Codes, Systems, and Graphical Models

2001
ISBN: 978-1-4612-6534-4
Verlag: Springer

Buch, Englisch, Band 123, 513 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 809 g

Reihe: The IMA Volumes in Mathematics and its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Rosenthal, Joachim

Marcus, Brian

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Technische Wissenschaften Energietechnik | Elektrotechnik Elektrotechnik
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

1. Overviews.- An introduction to the analysis of iterative coding systems.- Connections between linear systems and convolutional codes.- Multi-dimensional symbolic dynamical systems.- 2. Codes on Graphs.- Linear-congruence constructions of low-density parity-check codes.- On the effective weights of pseudocodewords 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.- 3: 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 Gröbner bases for the solution of polynomial congruences.- On iterative decoding of cycle codes of graphs.- 4. Convolutional Codes and Codes Over Rings.- 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.- 5. 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.