Marc Fossorier - Böcker

As the demand for data reliability increases, coding for error control becomes increasingly important in data transmission systems and has become an integral part of almost all data communication system designs. In recent years, various trellis-based soft-decoding algorithms for linear block codes have been devised. New ideas developed in the study of trellis structure of block codes can be used for improving decoding and analyzing the trellis complexity of convolutional codes. These recent developments provide practicing communication engineers with more choices when designing error control systems. This text combines trellises and trellis-based decoding algorithms for linear codes together in a simple and unified form. The approach is to explain the material in an easily understood manner with minimal mathematical rigour. The book is intended for practicing communication engineers who want to have a fast grasp and understanding of the subject. Only material considered essential and useful for practical applications is included. This book can also be used as a text for advanced courses on the subject.

As the demand for data reliability increases, coding for error control becomes increasingly important in data transmission systems and has become an integral part of almost all data communication system designs. In recent years, various trellis-based soft-decoding algorithms for linear block codes have been devised. New ideas developed in the study of trellis structure of block codes can be used for improving decoding and analyzing the trellis complexity of convolutional codes. These recent developments provide practicing communication engineers with more choices when designing error control systems. Trellises and Trellis-based Decoding Algorithms for Linear Block Codes combines trellises and trellis-based decoding algorithms for linear codes together in a simple and unified form. The approach is to explain the material in an easily understood manner with minimal mathematical rigor. Trellises and Trellis-based Decoding Algorithms for Linear Block Codes is intended for practicing communication engineers who want to have a fast grasp and understanding of the subject. Only material considered essential and useful for practical applications is included. This book can also be used as a text for advanced courses on the subject.

The 25 revised full papers presented here together with 7 invited papers address subjects such as 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.

TheAAECCsymposiumwasstartedinJune1983byAlainPoli(Toulouse),who, together with Roger Desq, Daniel Lazard, and Paul Camion, organized the ?rst conference. The meaning of the acronym AAECC changed from "Applied - gebra and Error Correcting Codes" to "Applied Algebra, Algebraic Algorithms, and Error Correcting Codes." One reason for this was the increasing importance of complexity, particularly for decoding algorithms. During the AAECC-12 s- posium the conference committee decided to enforce the theory and practice of the coding side as well as the cryptographic aspects. Algebra was conserved, as in the past, but was slightly more oriented to algebraic geometry codes, ?nite ?elds, complexity, polynomials, and graphs. For AAECC-15 the main subjects covered were: - Block codes. - Algebra and codes: rings, ?elds, AG codes. - Cryptography. - Sequences. - Algorithms, decoding algorithms. - Algebra: constructions in algebra, Galois groups, di?erential algebra, po- nomials. The talks of the six invited speakers characterized the aims of AAECC-15: - P. Sole ("Public Key Cryptosystems Based on Rings"). - S. Lin ("Combinatorics Low Density Parity Check Codes"). - J.Stern ("Cryptography and the Methodology of Provable Security"). - D. Costello ("Graph-Based Convolutional LDPC Codes"). - I. Shparlinsky ("Dynamical Systems Generated by Rational Functions"). - A. Lauder ("Algorithms for Multivariate Polynomials over Finite Fields").

This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999.The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Grobner bases and AG codes, and polynomials.