An Exploration of Non-Asymptotic Low-Density, Parity Check Erasure Codes for Wide-Area Storage Applications

James S. Plank and Michael G. Thomason.

Parallel Processing Letters, Volume 17, Number 1, March, 2007, pages 103-123.

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As peer-to-peer and widely distributed storage systems proliferate, the need to perform efficient erasure coding, instead of replication, is crucial to performance and efficiency. Low-Density Parity-Check (LDPC) codes have arisen as alternatives to standard erasure codes, such as Reed-Solomon codes, trading off vastly improved decoding performance for inefficiencies in the amount of data that must be acquired to perform decoding. The scores of papers written on LDPC codes typically analyze their collective and asymptotic behavior. Unfortunately, their practical application requires the generation and analysis of individual codes for finite systems.

This paper attempts to illuminate the practical considerations of LDPC codes for peer-to-peer and distributed storage systems. The three main types of LDPC codes are detailed, and a huge variety of codes are generated, then analyzed using simulation. This analysis focuses on the performance of individual codes for finite systems, and addresses several important heretofore unanswered questions about employing LDPC codes in real-world systems.

Keywords: Erasure codes, storage systems, fault-tolerance, peer-to-peer, low-density parity (LDPC) codes, Tornado codes.

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