Trellises And Trellis Based Decoding Algorithms For Linear Block Codes Part 3 The Map And Related Decoding Algirithms

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Trellises And Trellis Based Decoding Algorithms For Linear Block Codes

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Author : Shu Lin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes written by Shu Lin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

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 Part 3 The Map And Related Decoding Algirithms

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Author : National Aeronautics and Space Administration (NASA)
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-08-20

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes Part 3 The Map And Related Decoding Algirithms written by National Aeronautics and Space Administration (NASA) and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-20 with categories.

In a coded communication system with equiprobable signaling, MLD minimizes the word error probability and delivers the most likely codeword associated with the corresponding received sequence. This decoding has two drawbacks. First, minimization of the word error probability is not equivalent to minimization of the bit error probability. Therefore, MLD becomes suboptimum with respect to the bit error probability. Second, MLD delivers a hard-decision estimate of the received sequence, so that information is lost between the input and output of the ML decoder. This information is important in coded schemes where the decoded sequence is further processed, such as concatenated coding schemes, multi-stage and iterative decoding schemes. In this chapter, we first present a decoding algorithm which both minimizes bit error probability, and provides the corresponding soft information at the output of the decoder. This algorithm is referred to as the MAP (maximum aposteriori probability) decoding algorithm. Lin, Shu and Fossorier, Marc Goddard Space Flight Center NAG5-931; NAG5-2938...

Trellis And Turbo Coding

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Author : Christian B. Schlegel
language : en
Publisher: John Wiley & Sons
Release Date : 2004-09-07

Trellis And Turbo Coding written by Christian B. Schlegel and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-07 with Technology & Engineering categories.

Trellis and turbo coding are used to compress and clean communications signals to allow greater bandwidth and clarity Presents the basics, theory, and applications of these techniques with a focus on potential standard state-of-the art methods in the future Provides a classic basis for anyone who works in the area of digital communications A Wiley-IEEE Press Publication

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

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Author : National Aeronautics and Space Administration (NASA)
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-07-15

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 written by National Aeronautics and Space Administration (NASA) and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-15 with categories.

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...

The Art Of Error Correcting Coding

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Author : Robert H. Morelos-Zaragoza
language : en
Publisher: John Wiley & Sons
Release Date : 2006-07-11

The Art Of Error Correcting Coding written by Robert H. Morelos-Zaragoza and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-11 with Technology & Engineering categories.

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.

Error Correction Coding

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Author : Todd K. Moon
language : en
Publisher: John Wiley & Sons
Release Date : 2020-12-15

Error Correction Coding written by Todd K. Moon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Computers categories.

Providing in-depth treatment of error correction Error Correction Coding: Mathematical Methods and Algorithms, 2nd Edition provides a comprehensive introduction to classical and modern methods of error correction. The presentation provides a clear, practical introduction to using a lab-oriented approach. Readers are encouraged to implement the encoding and decoding algorithms with explicit algorithm statements and the mathematics used in error correction, balanced with an algorithmic development on how to actually do the encoding and decoding. Both block and stream (convolutional) codes are discussed, and the mathematics required to understand them are introduced on a "just-in-time" basis as the reader progresses through the book. The second edition increases the impact and reach of the book, updating it to discuss recent important technological advances. New material includes: Extensive coverage of LDPC codes, including a variety of decoding algorithms A comprehensive introduction to polar codes, including systematic encoding/decoding and list decoding An introduction to fountain codes Modern applications to systems such as HDTV, DVBT2, and cell phones Error Correction Coding includes extensive program files (for example, C++ code for all LDPC decoders and polar code decoders), laboratory materials for students to implement algorithms, and an updated solutions manual, all of which are perfect to help the reader understand and retain the content. The book covers classical BCH, Reed Solomon, Golay, Reed Muller, Hamming, and convolutional codes which are still component codes in virtually every modern communication system. There are also fulsome discussions of recently developed polar codes and fountain codes that serve to educate the reader on the newest developments in error correction.

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes Part 3 A Recursive Maximum Likelihood Decoding

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Author : National Aeronautics and Space Adm Nasa
language : en
Publisher: Independently Published
Release Date : 2018-10-18

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes Part 3 A Recursive Maximum Likelihood Decoding written by National Aeronautics and Space Adm Nasa and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-18 with Science categories.

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

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes Part 3 An Iterative Decoding Algorithm For Linear Block Codes Based On A Low

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Author : National Aeronautics and Space Adm Nasa
language : en
Publisher: Independently Published
Release Date : 2018-10-18

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes Part 3 An Iterative Decoding Algorithm For Linear Block Codes Based On A Low written by National Aeronautics and Space Adm Nasa and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-18 with Science categories.

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

Proceedings

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Author :
language : en
Publisher:
Release Date : 2002

Proceedings written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Digital communications categories.

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes

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Author : National Aeronautics and Space Administration (NASA)
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-07-17

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes written by National Aeronautics and Space Administration (NASA) and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-17 with categories.

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...