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Trellises And Trellis Based Decoding Algorithms For Linear Block Codes. Part 3 by United States. National Aeronautics And Space Administration.

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1NASA Technical Reports Server (NTRS) 19990009597: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3

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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.

“NASA Technical Reports Server (NTRS) 19990009597: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3” Metadata:

  • Title: ➤  NASA Technical Reports Server (NTRS) 19990009597: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3
  • Author: ➤  
  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 16.39 Mbs, the file-s for this book were downloaded 78 times, the file-s went public at Sat Oct 15 2016.

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2NASA Technical Reports Server (NTRS) 19990014061: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3; A Recursive Maximum Likelihood Decoding

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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.

“NASA Technical Reports Server (NTRS) 19990014061: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3; A Recursive Maximum Likelihood Decoding” Metadata:

  • Title: ➤  NASA Technical Reports Server (NTRS) 19990014061: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3; A Recursive Maximum Likelihood Decoding
  • Author: ➤  
  • Language: English

“NASA Technical Reports Server (NTRS) 19990014061: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3; A Recursive Maximum Likelihood Decoding” Subjects and Themes:

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The book is available for download in "texts" format, the size of the file-s is: 19.80 Mbs, the file-s for this book were downloaded 74 times, the file-s went public at Sat Oct 15 2016.

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3NASA Technical Reports Server (NTRS) 19990014065: 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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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.

“NASA Technical Reports Server (NTRS) 19990014065: 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” Metadata:

  • Title: ➤  NASA Technical Reports Server (NTRS) 19990014065: 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
  • Author: ➤  
  • Language: English

“NASA Technical Reports Server (NTRS) 19990014065: 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” Subjects and Themes:

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The book is available for download in "texts" format, the size of the file-s is: 13.32 Mbs, the file-s for this book were downloaded 63 times, the file-s went public at Sat Oct 15 2016.

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4NASA Technical Reports Server (NTRS) 19990014066: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3; The Map And Related Decoding Algirithms

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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.

“NASA Technical Reports Server (NTRS) 19990014066: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3; The Map And Related Decoding Algirithms” Metadata:

  • Title: ➤  NASA Technical Reports Server (NTRS) 19990014066: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3; The Map And Related Decoding Algirithms
  • Author: ➤  
  • Language: English

“NASA Technical Reports Server (NTRS) 19990014066: Trellises And Trellis-Based Decoding Algorithms For Linear Block Codes. Part 3; The Map And Related Decoding Algirithms” Subjects and Themes:

Edition Identifiers:

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The book is available for download in "texts" format, the size of the file-s is: 30.69 Mbs, the file-s for this book were downloaded 86 times, the file-s went public at Sat Oct 15 2016.

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