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Distributed storage systems suffer from significant repair traffic generateddue to frequent storage node failures. This paper shows that properly designedlow-density parity-check (LDPC) codes can substantially reduce the amount ofrequired block downloads for repair thanks to the sparse nature of their factorgraph representation. In particular, with a careful construction of the factorgraph, both low repair-bandwidth and high reliability can be achieved for agiven code rate. First, a formula for the average repair bandwidth of LDPCcodes is developed. This formula is then used to establish that the minimumrepair bandwidth can be achieved by forcing a regular check node degree in thefactor graph. Moreover, it is shown that given a fixed code rate, the variablenode degree should also be regular to yield minimum repair bandwidth, undersome reasonable minimum variable node degree constraint. It is also shown thatfor a given repair-bandwidth requirement, LDPC codes can yield substantiallyhigher reliability than currently utilized Reed-Solomon (RS) codes. Ourreliability analysis is based on a formulation of the general equation for themean-time-to-data-loss (MTTDL) associated with LDPC codes. The formulationreveals that the stopping number is closely related to the MTTDL. It is furthershown that LDPC codes can be designed such that a small loss ofrepair-bandwidth optimality may be traded for a large improvement inerasure-correction capability and thus the MTTDL.

LDPC Code Design for Distributed Storage: Balancing Repair Bandwidth, Reliability and Storage Overhead