Fundamentals of Codes, Graphs, and Iterative Decoding

List of Figures. List of Tables. Preface.

1: Digital Communication.
1.Basics.
2.Algorithms and Complexity.
3.Encoding and Decoding.
4.Bounds.
5.Overview of the Text.

2: Abstract Algebra.
1.Sets and Groups.
2.Rings, Domains, and Fields.
3.Vector Spaces and GF(pm).

4. Polynomials over Galois Fields.
5.Frequency Domain Analysis of Polynomials over GF(q) [x]/(xn-1). Linear Block Codes.
1.Basic Structure of Linear Codes.
2.Repetition and Parity Check Codes.
3.Hamming Codes.
4.Reed-Muller Codes.
5.Cyclic Codes.
6.Quadratic Residue Codes.
7.Golay Codes.
8.BCH and Reed-Solomon Codes.

4: Convolutional and Concatenated Codes.
1.Convolutional Encoders.
2.Analysis of Component Codes.
3.Concatenated Codes.
4.Analysis of Parallel Concatenated Codes.

5: Elements of Graph Theory.
1.Introduction.
2.Martingales.
3.Expansion.

6: Algorithms on Graphs.
1.Probability Models and Bayesian Networks.
2.Belief Propagation Algorithm.
3.Junction Tree Propagation Algorithm.
4.Message Passing and Error Control Decoding.
5.Message Passing in Loops.

7: Turbo Decoding.
1.Turbo Decoding.
2.Parallel Decoding.
3.Notes.

8: Low-Density Parity-Check Codes.
1.Basic Properties.
2.Simple Decoding Algorithms.
3.Explicit Construction.
4.Gallager's Decoding Algorithms.
5.Belief Propagation Decoding.
6.Notes.

9: Low-Density Generator Codes.
1.Introduction.
2.Decoding Analyses.
3.Good Degree Sequences.
4.Irregular Repeat-Accumulate Codes.
5.Cascaded Codes.
6.Notes. References.

Index