Cooperative Data Exchange based on MDS Codes

TL;DR

This paper introduces a polynomial-time deterministic algorithm for optimal cooperative data exchange using MDS codes, minimizing broadcast transmissions by leveraging linear combinations of packets.

Contribution

It presents a novel algorithm that determines the minimal number of broadcasts and the exact linear combinations using MDS codes for efficient data exchange.

Findings

Optimal broadcast transmission count computed efficiently.

Linear combinations of exactly d+1 packets are used.

Method extends to weighted and local omniscience scenarios.

Abstract

The cooperative data exchange problem is studied for the fully connected network. In this problem, each node initially only possesses a subset of the $K$ packets making up the file. Nodes make broadcast transmissions that are received by all other nodes. The goal is for each node to recover the full file. In this paper, we present a polynomial-time deterministic algorithm to compute the optimal (i.e., minimal) number of required broadcast transmissions and to determine the precise transmissions to be made by the nodes. A particular feature of our approach is that {\it each} of the $K-d$ transmissions is a linear combination of {\it exactly} $d+1$ packets, and we show how to optimally choose the value of $d.$ We also show how the coefficients of these linear combinations can be chosen by leveraging a connection to Maximum Distance Separable (MDS) codes. Moreover, we show that our method can be used to solve cooperative data exchange problems with weighted cost as well as the so-called successive local omniscience problem.