Wide-Sense Time-Invariant Block Codes in Their Generator Matrix

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


A wide-sense time-invariant block code is characterized by more than one generator polynomial periodically repeating in its generator matrix. Interleaved multiplication enables us to construct a code word. A quasi-cyclic code can be considered as a generalization of a cyclic code, with a characteristic block length, always integer multiple of the period. These codes are presented in a reordered form, traditionally adopted. An interpretation of known block codes with composite block length as quasi-cyclic codes is provided. They can be set in correspondence with cyclic or pseudo-cyclic codes in a non-binary alphabet. Encoder circuits for quasi-cyclic codes are discussed, always adopting the generator matrix model. Their evolution is described in a non-binary state diagram. Also for quasi-cyclic codes, the operations of code shortening, code puncturation, and code lengthening are possible, with reference to either the original form or a properly reordered form. A first introduction to array codes is given. Permutation circulants are adopted as very efficient tools for performing an interleaver function. Modified lengthened quasi-cyclic codes show the typical characteristics of wide-sense time-invariant convolutional codes. The concept of subcodes is extended to the case of quasi-cyclic codes. Finally, some trellises of quasi-cyclic codes are discussed, especially when they allow a simplified computational complexity in soft-decision decoding through a proper partitioning.


Generator Matrix Block Code LDPC Code Code Word Cyclic Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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