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    On encoding symbol degrees of array BP-XOR codes

    Paterson, Maura B. and Stinson, D.R. and Wang, Y. (2016) On encoding symbol degrees of array BP-XOR codes. Cryptography and Communications 8 (1), pp. 19-32. ISSN 1936-2447.

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    Abstract

    Low density parity check (LDPC) codes, LT codes and digital fountain techniques have received significant attention from both academics and industry in the past few years. By employing the underlying ideas of efficient Belief Propagation (BP) decoding process (also called iterative message passing decoding process) on binary erasure channels (BEC) in LDPC codes, Wang has recently introduced the concept of array BP-XOR codes and showed the necessary and sufficient conditions for MDS [k + 2,k] and [n,2] array BP-XOR codes. In this paper, we analyze the encoding symbol degree requirements for array BP-XOR codes and present new necessary conditions for array BP-XOR codes. These new necessary conditions are used as a guideline for constructing several array BP-XOR codes and for presenting a complete characterization (necessary and sufficient conditions) of degree two array BP-XOR codes and for designing new edge-colored graphs. Meanwhile, these new necessary conditions are used to show that the codes by Feng, Deng, Bao, and Shen in IEEE Transactions on Computers are incorrect.

    Metadata

    Item Type: Article
    Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s12095-015-0134-9
    Keyword(s) / Subject(s): Array codes, Encoding symble degrees, MDS array codes, Bounds on codes, Error corecting codes, 94B65, 94A45, 94B05
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Maura Paterson
    Date Deposited: 08 May 2015 08:28
    Last Modified: 20 Jun 2016 13:19
    URI: http://eprints.bbk.ac.uk/id/eprint/12070

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