LEADER 05539nam 22007695 450 001 996466073403316 005 20200701031023.0 010 $a3-540-30180-1 024 7 $a10.1007/b104335 035 $a(CKB)1000000000212664 035 $a(SSID)ssj0000192918 035 $a(PQKBManifestationID)11180332 035 $a(PQKBTitleCode)TC0000192918 035 $a(PQKBWorkID)10197076 035 $a(PQKB)10038542 035 $a(DE-He213)978-3-540-30180-6 035 $a(MiAaPQ)EBC3068435 035 $a(PPN)134123549 035 $a(EXLCZ)991000000000212664 100 $a20110116d2005 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aList Decoding of Error-Correcting Codes$b[electronic resource] $eWinning Thesis of the 2002 ACM Doctoral Dissertation Competition /$fby Venkatesan Guruswami 205 $a1st ed. 2005. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2005. 215 $a1 online resource (XX, 352 p.) 225 1 $aLecture Notes in Computer Science,$x0302-9743 ;$v3282 300 $a"Revised version of [the author's] doctoral dissertation, written under the supervision of Madhu Sudan and submitted to MIT in August 2001"--P. xi. 311 $a3-540-24051-9 320 $aIncludes bibliographical references (p. [337]-347) and index. 327 $a1 Introduction -- 1 Introduction -- 2 Preliminaries and Monograph Structure -- I Combinatorial Bounds -- 3 Johnson-Type Bounds and Applications to List Decoding -- 4 Limits to List Decodability -- 5 List Decodability Vs. Rate -- II Code Constructions and Algorithms -- 6 Reed-Solomon and Algebraic-Geometric Codes -- 7 A Unified Framework for List Decoding of Algebraic Codes -- 8 List Decoding of Concatenated Codes -- 9 New, Expander-Based List Decodable Codes -- 10 List Decoding from Erasures -- III Applications -- Interlude -- III Applications -- 11 Linear-Time Codes for Unique Decoding -- 12 Sample Applications Outside Coding Theory -- 13 Concluding Remarks -- A GMD Decoding of Concatenated Codes. 330 $aHow can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the rich theory of ?error-correcting codes?. This theory has traditionally gone hand in hand with the algorithmic theory of ?decoding? that tackles the problem of recovering from the errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally,itshowshowthenotionof?list-decoding? can be applied to recover from far more errors, for a wide variety of err- correcting codes, than achievable before. A brief bit of background: error-correcting codes are combinatorial str- tures that show how to represent (or ?encode?) information so that it is - silient to a moderate number of errors. Speci?cally, an error-correcting code takes a short binary string, called the message, and shows how to transform it into a longer binary string, called the codeword, so that if a small number of bits of the codewordare ?ipped, the resulting string does not look like any other codeword. The maximum number of errorsthat the code is guaranteed to detect, denoted d, is a central parameter in its design. A basic property of such a code is that if the number of errors that occur is known to be smaller than d/2, the message is determined uniquely. This poses a computational problem,calledthedecodingproblem:computethemessagefromacorrupted codeword, when the number of errors is less than d/2. 410 0$aLecture Notes in Computer Science,$x0302-9743 ;$v3282 606 $aData structures (Computer science) 606 $aCoding theory 606 $aInformation theory 606 $aAlgorithms 606 $aComputers 606 $aComputer science?Mathematics 606 $aData Structures and Information Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/I15009 606 $aCoding and Information Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/I15041 606 $aAlgorithm Analysis and Problem Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/I16021 606 $aModels and Principles$3https://scigraph.springernature.com/ontologies/product-market-codes/I18016 606 $aDiscrete Mathematics in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17028 606 $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018 615 0$aData structures (Computer science). 615 0$aCoding theory. 615 0$aInformation theory. 615 0$aAlgorithms. 615 0$aComputers. 615 0$aComputer science?Mathematics. 615 14$aData Structures and Information Theory. 615 24$aCoding and Information Theory. 615 24$aAlgorithm Analysis and Problem Complexity. 615 24$aModels and Principles. 615 24$aDiscrete Mathematics in Computer Science. 615 24$aAlgorithms. 676 $a005.7/2 686 $a54.10$2bcl 700 $aGuruswami$b Venkatesan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0508816 906 $aBOOK 912 $a996466073403316 996 $aList Decoding of Error-Correcting Codes$9771937 997 $aUNISA