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| Author | : Richard Wesley Hamming |
| Publisher | : Prentice Hall |
| Total Pages | : 280 |
| Release | : 1986 |
| Genre | : Computers |
| ISBN | : |
Focusing on both theory and practical applications, this volume combines in a natural way the two major aspects of information representation--representation for storage (coding theory) and representation for transmission (information theory).
| Author | : Gareth A. Jones |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 217 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1447103610 |
This text is an elementary introduction to information and coding theory. The first part focuses on information theory, covering uniquely decodable and instantaneous codes, Huffman coding, entropy, information channels, and Shannon’s Fundamental Theorem. In the second part, linear algebra is used to construct examples of such codes, such as the Hamming, Hadamard, Golay and Reed-Muller codes. Contains proofs, worked examples, and exercises.
| Author | : Steven Roman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 520 |
| Release | : 1992-06-04 |
| Genre | : Mathematics |
| ISBN | : 9780387978123 |
This book is an introduction to information and coding theory at the graduate or advanced undergraduate level. It assumes a basic knowledge of probability and modern algebra, but is otherwise self- contained. The intent is to describe as clearly as possible the fundamental issues involved in these subjects, rather than covering all aspects in an encyclopedic fashion. The first quarter of the book is devoted to information theory, including a proof of Shannon's famous Noisy Coding Theorem. The remainder of the book is devoted to coding theory and is independent of the information theory portion of the book. After a brief discussion of general families of codes, the author discusses linear codes (including the Hamming, Golary, the Reed-Muller codes), finite fields, and cyclic codes (including the BCH, Reed-Solomon, Justesen, Goppa, and Quadratic Residue codes). An appendix reviews relevant topics from modern algebra.
| Author | : Isaac Woungang |
| Publisher | : World Scientific |
| Total Pages | : 725 |
| Release | : 2010-02-26 |
| Genre | : Computers |
| ISBN | : 981446919X |
The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.All of the chapters are integrated in a manner that renders the book as a supplementary reference volume or textbook for use in both undergraduate and graduate courses on information and coding theory. As such, it will be a valuable text for students at both undergraduate and graduate levels as well as instructors, researchers, engineers, and practitioners in these fields.Supporting Powerpoint Slides are available upon request for all instructors who adopt this book as a course text.
| Author | : Steven Roman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 1996-11-26 |
| Genre | : Computers |
| ISBN | : 9780387947044 |
This book is intended to introduce coding theory and information theory to undergraduate students of mathematics and computer science. It begins with a review of probablity theory as applied to finite sample spaces and a general introduction to the nature and types of codes. The two subsequent chapters discuss information theory: efficiency of codes, the entropy of information sources, and Shannon's Noiseless Coding Theorem. The remaining three chapters deal with coding theory: communication channels, decoding in the presence of errors, the general theory of linear codes, and such specific codes as Hamming codes, the simplex codes, and many others.
| Author | : Alexei Ashikhmin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 192 |
| Release | : 2005 |
| Genre | : Computers |
| ISBN | : 0821836269 |
In these papers associated with the workshop of December 2003, contributors describe their work in fountain codes for lossless data compression, an application of coding theory to universal lossless source coding performance bounds, expander graphs and codes, multilevel expander codes, low parity check lattices, sparse factor graph representations of Reed-Solomon and related codes. Interpolation multiplicity assignment algorithms for algebraic soft- decision decoding of Reed-Solomon codes, the capacity of two- dimensional weight-constrained memories, networks of two-way channels, and a new approach to the design of digital communication systems. Annotation :2005 Book News, Inc., Portland, OR (booknews.com).
| Author | : Edgar Martinez-Moro |
| Publisher | : World Scientific |
| Total Pages | : 334 |
| Release | : 2013 |
| Genre | : Computers |
| ISBN | : 9814335754 |
Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.
| Author | : J. H. van Lint |
| Publisher | : Springer |
| Total Pages | : 146 |
| Release | : 2009-08-14 |
| Genre | : Mathematics |
| ISBN | : 3540366571 |
These lecture notes are the contents of a two-term course given by me during the 1970-1971 academic year as Morgan Ward visiting professor at the California Institute of Technology. The students who took the course were mathematics seniors and graduate students. Therefore a thorough knowledge of algebra. (a. o. linear algebra, theory of finite fields, characters of abelian groups) and also probability theory were assumed. After introducing coding theory and linear codes these notes concern topics mostly from algebraic coding theory. The practical side of the subject, e. g. circuitry, is not included. Some topics which one would like to include 1n a course for students of mathematics such as bounds on the information rate of codes and many connections between combinatorial mathematics and coding theory could not be treated due to lack of time. For an extension of the course into a third term these two topics would have been chosen. Although the material for this course came from many sources there are three which contributed heavily and which were used as suggested reading material for the students. These are W. W. Peterson's Error-Correcting Codes «(15]), E. R. Berlekamp's Algebraic Coding Theory «(5]) and several of the AFCRL-reports by E. F. Assmus, H. F. Mattson and R. Turyn ([2], (3), [4] a. o. ). For several fruitful discussions I would like to thank R. J. McEliece.
| Author | : L.R. Vermani |
| Publisher | : CRC Press |
| Total Pages | : 270 |
| Release | : 1996-07-01 |
| Genre | : Mathematics |
| ISBN | : 9780412573804 |
Coding theory came into existence in the late 1940's and is concerned with devising efficient encoding and decoding procedures. The book is intended as a principal text for first courses in coding and algebraic coding theory, and is aimed at advanced undergraduates and recent graduates as both a course and self-study text. BCH and cyclic, Group codes, Hamming codes, polynomial as well as many other codes are introduced in this textbook. Incorporating numerous worked examples and complete logical proofs, it is an ideal introduction to the fundamental of algebraic coding.
| Author | : Elwyn R Berlekamp |
| Publisher | : World Scientific |
| Total Pages | : 501 |
| Release | : 2015-03-26 |
| Genre | : Mathematics |
| ISBN | : 981463591X |
This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.
