Convertible Codes for Data and Device Heterogeneity

TL;DR

This paper introduces convertible codes that facilitate efficient transformation between codes in distributed storage, addressing data and device heterogeneity through theoretical bounds and explicit constructions, especially for Reed-Muller codes.

Contribution

It provides the first combined approach for handling data and device heterogeneity in distributed storage using convertible codes with explicit conversion procedures.

Findings

Derived lower bounds on read/write costs for linear code conversion.

Constructed explicit conversion procedures for Reed-Muller codes.

Unified approach to address both data and device heterogeneity.

Abstract

Distributed storage systems must handle both data heterogeneity, arising from non-uniform access demands, and device heterogeneity, caused by time-varying node reliability. In this paper, we study convertible codes, which enable the transformation of one code into another with minimum cost in the merge regime, addressing the latter. We derive general lower bounds on the read and write costs of linear code conversion, applicable to arbitrary linear codes. We then focus on Reed-Muller codes, which efficiently handle data heterogeneity, addressing the former issue, and construct explicit conversion procedures that, for the first time, combine both forms of heterogeneity for distributed data storage.