Codes, Systems, and Graphical Models

✍ Scribed by Tom Richardson, Rüdiger Urbanke (auth.), Brian Marcus, Joachim Rosenthal (eds.)

Publisher: Springer-Verlag New York
Year: 2001
Tongue: English
Leaves: 520
Series: The IMA Volumes in Mathematics and its Applications 123
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Coding theory, system theory, and symbolic dynamics have much in common. Among the central themes in each of these subjects are the 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 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.

✦ Table of Contents

Front Matter....Pages i-xi
Front Matter....Pages xiii-xiii
An Introduction to the Analysis of Iterative Coding Systems....Pages 1-37
Connections Between Linear Systems and Convolutional Codes....Pages 39-66
Multi-Dimensional Symbolic Dynamical Systems....Pages 67-82
Front Matter....Pages N1-N1
Linear-Congruence Constructions of Low-Density Parity-Check Codes....Pages 83-100
On the Effective Weights of Pseudocodewords for Codes Defined on Graphs with Cycles....Pages 101-112
Evaluation of Gallager Codes for Short Block Length and High Rate Applications....Pages 113-130
Two Small Gallager Codes....Pages 131-133
Mildly Non-Linear Codes....Pages 135-151
Capacity-Achieving Sequences....Pages 153-166
Hypertrellis: A Generalization of Trellis and Factor Graph....Pages 167-194
Front Matter....Pages N3-N3
BSC Thresholds for Code Ensembles Based on “Typical Pairs” Decoding....Pages 195-210
Properties of the Tailbiting BCJR Decoder....Pages 211-238
Iterative Decoding of Tail-Biting Trellises and Connections with Symbolic Dynamics....Pages 239-264
Algorithms for Decoding and Interpolation....Pages 265-282
An Algebraic Description of Iterative Decoding Schemes....Pages 283-298
Recursive Construction of GrÖbner Bases for the Solution of Polynomial Congruences....Pages 299-309
On Iterative Decoding of Cycle Codes of Graphs....Pages 311-326
Front Matter....Pages N5-N5
Convolutional Codes Over Finite Abelian Groups: Some Basic Results....Pages 327-346
Symbolic Dynamics and Convolutional Codes....Pages 347-360
Linear Codes and Their Duals Over Artinian Rings....Pages 361-379
Front Matter....Pages N5-N5
Unit Memory Convolutional Codes with Maximum Distance....Pages 381-396
Basic Properties of Multidimensional Convolutional Codes....Pages 397-414
Front Matter....Pages N7-N7
Length Distributions and Regular Sequences....Pages 415-437
Handelman’s Theorem on Polynomials with Positive Multiples....Pages 439-445
Topological Dynamics of Cellular Automata....Pages 447-485
A Spanning Tree Invariant for Markov Shifts....Pages 487-497
Back Matter....Pages 499-513

✦ Subjects

Analysis; Applications of Mathematics; Coding and Information Theory; Electrical Engineering

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