Binomial Product Generator LDPC Block Codes

  • Giovanni CancellieriEmail author
Part of the Signals and Communication Technology book series (SCT)


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.


Code Rate LDPC Code Parity Check Code Word Convolutional Code 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Information EngineeringPolytechnic University of MarcheAnconaItaly

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