Error Correction for Cooperative Data Exchange

TL;DR

This paper investigates error correction in cooperative data exchange systems with compromised clients, establishing bounds and demonstrating the existence of linear codes that ensure reliable message recovery despite failures.

Contribution

It introduces bounds on error correction capabilities and proves the existence of deterministic linear codes that achieve these bounds in CDE systems.

Findings

Deterministic linear codes can achieve the derived error correction bounds.

Probability models for random linear codes show resilience against a certain number of compromised clients.

The analysis applies to any network size and initial message distribution.

Abstract

This paper considers the problem of error correction for a cooperative data exchange (CDE) system, where some clients are compromised or failed and send false messages. Assuming each client possesses a subset of the total messages, we analyze the error correction capability when every client is allowed to broadcast only one linearly-coded message. Our error correction capability bound determines the maximum number of clients that can be compromised or failed without jeopardizing the final decoding solution at each client. We show that deterministic, feasible linear codes exist that can achieve the derived bound. We also evaluate random linear codes, where the coding coefficients are drawn randomly, and then develop the probability for a client to withstand a certain number of compromised or failed peers and successfully deduce the complete message for any network size and any initial message distributions.