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Author: Carlos Ricardo Peixoto Hartmann Publisher: ISBN: Category : Coding theory Languages : en Pages : 158
Book Description
Two related aspects of cyclic codes have been investigated. An attempt has been made to obtain a better understanding concerning their minimum distance, and to find decoding methods to decode beyond the BCH bound. A theory is presented which enables one to obtain better bounds for the minimum distance of a large number of nonprimitive BCH codes. The derivation of this new theory is based on the use of more than one set of consecutive roots of the generator polynomial. The new results are easily applicable since they are based, as the BCH bound, on the pattern of the roots of the generator polynomial. A general decoding method to decode beyond the BCH bound is outlined. In addition a decoding method to decode beyond the BCH bound codes with minimum distance greater than the BCH bound and with multiple sets of consecutive roots is introduced. (Author).
Author: Carlos Ricardo Peixoto Hartmann Publisher: ISBN: Category : Coding theory Languages : en Pages : 158
Book Description
Two related aspects of cyclic codes have been investigated. An attempt has been made to obtain a better understanding concerning their minimum distance, and to find decoding methods to decode beyond the BCH bound. A theory is presented which enables one to obtain better bounds for the minimum distance of a large number of nonprimitive BCH codes. The derivation of this new theory is based on the use of more than one set of consecutive roots of the generator polynomial. The new results are easily applicable since they are based, as the BCH bound, on the pattern of the roots of the generator polynomial. A general decoding method to decode beyond the BCH bound is outlined. In addition a decoding method to decode beyond the BCH bound codes with minimum distance greater than the BCH bound and with multiple sets of consecutive roots is introduced. (Author).
Author: Kenneth Kai Ming Tzeng Publisher: ISBN: Category : Languages : en Pages : 128
Book Description
The work is largely concerned with the decoding problems of error-correcting codes. A direct approach to the solution of Berlekamp's key equation for decoding Bose-Chaudhuri-Hocquenghem codes with the consequent derivation of a modified Berlekamp Iterative Algorithm is presented. Iterative decoding of a syndrome sequence in reverse has been meaningful. A class of reversible cyclic codes is proved to have minimum distance greater than the BCH bound and it has been shown that reverse-sequence iterative decoding is the most natural technique to be coupled with the forward-sequence iterative decoding to decode this class of reversible codes beyond the BCH bound. For cyclic codes with minimum distance greater than their BCH bound, a scheme called syndrome transformation decoding is proposed for decoding the codes beyond their BCH bound. With this scheme, the possible adaption of these codes to be used in compound channels to correct random errors as well as burst errors is shown in an example. Based on the concept of syndrome transformation decoding, cyclic codes for single and multiple solid-burst error correction have been constructed including a simple decoding procedure. (Author).
Author: Demeter Krupka Publisher: Elsevier ISBN: 0080954235 Category : Mathematics Languages : en Pages : 787
Book Description
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether's theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles- First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces
Author: Publisher: ISBN: Category : Aeronautics Languages : en Pages : 832
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author: L. R. Espeland Publisher: ISBN: Category : Error-correcting codes (Information theory) Languages : en Pages : 36
Book Description
An exhaustive computer search for the best, simply implemented, cyclic (20, 8) codes was carried out, and the procedures and results are reported here. Some forty almost equally good (20, 8) codes are identified, but, alas, none of them appear to be better than the familiar (15, 5) Bose-Chaudhuri-Hocquenghem code.
Author: Cunsheng Ding Publisher: World Scientific ISBN: 981461937X Category : Mathematics Languages : en Pages : 354
Book Description
This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes. This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.
Author: Stephen B. Wicker Publisher: Springer Science & Business Media ISBN: 1402072643 Category : Technology & Engineering Languages : en Pages : 241
Book Description
Fundamentals of Codes, Graphs, and Iterative Decoding is an explanation of how to introduce local connectivity, and how to exploit simple structural descriptions. Chapter 1 provides an overview of Shannon theory and the basic tools of complexity theory, communication theory, and bounds on code construction. Chapters 2 - 4 provide an overview of "classical" error control coding, with an introduction to abstract algebra, and block and convolutional codes. Chapters 5 - 9 then proceed to systematically develop the key research results of the 1990s and early 2000s with an introduction to graph theory, followed by chapters on algorithms on graphs, turbo error control, low density parity check codes, and low density generator codes.
Author: Carlos Ricardo Peixoto Hartmann
Author: Carlos Ricardo Peixoto Hartmann
Author: 
Author: Kenneth Kai Ming Tzeng
Author: Demeter Krupka
Author: 
Author: Elwyn R. Berlekamp
Author: L. R. Espeland
Author: Cunsheng Ding
Author: Florence Jessie MacWilliams
Author: Stephen B. Wicker