Trellis Decoding of Block Codes

Trellis Decoding of Block Codes PDF Author: Bahram Honary
Publisher: Springer Science & Business Media
ISBN: 1461562791
Category : Technology & Engineering
Languages : en
Pages : 277

Book Description
It is a great pleasure to be asked to write the Preface for this book on trellis decoding of error correcting block codes. The subject is extremely significant both theoretically and practically, and is very timely because of recent devel opments in the microelectronic implementation and range of application of error-control coding systems based on block codes. The authors have been notably active in signal processing and coding research and development for several years, and therefore very well placed to contribute to the state of the art on the subject of trellis decoding. In particular, the book represents a unique approach to many practical aspects of the topic. As the authors point out, there are two main classes of error control codes: block codes and convolutinal codes. Block codes came first historically and have a well-developed mathematical structure. Convolutional codes come later, and have developed heuristically, though a more formal treatment has emerged via recent developments in the theory of symbolic dynamics. Max imum likelihood (ML) decoding of powerful codes in both these classes is computationally complex in the general case; that is, ML decoding fails into the class of NP-hard computational problems. This arieses because the de coding complexity is an exponential function of key parameters of the code.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes PDF Author: Shu Lin
Publisher: Springer Science & Business Media
ISBN: 1461557453
Category : Technology & Engineering
Languages : en
Pages : 290

Book Description
As the demand for data reliability increases, coding for error control becomes increasingly important in data transmission systems and has become an integral part of almost all data communication system designs. In recent years, various trellis-based soft-decoding algorithms for linear block codes have been devised. New ideas developed in the study of trellis structure of block codes can be used for improving decoding and analyzing the trellis complexity of convolutional codes. These recent developments provide practicing communication engineers with more choices when designing error control systems. Trellises and Trellis-based Decoding Algorithms for Linear Block Codes combines trellises and trellis-based decoding algorithms for linear codes together in a simple and unified form. The approach is to explain the material in an easily understood manner with minimal mathematical rigor. Trellises and Trellis-based Decoding Algorithms for Linear Block Codes is intended for practicing communication engineers who want to have a fast grasp and understanding of the subject. Only material considered essential and useful for practical applications is included. This book can also be used as a text for advanced courses on the subject.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes PDF Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722847944
Category :
Languages : en
Pages : 94

Book Description
A code trellis is a graphical representation of a code, block or convolutional, in which every path represents a codeword (or a code sequence for a convolutional code). This representation makes it possible to implement Maximum Likelihood Decoding (MLD) of a code with reduced decoding complexity. The most well known trellis-based MLD algorithm is the Viterbi algorithm. The trellis representation was first introduced and used for convolutional codes [23]. This representation, together with the Viterbi decoding algorithm, has resulted in a wide range of applications of convolutional codes for error control in digital communications over the last two decades. There are two major reasons for this inactive period of research in this area. First, most coding theorists at that time believed that block codes did not have simple trellis structure like convolutional codes and maximum likelihood decoding of linear block codes using the Viterbi algorithm was practically impossible, except for very short block codes. Second, since almost all of the linear block codes are constructed algebraically or based on finite geometries, it was the belief of many coding theorists that algebraic decoding was the only way to decode these codes. These two reasons seriously hindered the development of efficient soft-decision decoding methods for linear block codes and their applications to error control in digital communications. This led to a general belief that block codes are inferior to convolutional codes and hence, that they were not useful. Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. Chapters 3 through 6 present the fundamental concepts, finite-state machine model, state space formulation, basic structural properties, state labeling, construction procedures, complexity, minimality, and sectionaliza...

Iterative Trellis Decoding for Block Codes

Iterative Trellis Decoding for Block Codes PDF Author: Frédéric Fontaine (Michel)
Publisher:
ISBN:
Category :
Languages : en
Pages : 242

Book Description


Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; An Iterative Decoding Algorithm for Linear Block Codes Based on a Low-

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; An Iterative Decoding Algorithm for Linear Block Codes Based on a Low- PDF Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781728906683
Category : Science
Languages : en
Pages : 26

Book Description
For long linear block codes, maximum likelihood decoding based on full code trellises would be very hard to implement if not impossible. In this case, we may wish to trade error performance for the reduction in decoding complexity. Sub-optimum soft-decision decoding of a linear block code based on a low-weight sub-trellis can be devised to provide an effective trade-off between error performance and decoding complexity. This chapter presents such a suboptimal decoding algorithm for linear block codes. This decoding algorithm is iterative in nature and based on an optimality test. It has the following important features: (1) a simple method to generate a sequence of candidate code-words, one at a time, for test; (2) a sufficient condition for testing a candidate code-word for optimality; and (3) a low-weight sub-trellis search for finding the most likely (ML) code-word. Lin, Shu and Fossorier, Marc Goddard Space Flight Center NAG5-931; NAG5-2938

