A Probabilistic Approach Towards Exact-Repair Regeneration Codes

TL;DR

This paper introduces a probabilistic method to establish the existence of exact-repair regeneration codes in distributed storage systems, expanding the known tradeoff region especially for systems where k=d, including a complete characterization for (n,3,3).

Contribution

It provides a probabilistic existence proof for exact-repair codes in (n,k,k) systems, improving the achievable tradeoff region without explicit code construction.

Findings

Achieves a new, larger tradeoff region for exact-repair codes.

Provides a complete tradeoff characterization for (n,3,3) systems.

Uses probabilistic methods to demonstrate code existence with high probability.

Abstract

Regeneration codes with exact-repair property for distributed storage systems is studied in this paper. For exact- repair problem, the achievable points of ({\alpha},{\beta}) tradeoff match with the outer bound only for minimum storage regenerating (MSR), minimum bandwidth regenerating (MBR), and some specific values of n, k, and d. Such tradeoff is characterized in this work for general (n, k, k), (i.e., k = d) for some range of per-node storage ({\alpha}) and repair-bandwidth ({\beta}). Rather than explicit code construction, achievability of these tradeoff points is shown by proving existence of exact-repair regeneration codes for any (n,k,k). More precisely, it is shown that an (n, k, k) system can be extended by adding a new node, which is randomly picked from some ensemble, and it is proved that, with high probability, the existing nodes together with the newly added one maintain properties of exact-repair regeneration codes. The new achievable region improves upon the existing code constructions. In particular, this result provides a complete tradeoff characterization for an (n,3,3) distributed storage system for any value of n.