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
1 - Coding and Capacity
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
Digital Data Communication and Storage
Digital communication systems are ubiquitous in our daily lives. The most obvious examples include cell phones, digital television via satellite or cable, digital radio, wireless internet connections via Wi-Fi and WiMax, and wired internet connection via cable modem. Additional examples include digital data-storage devices, including magnetic (“hard”) disk drives, magnetic tape drives, optical disk drives (e.g., CD, DVD, blu-ray), and flash drives. In the case of data-storage, information is communicated from one point in time to another rather than one point in space to another. Each of these examples, while widely different in implementation details, generally fits into a common digital communication framework first established by C. Shannon in his 1948 seminal paper, A Mathematical Theory of Communication. This framework is depicted in Figure 1.1, whose various components are described as follows.
Source and user (or sink). The information source may be originally in analog form (e.g., speech or music) and then later digitized, or it may be originally in digital form (e.g., computer files). We generally think of its output as a sequence of bits, which follow a probabilistic model. The user of the information may be a person, a computer, or some other electronic device.
Source encoder and source decoder. The encoder is a processor that converts the information source bit sequence into an alternative bit sequence with a more efficient representation of the information, i.e., with fewer bits. […]
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- Channel CodesClassical and Modern, pp. 1 - 27Publisher: Cambridge University PressPrint publication year: 2009