TY - BOOK ID - 5450267 TI - List decoding of error-correcting codes : winning thesis of the 2002 ACM doctoral dissertation competition PY - 2004 SN - 3540301801 3540240519 PB - Berlin ; New York : Springer, DB - UniCat KW - Error-correcting codes (Information theory) KW - Reed-Solomon codes. KW - Codes, Error-correcting (Information theory) KW - Error-detecting codes (Information theory) KW - Forbidden-combination check (Information theory) KW - Self-checking codes (Information theory) KW - Computer science. KW - Data structures (Computer science). KW - Coding theory. KW - Algorithms. KW - Computer science KW - Computers. KW - Computer Science. KW - Data Structures, Cryptology and Information Theory. KW - Coding and Information Theory. KW - Algorithm Analysis and Problem Complexity. KW - Models and Principles. KW - Discrete Mathematics in Computer Science. KW - Mathematics. KW - Automatic computers KW - Automatic data processors KW - Computer hardware KW - Computing machines (Computers) KW - Electronic brains KW - Electronic calculating-machines KW - Electronic computers KW - Hardware, Computer KW - Computer systems KW - Cybernetics KW - Machine theory KW - Calculators KW - Cyberspace KW - Computer mathematics KW - Discrete mathematics KW - Electronic data processing KW - Algorism KW - Algebra KW - Arithmetic KW - Data compression (Telecommunication) KW - Digital electronics KW - Information theory KW - Signal theory (Telecommunication) KW - Computer programming KW - Information structures (Computer science) KW - Structures, Data (Computer science) KW - Structures, Information (Computer science) KW - File organization (Computer science) KW - Abstract data types (Computer science) KW - Informatics KW - Science KW - Mathematics KW - Foundations KW - Signal processing KW - Artificial intelligence KW - Automatic control KW - Coding theory KW - Digital techniques KW - Data structures (Computer scienc. KW - Computer software. KW - Computational complexity. KW - Data Structures and Information Theory. KW - Complexity, Computational KW - Software, Computer KW - Information theory. KW - Computer science—Mathematics. KW - Communication theory KW - Communication UR - https://www.unicat.be/uniCat?func=search&query=sysid:5450267 AB - How 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. ER -