Codes, Systems, and Graphical Models

ISBN-13: 9781461265344 / Angielski / Miękka / 2013 / 513 str.

Brian Marcus; Joachim Rosenthal

Opis

Coding theory, system theory, and symbolic dynamics have much in common. A major new theme in this area of research is that of codes and systems based on graphical models. This volume contains survey and research articles from leading researchers at the interface of these subjects.

Spis treści

Foreword * Preface * Part I: Overviews * An introduction to the analysis of iterative coding * Connections between linear systems and convolutional codes * Multi-dimensional symbolic dynamical systems * Part II: Codes on Graphs * Linear-congruence constructions of low-density parity-check codes * On the effective weights of pseudocode words for codes defined on graphs with cycles * Evaluation of Gallager codes for short block length and high rate applications * Two small Gallager codes * Mildly non-linear codes * Capacity-achieving sequences * Hypertrellis: A generalization of trellis and factor graph * Part III: Decoding techniques * BSC thresholds for code ensembles based on 'typical pairs' decoding * Properties of the tailbiting BCJR decoder * Iterative decoding of tail-biting trellises and connections with symbolic dynamics * Algorithms for decoding and interpolation * An algebraic description of iterative decoding schemes * Recursive construction of Goebner bases for the solution of polynomial congruences * On iterative decoding of cycle codes of graphs * Part IV: Convolutional codes over finite Abelian groups: Some basic results * Symbolic dynamics and convolutional codes * Linear codes and their duals over artinian rings * Unit memory convolutional codes with maximum distance * Basic properties of multidimensional convolutional codes * Part V: Symbolic Dynamics and Automata Theory * Length distributions and regular sequences * Handelman's theorem on polynomials with positive multiples * Topological dynamics of cellular automata * A spanning tree invariant for Markov shifts * List of workshop participants

O autorze

Coding theory, system theory, and symbolic dynamics have much in common, including concerns for construction of state space representations, understanding of fundamental structural properties of sequence spaces, construction of input/output systems, and understanding the special role played by algebraic structure. A major new theme in this active area of research is codes and systems based on graphical models. This volume contains articles from leading researchers at the interface of these subjects, both survey articles for non-specialists and original research papers.