Book contents
- Frontmatter
- Contents
- Preface
- 1 Coding and Capacity
- 2 Finite Fields, Vector Spaces, Finite Geometries, and Graphs
- 3 Linear Block Codes
- 4 Convolutional Codes
- 5 Low-Density Parity-Check Codes
- 6 Computer-Based Design of LDPC Codes
- 7 Turbo Codes
- 8 Ensemble Enumerators for Turbo and LDPC Codes
- 9 Ensemble Decoding Thresholds for LDPC and Turbo Codes
- 10 Finite-Geometry LDPC Codes
- 11 Constructions of LDPC Codes Based on Finite Fields
- 12 LDPC Codes Based on Combinatorial Designs, Graphs, and Superposition
- 13 LDPC Codes for Binary Erasure Channels
- 14 Nonbinary LDPC Codes
- 15 LDPC Code Applications and Advanced Topics
- Index
Preface
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Coding and Capacity
- 2 Finite Fields, Vector Spaces, Finite Geometries, and Graphs
- 3 Linear Block Codes
- 4 Convolutional Codes
- 5 Low-Density Parity-Check Codes
- 6 Computer-Based Design of LDPC Codes
- 7 Turbo Codes
- 8 Ensemble Enumerators for Turbo and LDPC Codes
- 9 Ensemble Decoding Thresholds for LDPC and Turbo Codes
- 10 Finite-Geometry LDPC Codes
- 11 Constructions of LDPC Codes Based on Finite Fields
- 12 LDPC Codes Based on Combinatorial Designs, Graphs, and Superposition
- 13 LDPC Codes for Binary Erasure Channels
- 14 Nonbinary LDPC Codes
- 15 LDPC Code Applications and Advanced Topics
- Index
Summary
The title of this book, Channel Codes: Classical and Modern, was selected to reflect the fact that this book does indeed cover both classical and modern channel codes. It includes BCH codes, Reed–Solomon codes, convolutional codes, finite-geometry codes, turbo codes, low-density parity-check (LDPC) codes, and product codes. However, the title has a second interpretation. While the majority of this book is on LDPC codes, these can rightly be considered to be both classical (having been first discovered in 1961) and modern (having been rediscovered circa 1996). This is exemplified by David Forney's statement at his August 1999 IMA talk on codes on graphs, “It feels like the early days.” As another example of the classical/modern duality, finite-geometry codes were studied in the 1960s and thus are classical codes. However, they were rediscovered by Shu Lin et al. circa 2000 as a class of LDPC codes with very appealing features and are thus modern codes as well. The classical and modern incarnations of finite-geometry codes are distinguished by their decoders: one-step hard-decision decoding (classical) versus iterative soft-decision decoding (modern).
It has been 60 years since the publication in 1948 of Claude Shannon's celebrated A Mathematical Theory of Communication, which founded the fields of channel coding, source coding, and information theory. Shannon proved the existence of channel codes which ensure reliable communication provided that the information rate for a given code did not exceed the so-called capacity of the channel.
- Type
- Chapter
- Information
- Channel CodesClassical and Modern, pp. xv - xviiiPublisher: Cambridge University PressPrint publication year: 2009