| Document Type
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BL
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| Record Number
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1016490
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| Doc. No
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b770860
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| Main Entry
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Sason, Igal.
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| Title & Author
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Performance analysis of linear codes under maximum-likelihood decoding : : a tutorial /\ Igal Sason, Shlomo Shamai.
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| Publication Statement
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Boston :: Now Publishers,, ©2006.
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| Series Statement
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Foundations and trends in communications and information theory,; v. 3, issue 1/2
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| Page. NO
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1 online resource (ix, 222 pages) :: illustrations
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| ISBN
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1282823175
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: 1933019794
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: 9781282823174
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: 9781933019796
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1933019328
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| Notes
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"Originally published as Foundations and trends in communications and information technology [sic] volume 3, issues 1 and 2"--Page 4 of cover.
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Title from PDF title page (viewed July 10, 2008).
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| Bibliographies/Indexes
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Includes bibliographical references (pages 206-222).
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| Contents
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Cover -- Contents -- A Short Overview -- Introduction -- General approach for the derivation of improved upper bounds -- On Gallager bounds: Variations and applications -- Lower bounds on the decoding error probability -- Union Bounds: How Tight Can They Be? -- Union bounds -- Union bounds for turbo-like codes -- Improved Upper Bounds for Gaussian and Fading Channels -- The methodology of the bounding technique -- Improved upper bounds for the Gaussian channel -- Improved upper bounds for fading channels -- Concluding comments -- Gallager-Type Upper Bounds: Variations, Connections and Applications -- Introduction -- Gallager bounds for symmetric memoryless channels -- Interconnections between bounds -- Special cases of the DS2 bound -- Gallager-type bounds for the mismatched decoding regime -- Gallager-type bounds for parallel channels -- Some applications of the Gallager-type bounds -- Summary and conclusions -- Sphere-Packing Bounds on the Decoding Error Probability -- Introduction -- The 1959 Shannon lower bound for theAWGN channel -- The 1967 sphere-packing bound -- Sphere-packing bounds revisited for moderate block lengths -- Concluding comments -- Lower Bounds Based on de Caen's Inequality and Recent Improvements -- Introduction -- Lower bounds based on de Caen's inequality and variations -- Summary and conclusions -- Concluding Remarks -- Acknowledgments -- References.
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| Abstract
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This article is focused on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding. Though the ML decoding algorithm is prohibitively complex for most practical codes, their performance analysis under ML decoding allows to predict their performance without resorting to computer simulations. It also provides a benchmark for testing the sub-optimality of iterative (or other practical) decoding algorithms. This analysis also establishes the goodness of linear codes (or ensembles), determined by the gap between their achievable rates under optimal ML decoding and information theoretical limits. In this article, upper and lower bounds on the error probability of linear codes under ML decoding are surveyed and applied to codes and ensembles of codes on graphs. For upper bounds, we discuss various bounds where focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, we address de Caen's based bounds and their improvements, and also consider sphere-packing bounds with their recent improvements targeting codes of moderate block lengths.
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| Subject
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Coding theory.
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Decoders (Electronics)
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Error-correcting codes (Information theory)
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Coding theory.
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COMPUTERS-- Information Theory.
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Decoders (Electronics)
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Error-correcting codes (Information theory)
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TECHNOLOGY ENGINEERING-- Signals Signal Processing.
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| Dewey Classification
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621.382/2
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| LC Classification
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TK5102.96.S27 2006
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| Added Entry
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Shamai, Shlomo,1958-
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