and X channel are special cases obtained by using only 2 and 4 messages respectively. Starting from an achievable rate region similar to the Han-Kobayashi region, we obtain an achievable sum rate. For the Gaussian interference network, we determine which of the 6 messages are sufficient for maximizing the sum rate within this rate region for the low, mixed, and strong interference conditions. It is observed that 2 messages are sufficient in several cases.