LEADER 04292nam 2200589 a 450 001 9910483044903321 005 20200520144314.0 010 $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 $a20041027d2004 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aList decoding of error-correcting codes $ewinning thesis of the 2002 ACM doctoral dissertation competition /$fVenkatesan Guruswami 205 $a1st ed. 2005. 210 $aBerlin ;$aNew York $cSpringer$dc2004 215 $a1 online resource (XX, 352 p.) 225 1 $aLecture notes in computer science,$x0302-9743 ;$v3282 225 1 $aACM distinguished theses 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 ;$v3282. 410 0$aACM distinguished theses. 606 $aError-correcting codes (Information theory) 606 $aReed-Solomon codes 615 0$aError-correcting codes (Information theory) 615 0$aReed-Solomon codes. 676 $a005.7/2 686 $a54.10$2bcl 700 $aGuruswami$b Venkatesan$0508816 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483044903321 996 $aList Decoding of Error-Correcting Codes$9771937 997 $aUNINA