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; An Iterative Decoding Algorithm for Linear Block Codes Based on a Low-Weight Trellis Search

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; An Iterative Decoding Algorithm for Linear Block Codes Based on a Low-Weight Trellis Search PDF Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722916640
Category :
Languages : en
Pages : 24

Book Description
For long linear block codes, maximum likelihood decoding based on full code trellises would be very hard to implement if not impossible. In this case, we may wish to trade error performance for the reduction in decoding complexity. Sub-optimum soft-decision decoding of a linear block code based on a low-weight sub-trellis can be devised to provide an effective trade-off between error performance and decoding complexity. This chapter presents such a suboptimal decoding algorithm for linear block codes. This decoding algorithm is iterative in nature and based on an optimality test. It has the following important features: (1) a simple method to generate a sequence of candidate code-words, one at a time, for test; (2) a sufficient condition for testing a candidate code-word for optimality; and (3) a low-weight sub-trellis search for finding the most likely (ML) code-word. Lin, Shu and Fossorier, Marc Goddard Space Flight Center NAG5-931; NAG5-2938...

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; A Recursive Maximum Likelihood Decoding

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; A Recursive Maximum Likelihood Decoding PDF Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781728906454
Category : Science
Languages : en
Pages : 32

Book Description
The Viterbi algorithm is indeed a very simple and efficient method of implementing the maximum likelihood decoding. However, if we take advantage of the structural properties in a trellis section, other efficient trellis-based decoding algorithms can be devised. Recently, an efficient trellis-based recursive maximum likelihood decoding (RMLD) algorithm for linear block codes has been proposed. This algorithm is more efficient than the conventional Viterbi algorithm in both computation and hardware requirements. Most importantly, the implementation of this algorithm does not require the construction of the entire code trellis, only some special one-section trellises of relatively small state and branch complexities are needed for constructing path (or branch) metric tables recursively. At the end, there is only one table which contains only the most likely code-word and its metric for a given received sequence r = (r(sub 1), r(sub 2), ..., r(sub n)). This algorithm basically uses the divide and conquer strategy. Furthermore, it allows parallel/pipeline processing of received sequences to speed up decoding. Lin, Shu and Fossorier, Marc Goddard Space Flight Center NAG5-931; NAG5-29

Theoretical and Practical Aspects of the Trellis Decoding of Block Codes

Theoretical and Practical Aspects of the Trellis Decoding of Block Codes PDF Author: Luis Enrique Aguardo-Bayón
Publisher:
ISBN:
Category :
Languages : en
Pages : 151

Book Description


Simplified Trellis Decoding of Block Codes by Selective Pruning

Simplified Trellis Decoding of Block Codes by Selective Pruning PDF Author: Eric Bertrand
Publisher:
ISBN:
Category :
Languages : en
Pages :

Book Description
"Error correcting codes are of paramount importance for reliable communications. By adding redundancy to the transmitted data they allow the decoder to detect and correct errors. However in favorable channel conditions, a part of this redundancy can be removed in order to increase throughput. Unfortunately most coding schemes are poorly adapted to these higher coding rates. For example, the decoding of block codes grows exponentially with code length. In this thesis we propose a novel solution to this problem: selective trellis pruning." --

Information Theory and Coding - Solved Problems

Information Theory and Coding - Solved Problems PDF Author: Predrag Ivaniš
Publisher: Springer
ISBN: 3319493701
Category : Technology & Engineering
Languages : en
Pages : 517

Book Description
This book is offers a comprehensive overview of information theory and error control coding, using a different approach then in existed literature. The chapters are organized according to the Shannon system model, where one block affects the others. A relatively brief theoretical introduction is provided at the beginning of every chapter, including a few additional examples and explanations, but without any proofs. And a short overview of some aspects of abstract algebra is given at the end of the corresponding chapters. The characteristic complex examples with a lot of illustrations and tables are chosen to provide detailed insights into the nature of the problem. Some limiting cases are presented to illustrate the connections with the theoretical bounds. The numerical values are carefully selected to provide in-depth explanations of the described algorithms. Although the examples in the different chapters can be considered separately, they are mutually connected and the conclusions for one considered problem relate to the others in the book.