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 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 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 2018-07-17 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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...
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 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 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 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 Simplified Trellis Decoding of Block Codes by Selective Pruning written by Eric Bertrand and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "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." --
Download or read book Theoretical and Practical Aspects of the Trellis Decoding of Block Codes written by Luis Enrique Aguardo-Bayón and published by . This book was released on 1996 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Information Theory and Coding Solved Problems written by Predrag Ivaniš and published by Springer. This book was released on 2016-11-29 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Trellis and Turbo Coding written by Christian B. Schlegel and published by John Wiley & Sons. This book was released on 2015-08-19 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition has been extensively revised to reflect the progress in error control coding over the past few years. Over 60% of the material has been completely reworked, and 30% of the material is original. Convolutional, turbo, and low density parity-check (LDPC) coding and polar codes in a unified framework Advanced research-related developments such as spatial coupling A focus on algorithmic and implementation aspects of error control coding
Download or read book Reduced search Soft decision Trellis Decoding of Linear Block Codes written by Kurt R. Matis and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Trellis Decoding of 3 D Block Turbo Codes written by Bo Yin and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forward Error Correction (FEC) technique provides a method to detect and correct errors in transmitted data. It is also a valuable technique to reduce the power requirement, thus have an important role in these systems. This reduction in power requirement is achieved at the expense of an increase in bandwidth requirement. The objective is usually to find error control techniques that give good tradeoff between power and bandwidth requirements. In this thesis, we present results for FEC technique using Turbo Block Codes and Turbo Product Codes. It is shown that these codes, not only in theory but also in hardware implementation, are capable of providing significant performance gains over other error-correction schemes. This thesis investigates Trellis based iterative decoding techniques applied to concatenated coding schemes, Turbo Block Codes. We use RM(n, k) to construct 2-D and multi-dimensional Turbo Block Codes. Our objective is to get high code rates and long block sizes for more bandwidth efficiency and improving the performance of the optimised maximum a posterior decoding algorithm.
Download or read book Trellis Decoding of Reed Solomon and Related Linear Block Codes written by Werner Heinrich B̈üttner and published by . This book was released on 1999 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Good Trellises for IC Implementation of Viterbi Decoders for Linear Block Codes written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-05 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates trellis structures of linear block codes for the IC (integrated circuit) implementation of Viterbi decoders capable of achieving high decoding speed while satisfying a constraint on the structural complexity of the trellis in terms of the maximum number of states at any particular depth. Only uniform sectionalizations of the code trellis diagram are considered. An upper bound on the number of parallel and structurally identical (or isomorphic) subtrellises in a proper trellis for a code without exceeding the maximum state complexity of the minimal trellis of the code is first derived. Parallel structures of trellises with various section lengths for binary BCH and Reed-Muller (RM) codes of lengths 32 and 64 are analyzed. Next, the complexity of IC implementation of a Viterbi decoder based on an L-section trellis diagram for a code is investigated. A structural property of a Viterbi decoder called ACS-connectivity which is related to state connectivity is introduced. This parameter affects the complexity of wire-routing (interconnections within the IC). The effect of five parameters namely: (1) effective computational complexity; (2) complexity of the ACS-circuit; (3) traceback complexity; (4) ACS-connectivity; and (5) branch complexity of a trellis diagram on the VLSI complexity of a Viterbi decoder is investigated. It is shown that an IC implementation of a Viterbi decoder based on a non-minimal trellis requires less area and is capable of operation at higher speed than one based on the minimal trellis when the commonly used ACS-array architecture is considered. Lin, Shu and Moorthy, Hari T. and Uehara, Gregory T. Goddard Space Flight Center NAG5-2938...
Download or read book On Complexity of Trellis Structure of Linear Block Codes written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-09 with total page 38 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...
