On Zero Skip-Cost Generalized Fractional-Repetition Codes from Covering Designs
Wenjun Yu, Bo-Jun Yuan, Moshe Schwartz
TL;DR
This paper addresses constructing generalized fractional repetition (CFR) codes with zero skip cost using covering designs. It develops three constructive schemes—a trivial duplication-based method, a combination design method, and a recursive design approach—to achieve zero skip cost, with asymptotic expansion factors of 2 and 1, respectively, and demonstrates improved finite-case performance. A non-constructive probabilistic argument shows that for sufficiently large covering designs, zero skip cost can be achieved with expansion factor 1, removing the need for expansion in principle. The results broaden the design toolkit beyond Steiner systems, enabling zero-skip CFR codes across a wider parameter range and highlighting both practical constructions and theoretical existence proofs. These findings have practical implications for low-skip-cost data repair in distributed storage systems while pointing to open questions about efficient realization of the existential results and further non-asymptotic improvements.
Abstract
We study generalized fractional repetition codes that have zero skip cost, and which are based on covering designs. We show that a zero skip cost is always attainable, perhaps at a price of an expansion factor compared with the optimal size of fractional repetition codes based on Steiner systems. We provide three constructions, as well as show non-constructively, that no expansion is needed for all codes based on sufficiently large covering systems.