On Complexity of Decoding Binary Cyclic Codes Using Covering Polynomials
Author : Wonjin Sung
Publisher :
Page : 290 pages
File Size : 49,11 MB
Release : 1995
Category :
ISBN :
Author : Wonjin Sung
Publisher :
Page : 290 pages
File Size : 49,11 MB
Release : 1995
Category :
ISBN :
Author : Jaques Calmet
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 17,29 MB
Release : 1986-07
Category : Computers
ISBN : 9783540167761
Author : Norman Abramson
Publisher :
Page : 24 pages
File Size : 44,28 MB
Release : 1969
Category :
ISBN :
It is shown that the product of two cyclic codes with block lengths relatively prime can be described in terms of two interlaced codes. An improved characterization of the generating polynomial of the product code is provided in terms of the generating polynomials of the two original codes. It is shown that the product code and seven other codes related to the product code (called a code group) can all be obtained from four canonical polynomials which may be calculated using the Euclidean Algorithm. These results then lead to simple encoder realizations for cyclic code groups and to a decoding algorithm, called cascade decoding. (Author).
Author :
Publisher :
Page : 540 pages
File Size : 12,36 MB
Release : 1994
Category : Information theory
ISBN :
Author : Keith Saints
Publisher :
Page : 352 pages
File Size : 44,97 MB
Release : 1995
Category :
ISBN :
Author : J-P Barthelmy
Publisher : CRC Press
Page : 284 pages
File Size : 44,43 MB
Release : 2020-08-14
Category : Computers
ISBN : 1000159434
In this treatment of algorithmic complexity the authors explore an area fundamental to the study of the foundations of computer science. It is a topic which is at the interface of information theory, applied mathematics and computer language theory and which is rooted strongly in this book in the problems of computer communication.; Complexity theory classifies problems according to the difficulty of resolving them, while algorithms provide the computational method for solving those problems. Therefore, algorithmic complexity is concerned with establishing the best algorithm given the constraints of the computational environment and the degree of complexity.; The first three chapters present the context for a later in-depth look at applied areas of the subject, with an outline of classical complexity theory. This is followed by three chapters which explore the key area of information communication. Within this field, the book is particularly concerned with two contiguous areas which make contrasting demands on the application of algorithmic complexity. Cryptography demands the creation of extremely complex problems in order to achieve its goal of security, whereas in coding for communication the emphasis is on maximizing the compact nature of the message and providing the error correction necessary for the message to achieve optimum speed. The two must co-exist and the methods outlined in "Algorithmic Complexity" suggest a number of approaches to such problems based on extensive examples of the authors' experience.; This senior undergraduate book should be an essential read for those studying advanced topics in theoretical computer science and should provide an introduction to applied complexity for researchers and professionals alike.
Author : Marc Fossorier
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 25,74 MB
Release : 1999-11-03
Category : Computers
ISBN : 3540667237
This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999. The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.
Author : W. Cary Huffman
Publisher : CRC Press
Page : 998 pages
File Size : 25,91 MB
Release : 2021-03-26
Category : Computers
ISBN : 1351375105
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
Author : Shu Lin
Publisher : Cambridge University Press
Page : 843 pages
File Size : 13,47 MB
Release : 2021-12-09
Category : Computers
ISBN : 1316512622
An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.
Author : IEEE Information Theory Society
Publisher : Institute of Electrical & Electronics Engineers(IEEE)
Page : 548 pages
File Size : 19,32 MB
Release : 1994
Category : Computers
ISBN :