On error correcting algorithms for the cooperative data exchange problem

In the cooperative data exchange problem, a group of wireless clients use a shared broadcast channel to exchange packets from a given set X. Each of the clients has a subset of packets in X available to it as a side information. The clients transmit linear combinations of the packets one after the other, until all clients are able to recover all packets in X. This problem arises naturally in many practical settings, in particular in battlefield networks and peer-to-peer wireless networks. In this paper, we focus on the Error Correcting Data Exchange (ECDE) problem in which some of the clients participating in data exchange can be faulty. Faulty clients may transmit packets with arbitrary errors that can occur due to corruption or malicious behavior. Our goal is to identify a coding strategy that allows every non-faulty client to obtain the correct copies of all original packets in X. The paper makes the following contributions. First, we establish necessary and sufficient conditions for the existence of a feasible solution to Problem ECDE. Next, we focus on a special case in which at most one client is faulty. We prove that the problem is NP-hard even for this special case and present an approximation algorithm with provable performance guarantees. Our simulation results indicate that the algorithm performs well in practical settings.