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Fractional Repetition and Erasure Batch Codes

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Part of the CIM Series in Mathematical Sciences book series (CIMSMS,volume 3)

Abstract

Batch codes are a family of codes that represent a distributed storage system (DSS) of n nodes so that any batch of t data symbols can be retrieved by reading at most one symbol from each node. Fractional repetition codes are a family of codes for DSS that enable efficient uncoded repairs of failed nodes. In this work these two families of codes are combined to obtain fractional repetition batch (FRB) codes which provide both uncoded repairs and parallel reads of subsets of stored symbols. In addition, new batch codes which can tolerate node failures are considered. This new family of batch codes is called erasure combinatorial batch codes (ECBCs). Some properties of FRB codes and ECBCs and examples of their constructions based on transversal designs and affine planes are presented.

Keywords

  • Fractional repetition codes
  • Batch codes
  • Transversal designs
  • Affine planes

This research was supported in part by the Fine Fellowship and by the Israeli Science Foundation (ISF), Jerusalem, Israel, under Grant 10/12.

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Fig. 1

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Acknowledgements

The author thanks Tuvi Etzion and Mark Silberstein for the valuable discussions. The author also wishes to thank COST Action IC1104 “Random Network Coding and Designs over GF(q)” on travel support to present this work.

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Correspondence to Natalia Silberstein .

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Silberstein, N. (2015). Fractional Repetition and Erasure Batch Codes. In: Pinto, R., Rocha Malonek, P., Vettori, P. (eds) Coding Theory and Applications. CIM Series in Mathematical Sciences, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-17296-5_36

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