Fundamentals of Codes, Graphs, and Iterative Decoding

by Stephen B. Wicker

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.

248 pages, Paperback

First published October 31, 2002

Reviews

[Marcin · Rating 3 out of 5]

Short, easy to follow, fairly explanatory, be it basic math or matrix calculations, most of the information is given rather straightforwardly, yet the authors require of the readers more than basic "1+2=3" knowledge and practice in math. However once you're worthy or at least better prepared, those fundamentals of coding and other aspects presented in the book simply unveil almost all of the secrets. How far into the maths you must be to properly understand all the descriptions? If you're in a college working on a math degree or IT degree, the first year of the studies with math introduction would easily give you the upper hand. Otherwise you might need to jump for other books in search of explanations. Whatever the level of your math skills, I'd still highly suggest taking this book. Without preparation you're going to learn more, but life is made the way you learn a bit every single day, it's how it is... Is it worth your money and time? If you're into the topic, I certainly believe so. After all, it's fairly concise yet informative enough to earn a place on your bookshelf.