Access-optimal Linear MDS Convertible Codes for All Parameters

TL;DR

This paper introduces access-optimal linear MDS convertible codes that enable efficient code parameter changes in distributed storage, providing tight bounds and explicit constructions for all parameters, thus improving fault tolerance and storage efficiency.

Contribution

It establishes lower bounds on conversion access cost for all parameters and provides explicit constructions of access-optimal codes, extending previous limited results.

Findings

Lower bounds on access cost are tight for all parameters.

Explicit construction of access-optimal codes for all valid parameters.

A new degree-of-freedom is identified as crucial in code design beyond previous regimes.

Abstract

In large-scale distributed storage systems, erasure codes are used to achieve fault tolerance in the face of node failures. Tuning code parameters to observed failure rates has been shown to significantly reduce storage cost. Such tuning of redundancy requires "code conversion", i.e., a change in code dimension and length on already encoded data. Convertible codes are a new class of codes designed to perform such conversions efficiently. The access cost of conversion is the number of nodes accessed during conversion. Existing literature has characterized the access cost of conversion of linear MDS convertible codes only for a specific and small subset of parameters. In this paper, we present lower bounds on the access cost of conversion of linear MDS codes for all valid parameters. Furthermore, we show that these lower bounds are tight by presenting an explicit construction for access-optimal linear MDS convertible codes for all valid parameters. En route, we show that, one of the degrees-of-freedom in the design of convertible codes that was inconsequential in the previously studied parameter regimes, turns out to be crucial when going beyond these regimes and adds to the challenge in the analysis and code construction.