An Outer Bound for Linear Multi-Node Exact Repair Regenerating Codes

Abstract

In distributed storage, erasure codes provide fault-tolerance while reducing the storage overhead compared to replication. The network traffic cost during the repair of node failures, called repair bandwidth, is an important metric in code design. Regenerating codes are a class of erasure codes developed with the aim of reducing the repair bandwidth while maintaining a high level of fault-tolerance. They exhibit a tradeoff between the storage overhead per node and the repair bandwidth. However, a fundamental understanding of the storage-repair bandwidth tradeoff under exact repair is open in general. In this work, we consider the exact repair problem of multiple failures in a centralized way. Building upon techniques from the literature, we first provide an alternative proof of the functional repair bound. Then, we derive a new outer bound for linear centralized multi-node exact repair codes and illustrate its performance under various parameter settings. The derived outer bound shows that, in general, the centralized multi-node functional repair tradeoff is not achievable under linear exact repair.