DoF of a Cooperative X-Channel with an Application to Distributed Computing

TL;DR

This paper investigates the Degrees of Freedom in a cooperative X-channel with grouped transmitters and receivers, introducing a new interference alignment scheme that enhances data delivery in distributed computing.

Contribution

It proposes a novel interference alignment scheme for cooperative X-channels and derives new bounds for the sum Degrees of Freedom, with applications to distributed MapReduce frameworks.

Findings

New lower bounds for sum DoF when K/r is 2 or 3

Explicit DoF bounds for K/r ≥ 4

Improved normalized data delivery time in distributed computing

Abstract

We consider a cooperative X-channel with $\sf K$ transmitters (TXs) and $\sf K$ receivers (Rxs) where Txs and Rxs are gathered into groups of size $\sf r$ respectively. Txs belonging to the same group cooperate to jointly transmit a message to each of the $\sf K- \sf r$ Rxs in all other groups, and each Rx individually decodes all its intended messages. By introducing a new interference alignment (IA) scheme, we prove that when $\sf K/\sf r$ is an integer the sum Degrees of Freedom (SDoF) of this channel is lower bounded by $2\sf r$ if $\sf K/\sf r \in \{2,3\}$ and by $\frac{\sf K(\sf K-\sf r)-\sf r^2}{2\sf K-3\sf r}$ if $\sf K/\sf r \geq 4$. We also prove that the SDoF is upper bounded by $\frac{\sf K(\sf K-\sf r)}{2\sf K-3\sf r}$. The proposed IA scheme finds application in a wireless distributed MapReduce framework, where it improves the normalized data delivery time (NDT) compared to the state of the art.