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

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.