Introduction to the theory of error-correcting codes pless pdf

Toggle navigation. It considers such codes as Hamming codes and Golay codes, correction of double errors, use of finite fields, cyclic codes, BCH codes and weight distributions, as well as design of codes. In this second edition, the author includes more material on non-binary code and cyclic codes.

In addition some proofs have been simplified and there are many more examples and problems. The text has been aimed at mathematicians, electrical engineers and computer scientists. Introduction to the Theory of Error-correcting Codes. Categories: Error-correcting codes Information theory. Get Books. An introduction to the theory of error-correction codes, and in particular to linear block codes is provided in this book.

It considers such codes as Hamming codes and Golay codes, correction of double errors, use of finite fields, cyclic codes, BCH codes and weight distributions, as well as design of.

Introduction to the Theory of Error-Correcting Codes. Introduction to Coding Theory. Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration. Introduction to Coding Theory introduces the theory of error-correcting codes in.

A complete introduction to the many mathematical tools used tosolve practical problems in coding. Mathematicians have been fascinated with the theory oferror-correcting codes since the publication of Shannon's classicpapers fifty years ago.

A short summary of this paper. Introduction to the theory of error-correcting codes third edition. Kluwer Academic Publishers, Dordrecht. Contents: Preface. Informal introduction: Data processing, interval computations, and computational complexity. The notions of feasibility and NP-hardness: Brief introduction.

In the general case, the basic problem of interval computations is intractable. Basic problem of interval computations for polynomials of a fixed number of variables. Basic problem of interval computations for polynomials with bounded coefficients.

Fixed data processing algorithms, varying data: Still NP-hard. Fixed data, varying data processing algorithms: Still intractable. What if we only allow some arithmetic operations in data processing?

For fractionally-linear functions, a feasible algorithm solves the basic problem of interval computations. Solving interval linear systems is NP-hard. Interval linear systems: Search for feasible classes. Physical corollary: Prediction is not always possible, even for linear systems with known dynamics.

Engineering corollary: Signal processing is NP-hard. Bright sides of NP-hardness of interval computations I: NP-hard means that good interval heuristics can solve other hard problems. If input intervals are narrow enough, then interval computations are almost always easy.

Optimization--A first example of a numerical problem in which interval methods are used: Computational complexity and feasibility. Solving systems of equations. Approximations of interval functions. Solving differential equations.

Properties of interval matrices I: Main results. Properties of interval matrices II: Proofs and auxiliary results. Non- interval uncertainty I: Ellipsoid uncertainty and its generalizations. Non-interal uncertainty II: Multi-intervals and their generalizations. What if quantities are discrete? Error estimation for indirect measurements: Interval computation problem is slightly harder than a similar probabilistic computational problem.

In case of interval or more general uncertainty, no algorithm can choose the simplest representative. Error estimation for indirect measurements: Case of approximately known functions. From interval computations to modal mathematics. Beyond NP: Two roots good, one root better. Does "NP-hard" really mean 'intractable"? The worse, the better: Paradoxical computational complexity of interval computations and data processing. The Patterns Handbook: Techniaues. Strateoies, and Avvlications.

Edited by Linda Rising. Cambridge Univer- sity Press, New York. Contents: About the editor. Foreword James Coplien. Design patterns: Ele- ments of reusable architectures Linda Rising. An overview of patterns Russell Corfman. Patterns: Spreading the word Linda Rising. A training experience with patterns Brandon Goldfedder and Linda Rising.

Patterns: The new building blocks for reusable software architectures Diane Saunders. Examples and experience. Pattern writing Linda Rising. Writers workshop format. AGCS pattern template.