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Trellises And Trellis Based Decoding Algorithms For Linear Block Codes

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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

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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...

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...

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.

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 The Map And Related Decoding Algirithms

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Author : National Aeronautics and Space Adm Nasa
language : en
Publisher: Independently Published
Release Date : 2018-10-24

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes Part 3 The Map And Related Decoding Algirithms 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 2018-10-24 with Science 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

Map Algorithms For Decoding Linear Block Codes Based On Sectionalized Trellis Diagrams

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Author : National Aeronautics and Space Administration (NASA)
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-06

Map Algorithms For Decoding Linear Block Codes Based On Sectionalized Trellis Diagrams 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 2018-06 with categories.

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

Tail Biting Trellis Representation Of Codes

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Author : National Aeronautics and Space Administration (NASA)
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-06-11

Tail Biting Trellis Representation Of 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 2018-06-11 with categories.

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

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

Wireless Communications

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Author : Giorgio A. Vitetta
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-29

Wireless Communications written by Giorgio A. Vitetta 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 2013-03-29 with Technology & Engineering categories.

This book introduces the theoretical elements at the basis of various classes of algorithms commonly employed in the physical layer (and, in part, in MAC layer) of wireless communications systems. It focuses on single user systems, so ignoring multiple access techniques. Moreover, emphasis is put on single-input single-output (SISO) systems, although some relevant topics about multiple-input multiple-output (MIMO) systems are also illustrated. Comprehensive wireless specific guide to algorithmic techniques Provides a detailed analysis of channel equalization and channel coding for wireless applications Unique conceptual approach focusing in single user systems Covers algebraic decoding, modulation techniques, channel coding and channel equalisation

Trellises And Trellis Based Decoding Algorithms For Linear Block Codes

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