Download or read book 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 published by Createspace Independent Publishing Platform. This book was released on 2018-08-20 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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...
Download or read book Trellises and Trellis Based Decoding Algorithms for Linear Block Codes Part 3 a Recursive Maximum Likelihood Decoding written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-15 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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; NAG5-2938.
Download or read book 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 published by Createspace Independent Publishing Platform. This book was released on 2018-07-15 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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...
Download or read book 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 published by Independently Published. This book was released on 2018-10-18 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Trellises and Trellis Based Decoding Algorithms for Linear Block Codes written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-20 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decoding algorithms based on the trellis representation of a code (block or convolutional) drastically reduce decoding complexity. The best known and most commonly used trellis-based decoding algorithm is the Viterbi algorithm. It is a maximum likelihood decoding algorithm. Convolutional codes with the Viterbi decoding have been widely used for error control in digital communications over the last two decades. This chapter is concerned with the application of the Viterbi decoding algorithm to linear block codes. First, the Viterbi algorithm is presented. Then, optimum sectionalization of a trellis to minimize the computational complexity of a Viterbi decoder is discussed and an algorithm is presented. Some design issues for IC (integrated circuit) implementation of a Viterbi decoder are considered and discussed. Finally, a new decoding algorithm based on the principle of compare-select-add is presented. This new algorithm can be applied to both block and convolutional codes and is more efficient than the conventional Viterbi algorithm based on the add-compare-select principle. This algorithm is particularly efficient for rate 1/n antipodal convolutional codes and their high-rate punctured codes. It reduces computational complexity by one-third compared with the Viterbi algorithm. Lin, Shu Goddard Space Flight Center NAG5-931; NAG5-2938...
Download or read book Trellises and Trellis Based Decoding Algorithms for Linear Block Codes written by Shu Lin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Map Algorithms for Decoding Linear Block Codes Based on Sectionalized Trellis Diagrams written by National Aeronautics and Space Adm Nasa and published by Independently Published. This book was released on 2018-09-16 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The MAP algorithm is a trellis-based maximum a posteriori probability decoding algorithm. It is the heart of the turbo (or iterative) decoding which achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variations, such as Log-MAP and Max-Log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bi-directional and parallel MAP decodings.Lin, ShuGoddard Space Flight CenterALGORITHMS; DECODING; LINEAR SYSTEMS; PROBABILITY THEORY; ERRORS; COMPUTATION
Download or read book Trellis and Turbo Coding written by Christian B. Schlegel and published by John Wiley & Sons. This book was released on 2004-09-07 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Tail Biting Trellis Representation of Codes written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-11 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents two new iterative algorithms for decoding linear codes based on their tail biting trellises, one is unidirectional and the other is bidirectional. Both algorithms are computationally efficient and achieves virtually optimum error performance with a small number of decoding iterations. They outperform all the previous suboptimal decoding algorithms. The bidirectional algorithm also reduces decoding delay. Also presented in the paper is a method for constructing tail biting trellises for linear block codes.Shao. Rose Y. and Lin, Shu and Fossorier, MarcGoddard Space Flight CenterALGORITHMS; APPLICATIONS PROGRAMS (COMPUTERS); TRELLIS CODING; MATHEMATICAL MODELS; VITERBI DECODERS; COMPUTERIZED SIMULATION; FLOW CHARTS; ITERATION; BLOCK DIAGRAMS; MATRICES (MATHEMATICS); CONVOLUTION INTEGRALS
Download or read book Efficient Near optimum Decoding Algorithms and Trellis Structure for Linear Block Codes written by Hari Thirumoorthy and published by . This book was released on 1996 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Error Correction Coding written by Todd K. Moon and published by John Wiley & Sons. This book was released on 2020-12-15 with total page 999 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Art of Error Correcting Coding written by Robert H. Morelos-Zaragoza and published by John Wiley & Sons. This book was released on 2006-07-11 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Proceedings written by and published by . This book was released on 2002 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterative Trellis Decoding for Block Codes written by Frédéric Fontaine (Michel) and published by . This book was released on 1999 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conference Record written by and published by . This book was released on 2004 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Trellis Decoding of Block Codes written by Bahram Honary and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On Complexity of Trellis Structure of Linear Block Codes written by National Aeronautics and Space Adm Nasa and published by Independently Published. This book was released on 2018-10-17 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: The trellis structure of linear block codes (LBCs) is discussed. The state and branch complexities of a trellis diagram (TD) for a LBC is investigated. The TD with the minimum number of states is said to be minimal. The branch complexity of a minimal TD for a LBC is expressed in terms of the dimensions of specific subcodes of the given code. Then upper and lower bounds are derived on the number of states of a minimal TD for a LBC, and it is shown that a cyclic (or shortened cyclic) code is the worst in terms of the state complexity among the LBCs of the same length and dimension. Furthermore, it is shown that the structural complexity of a minimal TD for a LBC depends on the order of its bit positions. This fact suggests that an appropriate permutation of the bit positions of a code may result in an equivalent code with a much simpler minimal TD. Boolean polynomial representation of codewords of a LBC is also considered. This representation helps in study of the trellis structure of the code. Boolean polynomial representation of a code is applied to construct its minimal TD. Particularly, the construction of minimal trellises for Reed-Muller codes and the extended and permuted binary primitive BCH codes which contain Reed-Muller as subcodes is emphasized. Finally, the structural complexity of minimal trellises for the extended and permuted, and double-error-correcting BCH codes is analyzed and presented. It is shown that these codes have relatively simple trellis structure and hence can be decoded with the Viterbi decoding algorithm. Lin, Shu Unspecified Center NAG5-931