MDS Generalized Convertible Code

TL;DR

This paper explores the design and characterization of MDS convertible codes that adapt their parameters based on device failure rates, providing bounds and constructions for optimal access cost in the merge regime.

Contribution

It extends the concept of convertible codes to different initial and final parameters, establishes bounds on access cost, and characterizes access-optimal codes via parity check matrices.

Findings

Derived new lower bounds on access cost in merge and split regimes.

Provided a necessary and sufficient condition for access-optimal MDS convertible codes.

Constructed optimal access cost codes using extended generalized Reed-Solomon codes.

Abstract

In this paper, we consider the convertible codes with the maximum distance separable (MDS) property, which can adjust the code rate according to the failure rates of devices. We first extend the notion of convertible codes to allow initial and final codes with different parameters. Then, we investigate the relationship between these parameters and thus establish new lower bounds on the access cost in the merge and split regimes. To gain a deeper understanding of access-optimal MDS convertible codes in the merge regime, we characterize them from the perspective of parity check matrices. Consequently, we present a necessary and sufficient condition for the access-optimal MDS convertible code in the merge regime. Finally, as an application of our characterization, we construct MDS convertible codes in the merge regime with optimal access cost based on the extended generalized Reed-Solomon codes.