Lower Bounds on Conversion Bandwidth for MDS Convertible Codes in Split Regime
🤖 AI Summary
This work investigates the fundamental lower bound on conversion bandwidth for MDS convertible codes in the split regime. To address the challenge of characterizing the minimum bandwidth cost during parameter conversion, we introduce a novel linear-algebraic analytical framework that integrates information-theoretic and coding-theoretic techniques to derive a tight lower bound. The bound is provably tight when ( r^F leq r^I leq k^F ), thereby establishing, for the first time, the optimality of the Maturana–Rashmi construction under this regime. Moreover, our bound significantly improves upon prior results in specific parameter regimes. Beyond closing a long-standing theoretical gap in bandwidth lower bounds for convertible codes in the split regime, this work provides essential foundational insights for the design of bandwidth-efficient convertible erasure codes.
Application Category
📝 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 $r^Fle r^Ile k^F$, implying that our bounds are tight in this case.
Problem
Research questions and friction points this paper is trying to address.
Establishing tighter bandwidth bounds for MDS convertible codes
Improving previous bandwidth cost results in specific regimes
Demonstrating tight bounds matching existing construction performance
Innovation
Methods, ideas, or system contributions that make the work stand out.
New lower bounds on bandwidth costs
Linear-algebraic framework for convertible codes
Improved bounds matching existing construction performance
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