Regenerating codes with minimal disk I/O cost achieving optimal tradeoff between storage and repair bandwidth

Abstract

Regenerating codes achieve the fundamental tradeoff between storage efficiency and repair bandwidth in distributed storage systems. Beyond these two parameters, disk I/O cost is an important measure of repair efficiency, capturing the number of stored packets accessed at the helper nodes during repair. A repair scheme is access-optimal if each helper reads exactly as many packets as it transmits, and is help-by-transfer if each helper sends stored packets directly to the newcomer without local computation. In this paper, we study functional repair of a single node failure in the regime where all surviving nodes participate as helpers. We introduce a framework based on signal flow graphs and gammoids, which separates the combinatorial structure of the repair process from its linear-algebraic realization. Within this framework, we construct functional-repair regenerating codes that attain every point on the optimal storage-bandwidth tradeoff curve. The proposed codes are help-by-transfer and access-optimal. Moreover, they operate over a fixed finite field and preserve the data-recovery property under an arbitrarily long sequence of repairs.