A Practical Guide to Error-Control Coding Using MATLAB -- Contents -- Preface -- Chapter 1: Error Control in Digital Communications and Storage -- 1.1 Error Control Coding at a Glance -- 1.1.1 Codes for Error Control -- 1.1.2 Important Concepts -- 1.2 Channel Capacity and Shannon's Theorem -- 1.3 Considerations When Selecting Coding Schemes -- References -- Selected Bibliography -- Chapter 2: Brief Introduction to Abstract Algebra -- 2.1 Elementary Algebraic Structures -- 2.1.1 Group -- 2.1.2 Field -- 2.2 Galois Field and Its Arithmetic -- 2.2.1 Galois Field -- 2.2.2 Arithmetic in GF (2m) -- 2.3 Implementation of GF (2m) Arithmetic -- 2.3.1 Arithmetic with Polynomial Representation -- 2.3.2 Arithmetic with Power Representation -- 2.3.3 A Special Case: Inversion -- Problems -- References -- Selected Bibliography -- Chapter 3: Binary Block Codes -- 3.1 Linear Block Codes -- 3.1.1 Code Construction and Properties -- 3.1.2 Decoding Methods -- 3.1.3 Performance of Linear Block Codes -- 3.1.4 Encoder and Decoder Designs -- 3.1.5 Hamming Codes -- 3.2 Cyclic Codes -- 3.2.1 Basic Principles -- 3.2.2 Shift Register-Based Encoder and Decoder -- 3.2.3 Shortened Cyclic Codes and CRC -- 3.3 BCH Codes -- 3.3.1 Introduction -- 3.3.2 BCH Bound and Vandermonde Matrix -- 3.3.3 Decoding BCH Codes -- Problems -- References -- Selected Bibliography -- Chapter 4: Reed-Solomon Codes -- 4.1 Introduction to RS Codes -- 4.1.1 Prelude: Nonbinary BCH Codes -- 4.1.2 Reed-Solomon Codes -- 4.2 Decoding of RS Codes -- 4.2.1 General Remarks -- 4.2.2 Determining the Error Location Polynomial -- 4.2.3 Frequency-Domain Decoding -- 4.2.4 Error and Erasure Decoding -- 4.3 RS Decoder: From Algorithm to Architecture -- 4.3.1 Syndrome Computation Circuit -- 4.3.2 Architectures for Berlekamp-Massey Algorithm -- 4.3.3 Circuit for Chien Search and Forney's Algorithm.

4.4 Standardized RS Codes -- Problems -- References -- Chapter 5: Convolutional Codes -- 5.1 Fundamentals of Convolutional Codes -- 5.1.1 Code Generation and Representations -- 5.1.2 Additional Matters -- 5.2 Decoding of Convolutional Codes -- 5.2.1 Optimum Convolutional Decoding and Viterbi Algorithm -- 5.2.2 Sequential Decoding -- 5.3 Designing Viterbi Decoders -- 5.3.1 Typical Design Issues -- 5.3.2 Design for High Performance -- 5.4 Good Convolutional Codes -- 5.4.1 Catastrophic Error Propagation -- 5.4.2 Some Known Good Convolutional Codes -- 5.5 Punctured Convolutional Codes -- Problems -- References -- Selected Bibliography -- Chapter 6: Modern Codes -- 6.1 Turbo Codes -- 6.1.1 Code Concatenation -- 6.1.2 Concatenating Codes in Parallel: Turbo Code -- 6.1.3 Iterative Decoding of Turbo Codes -- 6.1.4 Implementing MAP -- 6.2 Low-Density Parity-Check Codes -- 6.2.1 Codes with Sparse Parity-Check Matrix -- 6.2.2 Decoding and Encoding Algorithms -- 6.2.3 High-Level Architecture Design for LDPC Decoders -- Problems -- References -- Selected Bibliography -- About the Author -- Index.