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: 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: Richard E. Blahut Publisher: Cambridge University Press ISBN: 1139435078 Category : Technology & Engineering Languages : en Pages : 617
Book Description
The need to transmit and store massive amounts of data reliably and without error is a vital part of modern communications systems. Error-correcting codes play a fundamental role in minimising data corruption caused by defects such as noise, interference, crosstalk and packet loss. This book provides an accessible introduction to the basic elements of algebraic codes, and discusses their use in a variety of applications. The author describes a range of important coding techniques, including Reed-Solomon codes, BCH codes, trellis codes, and turbocodes. Throughout the book, mathematical theory is illustrated by reference to many practical examples. The book was first published in 2003 and is aimed at graduate students of electrical and computer engineering, and at practising engineers whose work involves communications or signal processing.
Author: Publisher: ISBN: Category : Languages : en Pages : 49
Book Description
The Berlekamp-Massey Algorithm (BMA) is commonly used in BCH decoding, but the Fundamental Iterative Algorithm (FIA) can, in many instances, correct more errors. The trade off lies in hardware complexity. The BMA has concise stages that do not require addressable memory, whereas the FIA struggles with memory management and complex stages. For the (17,9) BCH code over GF(256) with g(x)=m1(x), the FIA can correct up to two errors, but the BMA can correct only one error. Also, for a BER of 10( -5), the coding gains for the BMA and FIA are -.25dB and 1.4dB, respectively, which makes the FIA seem to be the better algorithm. The main drawback is the FIA is approximately 20 times more complex than the BMA. Also, the FIA does not have a critical path that is easily identified.
Author: John L. Fan Publisher: Springer Science & Business Media ISBN: 9780792374558 Category : Computers Languages : en Pages : 284
Book Description
Constrained Coding and Soft Iterative Decoding is the first work to combine the issues of constrained coding and soft iterative decoding (e.g., turbo and LDPC codes) from a unified point of view. Since constrained coding is widely used in magnetic and optical storage, it is necessary to use some special techniques (modified concatenation scheme or bit insertion) in order to apply soft iterative decoding. Recent breakthroughs in the design and decoding of error-control codes (ECCs) show significant potential for improving the performance of many communications systems. ECCs such as turbo codes and low-density parity check (LDPC) codes can be represented by graphs and decoded by passing probabilistic (a.k.a. `soft') messages along the edges of the graph. This message-passing algorithm yields powerful decoders whose performance can approach the theoretical limits on capacity. This exposition uses `normal graphs,' introduced by Forney, which extend in a natural manner to block diagram representations of the system and provide a simple unified framework for the decoding of ECCs, constrained codes, and channels with memory. Soft iterative decoding is illustrated by the application of turbo codes and LDPC codes to magnetic recording channels. For magnetic and optical storage, an issue arises in the use of constrained coding, which places restrictions on the sequences that can be transmitted through the channel; the use of constrained coding in combination with soft ECC decoders is addressed by the modified concatenation scheme also known as `reverse concatenation.' Moreover, a soft constraint decoder yields additional coding gain from the redundancy in the constraint, which may be of practical interest in the case of optical storage. In addition, this monograph presents several other research results (including the design of sliding-block lossless compression codes, and the decoding of array codes as LDPC codes). Constrained Coding and Soft Iterative Decoding will prove useful to students, researchers and professional engineers who are interested in understanding this new soft iterative decoding paradigm and applying it in communications and storage systems.
Author: Robert H. Morelos-Zaragoza Publisher: John Wiley & Sons ISBN: 0470035692 Category : Technology & Engineering Languages : en Pages : 278
Book Description
Building on the success of the first edition, which offered a practical introductory approach to the techniques of error concealment, this book, now fully revised and updated, provides a comprehensive treatment of the subject and includes a wealth of additional features. The Art of Error Correcting Coding, Second Edition explores intermediate and advanced level concepts as well as those which will appeal to the novice. All key topics are discussed, including Reed-Solomon codes, Viterbi decoding, soft-output decoding algorithms, MAP, log-MAP and MAX-log-MAP. Reliability-based algorithms GMD and Chase are examined, as are turbo codes, both serially and parallel concatenated, as well as low-density parity-check (LDPC) codes and their iterative decoders. Features additional problems at the end of each chapter and an instructor’s solutions manual Updated companion website offers new C/C ++programs and MATLAB scripts, to help with the understanding and implementation of basic ECC techniques Easy to follow examples illustrate the fundamental concepts of error correcting codes Basic analysis tools are provided throughout to help in the assessment of the error performance block and convolutional codes of a particular error correcting coding (ECC) scheme for a selection of the basic channel models This edition provides an essential resource to engineers, computer scientists and graduate students alike for understanding and applying ECC techniques in the transmission and storage of digital information.
Author: Kenneth Kai Ming Tzeng
Author: Carlos Ricardo Peixoto Hartmann
Author: 
Author: Scott A. Vanstone
Author: José Antonio Vanderhorst
Author: Richard E. Blahut
Author: 
Author: John L. Fan
Author: Robert H. Morelos-Zaragoza
Author: Kenneth Dubbs