Exact tradeoffs found for repairing failed storage systems
Exact Storage-Repair-Bandwidth Tradeoffs for $(6,5,5)$ and $(7,6,6)$ Exact-Repair Regenerating Codes
Information Theory
Summary
Storing data safely across many computers means you need to fix lost pieces quickly and without using too much space or communication. This paper finds the exact best balance between how much data each computer stores and how much information needs to be shared to repair a failure in certain setups with six or seven storage nodes. The authors also confirm that an existing layered coding method perfectly matches this balance. They used advanced mathematical tools, assisted by AI, to prove these limits exactly.
What this means in practice
- •For distributed storage engineers: Design storage systems that minimize data stored and communication needed to repair failed nodes using proven optimal parameters for (6,5,5) and (7,6,6) configurations.
- •For network protocol designers: Incorporate exact storage and repair tradeoff knowledge to improve reliability and efficiency in data recovery protocols for cloud storage networks.
A theory result. No direct application yet.
Authors
Chao Tian
Abstract
This note provides exact information-theoretic outer bounds that completely characterize the storage-repair-bandwidth tradeoff regions for the cases $(n,k,d)=(6,5,5)$ and $(7,6,6)$. The layered code proposed by Tian et al. achieves the tradeoff and is thus optimal. GPT-6 Astra assisted in the discovery of these bounds, based on a new conditioning argument and a structured search over the restricted subsets of entropy linear program constraints. The proofs are given as exact integer-valued certificates, which are difficult for direct human verification, and a Python verifier is included as part of the package, together with the certificates.