© 2015

Polynomial Theory of Error Correcting Codes

  • Enables the reader gradually to gain a clear understanding of the theory with the aid of more than 100 examples

  • Allows rapid location of information by means of a list of more than 150 indexed definitions

  • Offers technicians a new perspective through a unitary approach to block and convolutional codes


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

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Generator Matrix

  3. Parity Check Matrix

  4. Modern Coding

    1. Front Matter
      Pages 471-471
    2. Giovanni Cancellieri
      Pages 473-502
    3. Giovanni Cancellieri
      Pages 503-543
    4. Giovanni Cancellieri
      Pages 545-580
    5. Giovanni Cancellieri
      Pages 581-622
  5. Back Matter
    Pages 623-732

About this book


The book offers an original view on channel coding, based on a unitary approach to block and convolutional codes for error correction. It presents both new concepts and new families of codes. For example, lengthened and modified lengthened cyclic codes are introduced as a bridge towards time-invariant convolutional codes and their extension to time-varying versions. The novel families of codes include turbo codes and low-density parity check (LDPC) codes, the features of which are justified from the structural properties of the component codes. Design procedures for regular LDPC codes are proposed, supported by the presented theory. Quasi-cyclic LDPC codes, in block or convolutional form, represent one of the most original contributions of the book. The use of more than 100 examples allows the reader gradually to gain an understanding of the theory, and the provision of a list of more than 150 definitions, indexed at the end of the book, permits rapid location of sought information.


Digital Communications Digital Error Control Error Correcting Codes Generator Matrix Parity Check Matrix Reliable Data Transmission

Authors and affiliations

  1. 1.Information EngineeringPolytechnic University of MarcheAnconaItaly

About the authors

Giovanni Cancellieri is full professor of Telecommunications at Polytechnic University of Marche, Italy. His main research activities relate to optical communications, multimedia services, networks, mobile communications, and channel coding. He is a member of various worldwide and European technical associations and standardization bodies.

Bibliographic information

  • Book Title Polynomial Theory of Error Correcting Codes
  • Authors Giovanni Cancellieri
  • Series Title Signals and Communication Technology
  • Series Abbreviated Title Signals, Communication Technology
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-01726-6
  • Softcover ISBN 978-3-319-37870-1
  • eBook ISBN 978-3-319-01727-3
  • Series ISSN 1860-4862
  • Series E-ISSN 1860-4870
  • Edition Number 1
  • Number of Pages XVIII, 732
  • Number of Illustrations 320 b/w illustrations, 0 illustrations in colour
  • Topics Signal, Image and Speech Processing
    Field Theory and Polynomials
    Arithmetic and Logic Structures
  • Buy this book on publisher's site
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“This well-written book offers a structural and comprehensive view of the polynomial theory of many classes of error correcting codes to a general reader. In particular, nearly 500 examples and many nice figures are very helpful.” (Qiang and Wang, zbMATH 1401.94004, 2019)

“The unified approach of polynomials makes this book quite interesting. It will be quite useful for researchers and engineers working in the field. It can also be used as supplementary material for an advanced undergraduate course or a graduate-level course in coding theory. … the book is good reading. I enjoyed it and I strongly recommend it to any coding theorists.” (Manish Gupta, Computing Reviews, August, 2015)