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Polynomial Theory of Error Correcting Codes pp 545–580Cite as

Binomial Product Generator LDPC Block Codes

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

Abstract

Generalized parity check codes in serial concatenation or in parallelepiped concatenation form composite codes whose properties are similar to those of array codes. These two families of codes are comprehensively named binomial product generator codes (BPG codes). In fact, short low-weight code words in them are constructed as the product of a certain number of binomials. They are good LDPC block codes whose performance can be improved avoiding the occurrence of equalities in their construction parameters. The minimum distance, always even, can be predicted. The study of improper array codes is developed more in detail. Generalized array codes, which are still quasi-cyclic, but non-uniform, are analyzed. Their generator matrix, formed by time-varying circulants, is calculated. One further possible variant of improper array codes is presented. A particular class of high-rate quasi-cyclic codes, whose parity check matrix is made by only one layer of circulants, are studied. Their minimum distance is calculated. This class of codes can be transformed, by proper unwrapping, into good high-rate convolutional codes, whose performance can be easily predicted.

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Authors and Affiliations

  1. Information Engineering, Polytechnic University of Marche, Ancona, Italy

    Giovanni Cancellieri

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  1. Giovanni Cancellieri
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Correspondence to Giovanni Cancellieri .

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© 2015 Springer International Publishing Switzerland

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Cancellieri, G. (2015). Binomial Product Generator LDPC Block Codes. In: Polynomial Theory of Error Correcting Codes. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-01727-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-01727-3_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01726-6

  • Online ISBN: 978-3-319-01727-3

  • eBook Packages: EngineeringEngineering (R0)

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