Fairest Constant Sum-rate Transmission for Cooperative Data Exchange: An M-convex Minimization Approach

TL;DR

This paper introduces an M-convex minimization approach to optimize fairness in cooperative data exchange, ensuring even distribution of communication load while achieving universal recovery among wireless clients.

Contribution

It formulates the fairness problem as an M-convex minimization, proving its properties and proposing an efficient steepest descent algorithm for solution.

Findings

SDA outperforms DA in convergence and complexity for up to five clients.

The problem is shown to be M-convex, linking to submodular resource allocation.

Proposes a novel approach to fairness in cooperative data exchange.

Abstract

We consider the fairness in cooperative data exchange (CDE) problem among a set of wireless clients. In this system, each client initially obtains a subset of the packets. They exchange packets in order to reconstruct the entire packet set. We study the problem of how to find a transmission strategy that distributes the communication load most evenly in all strategies that have the same sum-rate (the total number of transmissions) and achieve universal recovery (the situation when all clients recover the packet set). We formulate this problem by a discrete minimization problem and prove its $M$-convexity. We show that our results can also be proved by the submodularity of the feasible region shown in previous works and are closely related to the resource allocation problems under submodular constraints. To solve this problem, we propose to use a steepest descent algorithm (SDA) based on $M$-convexity. By varying the number of clients and packets, we compare SDA with a deterministic algorithm (DA) based on submodularity in terms of convergence performance and complexity. The results show that for the problem of finding the fairest and minimum sum-rate strategy for the CDE problem SDA is more efficient than DA when the number of clients is up to five.