Lower Bounds on Conversion Bandwidth for MDS Convertible Codes in Split Regime

TL;DR

This paper establishes new lower bounds on the bandwidth costs of MDS convertible codes, improving existing results and matching known constructions in specific parameter regimes.

Contribution

It introduces linear-algebraic bounds that enhance understanding of bandwidth costs and demonstrate tightness in certain cases.

Findings

Bounds improve previous results in some regimes

Bounds match the bandwidth cost of existing constructions for certain parameters

Bounds are tight when r^F ≤ r^I ≤ k^F

Abstract

We propose several new lower bounds on the bandwidth costs of MDS convertible codes using a linear-algebraic framework. The derived bounds improve previous results in certain parameter regimes and match the bandwidth cost of the construction proposed by Maturana and Rashmi (2022 IEEE International Symposium on Information Theory) for $r^F\le r^I\le k^F$, implying that our bounds are tight in this case.