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Batch and PIR Codes and Their Connections to Locally Repairable Codes

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Network Coding and Subspace Designs

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

Two related families of codes are studied: batch codes and codes for private information retrieval. These two families can be viewed as natural generalizations of locally repairable codes, which were extensively studied in the context of coding for fault tolerance in distributed data storage systems. Bounds on the parameters of the codes, as well as basic constructions, are presented. Connections between different code families are discussed.

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Notes

  1. 1.

    This result is proven in Theorem 6, Chap. “An Overview of Coding for Distributed Storage Systems”.

  2. 2.

    In particular, the use of matroids in bounding the parameters of various families of codes with locality is thoroughly treated in chapter “Matroid Theory and Storage Codes: Bounds and Constructions”.

  3. 3.

    Please note that generally it does not follow here that the bounds for LRCs with locality of all symbols are applicable to systematic batch or PIR codes.

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Acknowledgements

The material in this chapter has benefited a lot from discussions of the author with his students and colleagues, including Venkatesan Guruswami, Camilla Hollanti, Helger Lipmaa, Sushanta Paudyal, Eldho Thomas, Alexander Vardy, Hui Zhang and Jens Zumbrägel. This work is supported in part by the grants PUT405 and IUT2-1 from the Estonian Research Council and by the EU COST Action IC1104.

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Authors and Affiliations

  1. Institute of Computer Science, University of Tartu, 50409, Tartu, Estonia

    Vitaly Skachek

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Correspondence to Vitaly Skachek .

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Editors and Affiliations

  1. Department of Mathematics and Systems Analysis, Aalto University, Espoo, Finland

    Marcus Greferath

  2. Faculty of Electrical Engineering and Computing, Department of Applied Mathematics, University of Zagreb, Zagreb, Croatia

    Mario Osvin Pavčević

  3. Yahoo Research, Haifa, Israel

    Natalia Silberstein

  4. Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, Barcelona, Spain

    María Ángeles Vázquez-Castro

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Skachek, V. (2018). Batch and PIR Codes and Their Connections to Locally Repairable Codes. In: Greferath, M., Pavčević, M., Silberstein, N., Vázquez-Castro, M. (eds) Network Coding and Subspace Designs. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-70293-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-70293-3_16

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