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Mathematical Methods in Computer Science : Essays in Memory of Thomas Beth
This Festschrift volume contains the proceedings of the conference Mathematical Methods in Computer Science, MMICS 2008, which was held during December 17-19, 2008, in Karlsruhe, Germany, in memory of Thomas Beth.The themes of the conference reflected the many interests of Thomas Beth. Although, these interests might seem diverse, mathematical methods and especially algebra as a language constituted the common denominator of all of his scientific achievements.
List decoding of error-correcting codes : Winning thesis of the 2002 ACM doctoral dissertation competition
Presents some spectacular new results in the area of decoding algorithms for error-correcting codes. Specifically, it shows how the notion of “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, called the decoding problem : compute the message from a corrupted codeword, when the number of errors is less than d/2.
