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Error Correcting Codes Based on Probabilistic Decoding and Sparse Matrices

  • Hironori Uchikawa
Chapter
Part of the Mathematics for Industry book series (MFI, volume 5)

Abstract

These days we encounter many digital storage and communication devices in our daily lives. They contain error correcting codes that operate when data is read from storage devices or received via communication devices. For example, you can listen to music on a compact disc even if its surface is scratched. This article introduces low density parity check (LDPC) codes and the sum-product decoding algorithm. LDPC codes, one class of error correcting codes, have been used for practical applications such as hard disk drives and satellite digital broadcast systems because their performance closely approaches the theoretical limit with manageable computational complexity. In particular, it is shown that an optimal decoding algorithm from the viewpoint of probabilistic inference can be derived with LDPC codes.

Keywords

LDPC Error correcting Probabilistic decoding Sparse Sum-product algorithm MAP 

References

  1. 1.
    R.G. Gallager, in Low-Density Parity-Check Codes (MIT Press, Cambridge, 1963)Google Scholar
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    S. Lin, D.J. Costello, in Error Control Coding, 2nd edn. (Prentice Hall, Englewood Cliffs, 2004)Google Scholar
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    T.J. Richardson, R. Urbanke, in Modern Coding Theory (Cambridge University Press, Cambridge, 2008)Google Scholar
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    W.E. Ryan, S. Lin, in Channel Codes: Classical and Modern (Cambridge University Press, Cambridge, 2009)Google Scholar
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    C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. (1948)Google Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Center for Semiconductor Research and DevelopmentToshiba Corporation, Semiconductor & Storage Products CompanyYokohamaJapan

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