Cooperative Data Exchange with Unreliable Clients

TL;DR

This paper extends cooperative data exchange models to include unreliable clients, deriving exact and approximate solutions for the minimum number of transmissions needed for reliable clients to recover all packets, even with client unreliability.

Contribution

It introduces a generalized model accounting for unreliable clients and provides a closed-form solution for one unreliable client and an approximation for multiple unreliable clients.

Findings

Exact minimum transmissions for one unreliable client.

Approximate solutions for multiple unreliable clients.

High probability of success as number of packets increases.

Abstract

Consider a set of clients in a broadcast network, each of which holds a subset of packets in the ground set X. In the (coded) cooperative data exchange problem, the clients need to recover all packets in X by exchanging coded packets over a lossless broadcast channel. Several previous works analyzed this problem under the assumption that each client initially holds a random subset of packets in X. In this paper we consider a generalization of this problem for settings in which an unknown (but of a certain size) subset of clients are unreliable and their packet transmissions are subject to arbitrary erasures. For the special case of one unreliable client, we derive a closed-form expression for the minimum number of transmissions required for each reliable client to obtain all packets held by other reliable clients (with probability approaching 1 as the number of packets tends to infinity). Furthermore, for the cases with more than one unreliable client, we provide an approximation solution in which the number of transmissions per packet is within an arbitrarily small additive factor from the value of the optimal solution.