Codes, Systems, and Graphical Models

1. Front Matter

   Pages i-xi

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2. Overviews

   1. Front Matter

      Pages xiii-xiii

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   2. An Introduction to the Analysis of Iterative Coding Systems

      • Tom Richardson, Rüdiger Urbanke

      Pages 1-37

   3. Connections Between Linear Systems and Convolutional Codes

      • Joachim Rosenthal

      Pages 39-66

   4. Multi-Dimensional Symbolic Dynamical Systems

      • Klaus Schmidt

      Pages 67-82

3. Codes on Graphs

   1. Front Matter

      Pages N1-N1

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   2. Linear-Congruence Constructions of Low-Density Parity-Check Codes

      • J. Bond, S. Hui, H. Schmidt

      Pages 83-100

   3. On the Effective Weights of Pseudocodewords for Codes Defined on Graphs with Cycles

      • G. David Forney Jr., Ralf Koetter, Frank R. Kschischang, Alex Reznik

      Pages 101-112

   4. Evaluation of Gallager Codes for Short Block Length and High Rate Applications

      • David J. C. MacKay, Matthew C. Davey

      Pages 113-130

   5. Two Small Gallager Codes

      • David J. C. MacKay, Matthew C. Davey

      Pages 131-133

   6. Mildly Non-Linear Codes

      • Alan Parks

      Pages 135-151

   7. Capacity-Achieving Sequences

      • M. A. Shokrollahi

      Pages 153-166

   8. Hypertrellis: A Generalization of Trellis and Factor Graph

      • Wai Ho Mow

      Pages 167-194

4. Decoding Techniques

   1. Front Matter

      Pages N3-N3

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   2. BSC Thresholds for Code Ensembles Based on “Typical Pairs” Decoding

      • Srinivas Aji, Hui Jin, Aamod Khandekar, David J. C. MacKay, Robert J. Mceliece

      Pages 195-210

   3. Properties of the Tailbiting BCJR Decoder

      • John B. Anderson, Kemal E. Tepe

      Pages 211-238

   4. Iterative Decoding of Tail-Biting Trellises and Connections with Symbolic Dynamics

      • G. David Forney Jr., Frank R. Kschischang, Brian Marcus, Selim Tuncel

      Pages 239-264

   5. Algorithms for Decoding and Interpolation

      • Margreet Kuijper

      Pages 265-282

   6. An Algebraic Description of Iterative Decoding Schemes

      • Elke Offer, Emina Soljanin

      Pages 283-298

   7. Recursive Construction of GrÖbner Bases for the Solution of Polynomial Congruences

      • Henry O’keeffe, Patrick Fitzpatrick

      Pages 299-309

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.

• Graphical Models
• Symbol
• Symbolic Dynamics
• Systems Theory
• algorithms
• analysis
• code
• coding theory

• IBM Almaden Research Center, San Jose, USA

  Brian Marcus

• Department of Mathematics, University of Notre Dame, NotreDame, USA

  Joachim Rosenthal

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