On the Capacity and Generalized Degrees of Freedom of the X Channel

TL;DR

This paper investigates the capacity and degrees of freedom of the two-user Gaussian X channel, providing new capacity characterizations and extending noisy interference results from interference channels to X channels.

Contribution

It offers the first sum capacity characterization for the deterministic X channel and extends noisy interference capacity results to the X channel model.

Findings

Sum capacity of the deterministic symmetric X channel is characterized.

Generalized degrees of freedom for the Gaussian X channel are derived.

X channel with noisy interference has the same sum capacity as the interference channel.

Abstract

We explore the capacity and generalized degrees of freedom of the two-user Gaussian X channel, i.e. a generalization of the 2 user interference channel where there is an independent message from each transmitter to each receiver. There are three main results in this paper. First, we characterize the sum capacity of the deterministic X channel model under a symmetric setting. Second, we characterize the generalized degrees of freedom of the Gaussian X channel under a similar symmetric model. Third, we extend the noisy interference capacity characterization previously obtained for the interference channel to the X channel. Specifically, we show that the X channel associated with noisy (very weak) interference channel has the same sum capacity as the noisy interference channel.