Small Parity-Check Erasure Codes - Exploration and Observations

James S. Plank, Adam L. Buchsbaum, Rebecca L. Collins and Michael G. Thomason.

Appearing in DSN-2005: The International Conference on Dependable Systems and Networks, Yokohama, Japan, June, 2005.

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If the material in this paper interests you, please also read the expanded version of the paper: Technical Report UT-CS-04-537, University of Tennessee, November, 2004.


Erasure codes have profound uses in wide- and medium-area storage applications. While infinite-size codes have been developed with optimal properties, there remains a need to develop small codes with optimal properties. In this paper, we provide a framework for exploring very small codes, and we use this framework to derive optimal and near-optimal ones for discrete numbers of data bits and coding bits. These codes have heretofore been unknown and unpublished, and should be useful in practice. We also use our exploration to make observations about upper bounds for these codes, in order to gain a better understanding of them and to lead the way for future derivations of larger, optimal and near-optimal codes.
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