# Coding Theory. Algorithms, Architectures and Applications

• ID: 2170475
• Book
• 352 Pages
• John Wiley and Sons Ltd
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One of the most important key technologies for digital communication systems as well as storage media is coding theory. It provides a means to transmit information across time and space over noisy and unreliable communication channels.

Coding Theory: Algorithms, Architectures and Applications provides a concise overview of channel coding theory and practice, as well as the accompanying signal processing architectures. The book is unique in presenting algorithms, architectures, and applications of coding theory in a unified framework. It covers the basics of coding theory before moving on to discuss algebraic linear block and cyclic codes, turbo codes and low density parity check codes and space–time codes. Coding Theory provides algorithms and architectures used for implementing coding and decoding strategies as well as coding schemes used in practice especially in communication systems.

Feature of the book include:

• Unique presentation–like style for summarising main aspects
• Practical issues for implementation of coding techniques
• Sound theoretical approach to practical, relevant coding methodologies
• Covers standard coding schemes such as block and convolutional codes, coding schemes such as Turbo and LDPC codes, and space time codes currently in research, all covered in a common framework with respect to their applications.

This book is ideal for postgraduate and undergraduate students of communication and information engineering, as well as computer science students. It will also be of use to engineers working in the industry who want to know more about the theoretical basics of coding theory and their application in currently relevant communication systems.

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Preface.

1 Introduction.

1.1 Communication Systems.

1.2 Information Theory.

1.2.1 Entropy.

1.2.2 Channel Capacity.

1.2.3 Binary Symmetric Channel.

1.2.4 AWGN Channel.

1.3 A Simple Channel Code.

2 Algebraic Coding Theory.

2.1 Fundamentals of Block Codes.

2.1.1 Code Parameters.

2.1.2 Maximum Likelihood Decoding.

2.1.3 Binary Symmetric Channel.

2.1.4 Error Detection and Error Correction.

2.2 Linear Block Codes.

2.2.1 Definition of Linear Block Codes.

2.2.2 Generator Matrix.

2.2.3 Parity Check Matrix.

2.2.4 Syndrome and Cosets.

2.2.5 Dual Code.

2.2.6 Bounds for Linear Block Codes.

2.2.7 Code Constructions.

2.2.8 Examples of Linear Block Codes.

2.3 Cyclic Codes.

2.3.1 Definition of Cyclic Codes.

2.3.2 Generator Polynomial.

2.3.3 Parity Check Polynomial.

2.3.4 Dual Codes.

2.3.5 Linear Feedback Shift Registers.

2.3.6 BCH Codes.

2.3.7 Reed–Solomon Codes.

2.3.8 Algebraic Decoding Algorithm.

2.4 Summary.

3 Convolutional Codes.

3.1 Encoding of Convolutional Codes.

3.1.1 Convolutional Encoder.

3.1.2 Generator Matrix in Time–Domain.

3.1.3 State Diagram of a Convolutional Encoder.

3.1.4 Code Termination.

3.1.5 Puncturing.

3.1.6 Generator Matrix in D–Domain.

3.1.7 Encoder Properties.

3.2 Trellis Diagram and Viterbi’s Algorithm.

3.2.1 Minimum Distance Decoding.

3.2.2 Trellises.

3.2.3 Viterbi Algorithm.

3.3 Distance Properties and Error Bounds.

3.3.1 Free Distance.

3.3.2 Active Distances.

3.3.3 Weight Enumerators for Terminated Codes.

3.3.4 Path Enumerators.

3.3.5 Pairwise Error Probability.

3.3.6 Viterbi Bound.

3.4 Soft Input Decoding.

3.4.1 Euclidean Metric.

3.4.2 Support of Punctured Codes.

3.4.3 Implementation Issues.

3.5 Soft Output Decoding.

3.5.1 Derivation of APP Decoding.

3.5.2 APP Decoding in the Log–Domain.

3.6 Convolutional Coding in Mobile Communications.

3.6.1 Coding of Speech Data.

3.6.2 Hybrid ARQ.

3.6.3 EGPRS Modulation and Coding.

3.6.4 Retransmission Mechanism.

3.6.6 Incremental Redundancy.

3.7 Summary.

4 Turbo Codes.

4.1 LDPC Codes.

4.1.1 Codes Based on Sparse Graphs.

4.1.2 Decoding for the Binary Erasure Channel.

4.1.3 Log–Likelihood Algebra.

4.1.4 Belief Propagation.

4.2 A First Encounter with Code Concatenation.

4.2.1 Product Codes.

4.2.2 Iterative Decoding of Product Codes.

4.3 Concatenated Convolutional Codes.

4.3.1 Parallel Concatenation.

4.3.2 The UMTS Turbo Code.

4.3.3 Serial Concatenation.

4.3.4 Partial Concatenation.

4.3.5 Turbo Decoding.

4.4 EXIT Charts.

4.4.1 Calculating an EXIT Chart.

4.4.2 Interpretation.

4.5 Weight Distribution.

4.5.1 Partial Weights.

4.5.2 ExpectedWeight Distribution.

4.6 Woven Convolutional Codes.

4.6.1 Encoding Schemes.

4.6.2 Distance Properties of Woven Codes.

4.6.3 Woven Turbo Codes.

4.6.4 Interleaver Design.

4.7 Summary.

5 Space–Time Codes.

5.1 Introduction.

5.1.1 Digital Modulation Schemes.

5.1.2 Diversity.

5.2 Spatial Channels.

5.2.1 Basic Description.

5.2.2 Spatial Channel Models.

5.2.3 Channel Estimation.

5.3 Performance Measures.

5.3.1 Channel Capacity.

5.3.2 Outage Probability and Outage Capacity.

5.3.3 Ergodic Error Probability.

5.4 Orthogonal Space–Time Block Codes.

5.4.1 Alamouti’s Scheme.

5.4.2 Extension to more than two Transmit Antennas.

5.4.3 Simulation Results.

5.5 Spatial Multiplexing.

5.5.1 General Concept.

5.5.2 Iterative APP Preprocessing and Per–Layer Decoding.

5.5.3 Linear Multi–Layer Detection.

5.5.4 Original Bell Labs Layered Space Time (BLAST) Detection.

5.5.5 QL Decomposition and Interference Cancellation.

5.5.6 Performance of Multi–Layer Detection Schemes.

5.5.7 Unified Description by Linear Dispersion Codes.

5.6 Summary.

A. Algebraic Structures.

A.1 Groups, Rings and Finite Fields.

A.1.1 Groups.

A.1.2 Rings.

A.1.3 Finite Fields.

A.2 Vector Spaces.

A.3 Polynomials and Extension Fields.

A.4 Discrete Fourier Transform.

B. Linear Algebra.

C. Acronyms.

Bibliography.

Index.

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