الصفحة 1
الصفحة 1
Codes et turbocodes = Codes and turbo codes
Devoted to one of the essential functions of modern telecommunications systems: channel coding, or error-correcting coding. At the crossroads of information theory, mathematics, and electronics, channel coding has undergone numerous developments since the foundational work of Claude Shannon. Algebraic codes, convolutional codes, and concatenated codes decoded iteratively form the core of the book, which also includes a presentation of digital modulations, to which channel coding is closely linked, forming the heart of the physical layer of telecommunications systems. The most important theoretical aspects are presented, and the construction of the codes is detailed and justified. Decoding algorithms are developed and, where possible, accompanied by simulation results that demonstrate their error-correcting capabilities and applications.
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.
Applied algebra, algebraic algorithms and error-correcting codes ; 17th International Symposium, AAECC-17, Bangalore, India, December 16-20, 2007, Proceedings
Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.
Applied algebra, algebraic algorithms and error-correcting codes ; 16th International Symposium, AAECC-16, Las Vegas, NV, USA, February 20-24, 2006, Proceedings
This book constitutes the refereed proceedings of the 16th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-16, held in Las Vegas, NV, USA in February 2006. The 25 revised full papers presented together with 7 invited papers were carefully reviewed and selected from 32 submissions. Among the subjects addressed are block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.
