Keyun Cheng

Reading Notes: ISIT’20 Access-optimal Convertible Codes

Title: Access-optimal Linear MDS Convertible Codes for All Parameters

Conference (ISIT’20): Link

Journal (): Link

Summary

This paper is a follow-up work on Convertible codes (TIT’19, Maturana). It presents the lower bound for access costs for all achievable parameters, and presents an explicit construction of access-optimal linear MDS convertible codes which exactly matches the lower bounds.

Main Contributions

• Beyond merge regime, it defines and studies split regimes (inverse problem of merge regime)l; and also general regime by formulating it as a combination of merge and split regimes. For both types of regimes, they show and prove the access optimality.

• In the design of general regime, a “degree-of-freedom” called partitions plays crucial roles (inconsequential for split and merge regimes)

Strength

• It generalizes the “regimes” over convertible codes (the requirements of k and k’), and provides explicit constructions for all regimes. From the practical perspective, the code is constructable.

Weakness

• I’m not sure whether there is field size requirements for generalized regimes for a given (n, k) and (n’, k’) pairs, which is not discussed in this paper.