Информатика и вычислительная техника
  • формат pdf
  • размер 7.87 МБ
  • добавлен 26 октября 2011 г.
Huffman W.C., Pless V. Fundamentals of Error-Correcting Codes
Издательство Cambridge University Press, 2003, -665 pp.

Coding theory originated with the 1948 publication of the paper A mathematical theory of communication by Claude Shannon. For the past half century, coding theory has grown into a discipline intersecting mathematics and engineering with applications to almost every area of communication such as satellite and cellular telephone transmission, compact disc recording, and data storage.
During the 50th anniversary year of Shannon’s seminal paper, the two volume Handbook of Coding Theory, edited by the authors of the current text, was published by Elsevier Science. That Handbook, with contributions from 33 authors, covers a wide range of topics at the frontiers of research. As editors of the Handbook, we felt it would be appropriate to produce a textbook that could serve in part as a bridge to the Handbook. This textbook is intended to be an in-depth introduction to coding theory from both a mathematical and engineering viewpoint suitable either for the classroom or for individual study. Several of the topics are classical, while others cover current subjects that appear only in specialized books and joual publications. We hope that the presentation in this book, with its numerous examples and exercises, will serve as a lucid introduction that will enable readers to pursue some of the many themes of coding theory.
Fundamentals of Error-Correcting Codes is a largely self-contained textbook suitable for advanced undergraduate students and graduate students at any level. A prerequisite for this book is a course in linear algebra. A course in abstract algebra is recommended, but not essential. This textbook could be used for at least three semesters. A wide variety of examples illustrate both theory and computation. Over 850 exercises are interspersed at points in the text where they are most appropriate to attempt. Most of the theory is accompanied by detailed proofs, with some proofs left to the exercises. Because of the number of examples and exercises that directly illustrate the theory, the instructor can easily choose either to emphasize or deemphasize proofs.
Basic concepts of linear codes.
Bounds on the size of codes.
Finite fields.
Cyclic codes.
BCH and Reed–Solomon codes.
Duadic codes.
Weight distributions.
Self-dual codes.
Some favorite self-dual codes.
Covering radius and cosets.
Codes over Z4.
Codes from algebraic geometry.
Convolutional codes.
Soft decision and iterative decoding.
Смотрите также

Betten (etc.) Error-Correcting Linear Codes. Classification by Isometry and Applications

  • формат pdf
  • размер 6.67 МБ
  • добавлен 05 декабря 2011 г.
Издательство Springer, 2006, -818 pp. The fascinating theory of error-correcting codes is a rather new addition to the list of mathematical disciplines. It grew out of the need to communicate information electronically, and is currently no more than 60 years old. Being an applied discipline by definition, a surprisingly large number of pure mathematical areas tie into Coding Theory. If one were to name just the most important connections, one wo...

Cameron P.J. Combinatorics - Topics, Techniques, Algorithms

  • формат djvu
  • размер 4.17 МБ
  • добавлен 04 октября 2011 г.
Издательство Cambridge University Press, 1995, -355 pp. If anything at all can be deduced from the two quotations at the top of this page, perhaps it is this: Combinatorics is an essential part of the human spirit; but it is a difficult subject foi the abstract, axiomatising Bourbaki school of mathematics to comprehend. Nevertheless, the advent of computers and electronic communications have made it a more important subject than ever. . This is a...

Csisz?r I., Katona G., Tardos G. (eds.) Entropy, Search, Complexity

  • формат pdf
  • размер 1.51 МБ
  • добавлен 22 октября 2011 г.
Издательство Springer, 2007, -261 pp. J?nos Bolyai Mathematical Society. The present volume is a collection of survey papers in the fields given in the title. They summarize the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. The volume is slightly related to the twin conferences...

Fragouli C., Soljanin E. Network Coding Fundamentals

  • формат pdf
  • размер 958.71 КБ
  • добавлен 31 января 2012 г.
Из серии Foundations and Trends in Networking издательства NOWPress, 2007, -149 pp. Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. This tutorial addresses the first most natural questions one would ask about this new technique: how network coding works and what are its benefits, how netwo...

Laywine C.F., Mullen G.L. Discrete Mathematics Using Latin Squares

  • формат djvu
  • размер 2.47 МБ
  • добавлен 22 октября 2011 г.
Издательство John Wiley, 1998, -163 pp. This book is designed as a textbook. Its aim is to introduce various areas and applications in discrete mathematics via the use of Latin squares. Latin squares have been studied for centuries. They have a very fascinating history and, more important, many practical applications in areas of science, engineering, and statistics as well as being used widely within mathematics itself. In recognition of the sig...

Lin S., Costello D. Error Control Coding Fundamentals and Applications

  • формат pdf
  • размер 5.8 МБ
  • добавлен 28 октября 2011 г.
Издательство Prentice-Hall, 1983, -624 pp. This book owes its beginnings to the pioneering work of Claude Shannon in 1948 on achieving reliable communication over a noisy transmission channel. Shannon's central theme was that if the signaling rate of the system is less than the channel capacity, reliable communication can be achieved if one chooses proper encoding and decoding techniques. The design of good codes and of efficient decoding method...

Nebe G., Rains E.M., Sloane N.J.A. Self-Dual Codes and Invariant Theory

  • формат pdf
  • размер 3.11 МБ
  • добавлен 30 ноября 2011 г.
Издательство Springer, 2006, -447 pp. This book has two goals. On the one hand it develops a completely new unifying theory of self-dual codes that enables us to prove a far-reaching generalization of Gleason’s theorem on weight enumerators of self-dual codes. On the other hand it is an encyclopedia that gives a very extensive list of Types of self-dual codes and their properties—the associated Clifford-Weil groups and their invariants, in parti...

Nowakowski R.J. Games of no Chance

  • формат pdf
  • размер 6.32 МБ
  • добавлен 28 октября 2011 г.
Издательство MRSI, 1996, -482 pp. Combinatorial Game Theory, as an academic discipline, is still in its infancy. Many analyses of individual games have appeared in print, starting in 1902 with C. L. Bouton's analysis of the game of Nim. (For exact references to the works mentioned here, please see A. Fraenkel's bibliography on pages 493. It is was not until the 1930's that a consistent theory for impartial games was developed, independently, by...

Oggier F., Viterbo E. Algebraic Number Theory and Code Design for Rayleigh Fading Channels

  • формат pdf
  • размер 1.06 МБ
  • добавлен 28 октября 2011 г.
Из серии Foundations and Trends in Communications and Information Theory издательства NOWPress, 2004, -97 pp. Elementary number theory was the basis of the development of error correcting codes in the early years of coding theory. Finite fields were the key tool in the design of powerful binary codes and gradually entered in the general mathematical background of communications engineers. Thanks to the technological developments and increased pr...

Pretzel O. Error-Correcting Codes and Finite Fields

  • формат djvu
  • размер 13.06 МБ
  • добавлен 28 октября 2011 г.
Издательство Clarendon Press, 1992, -205 pp. This book arose out of a series of courses given to students of mathematics and electrical engineering at Imperial College. The theory of error-correcting block codes combines mathematical elegance and practical utility to an unusual degree. Thus, the intention of the courses was twofold. On the one hand I wished to introduce the mathematicians to some attractive practical problems and to address,thes...