Assuming little previous mathematical knowledge, Error Correcting Codes provides a sound introduction to key areas of the subject. Topics have been chosen for their importance and practical significance, which Baylis demonstrates in a rigorous but gentle mathematical style.Coverage includes optimal codes; linear and non-linear codes; general techniques of decoding errors and erasures; error detection; syndrome decoding, and much more. Error Correcting Codes contains not only straight maths, but also exercises on more investigational problem solving. Chapters on number theory and polynomial algebra are included to support linear codes and cyclic codes, and an extensive reminder of relevant topics in linear algebra is given. Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided.Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical fields, software engineering, communications engineering, computer science and information technology, and to organizations with substantial research and development in those areas.
Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint.
5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 ...
This text offers both "classical" coding theory-such as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codes-as well as modern codes and decoding methods, including turbo codes, LDPC codes, repeat-accumulate codes, space time ...
The digital companion of the book is a non-printable .pdf document with hyperlinks. The examples included in the book can be run with just a mouse click and modified and saved by users for their own purpose.
An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.
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Show that in a binary group block code either all the code words have even weight or half have even weight , half odd . ( Hint : Show that the code words of even ... Assume the matrix M given in the example of Section 3.6 . 3.13 .
In-depth introduction to coding theory from both an engineering and mathematical viewpoint.
Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3, Grenoble, France, July 15-19, 1985. Proceedings
The definition-theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible.