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Wide-Sense Time-Invariant Convolutional Codes in Their Parity Check Matrix

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

Abstract

The circuit for syndrome calculation in a convolutional code is introduced. The most general method for obtaining the parity check matrix in a convolutional code, starting from its generator matrix, is presented. The minimal encoder circuit is discussed. Wide-sense time-invariant convolutional codes form a closed ensemble. Code puncturation is studied for convolutional codes looking at their parity check matrix. Tail-biting w.s. time-invariant convolutional codes are examined, considering both the generator and the parity check matrix. Unwrapping a quasi-cyclic code for obtaining convolutional codes, in general w.s. time-invariant, leads to a second conceptual bridge between these two classes of codes, in particular regarding their parity check matrix. This observation is important especially for low-density parity-check codes (LDPC codes). Array codes are now interpreted as LDPC block codes without short cycles of 1-symbols. It is possible to obtain an unwrapped form for such codes, in order to construct interesting LDPC convolutional codes. The equivalence between an array code with two component codes and a direct product code between two parity check codes is demonstrated. The concept of truncated circulants is transferred to a description based on the parity check matrix.

Keywords

LDPC Code Parity Check Convolutional Code Parity Check Matrix Component 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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