Codes, Systems, and Graphical Models

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