A Practical Guide to Error-Control Coding Using MATLAB

This practical resource provides engineers with a comprehensive understanding of error control coding, an essential and widely applied area in modern digital communications. The goal of error control coding is to encode information in such a way that even if the channel (or storage medium) introduces errors, the receiver can correct the errors and recover the original transmitted information. This book includes the most useful modern and classic codes, including block, Reed Solomon, convolutional, turbo, and LDPC codes. Professionals find clear guidance on code construction, decoding algorithms, and error correcting performances. Moreover, this unique book introduces computer simulations integrally to help readers master key concepts. Including a companion DVD with MATLAB programs and supported with over 540 equations, this hands-on reference provides an in-depth treatment of a wide range of practical implementation issues. DVD is included! It contains carefully designed MATLAB programs that practitioners can apply to their projects in the field. A Practical Guide to Error-Control Coding Using MATLAB......Page 2 Contents......Page 6 Preface......Page 10 1.1.1 Codes for Error Control......Page 12 1.1.2 Important Concepts......Page 16 1.2 Channel Capacity and Shannon’s Theorem......Page 25 1.3 Considerations When Selecting Coding Schemes......Page 27 Selected Bibliography......Page 28 2.1.1 Group......Page 30 2.1.2 Field......Page 33 2.2.1 Galois Field......Page 36 2.2.2 Arithmetic in GF (2m)......Page 44 2.3.1 Arithmetic with Polynomial Representation......Page 47 2.3.2 Arithmetic with Power Representation......Page 50 2.3.3 A Special Case: Inversion......Page 51 Problems......Page 54 Selected Bibliography......Page 55 3.1.1 Code Construction and Properties......Page 56 3.1.2 Decoding Methods......Page 62 3.1.3 Performance of Linear Block Codes......Page 71 3.1.4 Encoder and Decoder Designs......Page 76 3.1.5 Hamming Codes......Page 77 3.2 Cyclic Codes......Page 84 3.2.1 Basic Principles......Page 85 3.2.2 Shift Register–Based Encoder and Decoder......Page 92 3.2.3 Shortened Cyclic Codes and CRC......Page 102 3.3 BCH Codes......Page 106 3.3.1 Introduction......Page 108 3.3.2 BCH Bound and Vandermonde Matrix......Page 111 3.3.3 Decoding BCH Codes......Page 112 Problems......Page 121 References......Page 122 Selected Bibliography......Page 123 4.1.1 Prelude: Nonbinary BCH Codes......Page 124 4.1.2 Reed-Solomon Codes......Page 128 4.2.1 General Remarks......Page 134 4.2.2 Determining the Error Location Polynomial......Page 135 4.2.3 Frequency-Domain Decoding......Page 146 4.2.4 Error and Erasure Decoding......Page 151 4.3.2 Architectures for Berlekamp-Massey Algorithm......Page 154 4.4 Standardized RS Codes......Page 160 Problems......Page 161 References......Page 162 5.1.1 Code Generation and Representations......Page 164 5.1.2 Additional Matters......Page 172 5.2 Decoding of Convolutional Codes......Page 176 5.2.1 Optimum Convolutional Decoding and Viterbi Algorithm......Page 177 5.2.2 Sequential Decoding......Page 190 5.3.1 Typical Design Issues......Page 200 5.3.2 Design for High Performance......Page 208 5.4 Good Convolutional Codes......Page 212 5.5 Punctured Convolutional Codes......Page 213 References......Page 221 Selected Bibliography......Page 223 6.1.1 Code Concatenation......Page 224 6.1.2 Concatenating Codes in Parallel: Turbo Code......Page 229 6.1.3 Iterative Decoding of Turbo Codes......Page 239 6.1.4 Implementing MAP......Page 261 6.2 Low-Density Parity-Check Codes......Page 263 6.2.1 Codes with Sparse Parity-Check Matrix......Page 265 6.2.2 Decoding and Encoding Algorithms......Page 270 6.2.3 High-Level Architecture Design for LDPC Decoders......Page 281 Problems......Page 283 References......Page 285 Selected Bibliography......Page 287 About the Author......Page 288 Index......Page 290

This practical resource provides you with a comprehensive understanding of error control coding, an essential and widely applied area in modern digital communications. The goal of error control coding is to encode information in such a way that even if the channel (or storage medium) introduces errors, the receiver can correct the errors and recover the original transmitted information. This book includes the most useful modern and classic codes, including block, Reed Solomon, convolutional, turbo, and LDPC codes. You find clear guidance on code construction, decoding algorithms, and error correcting performances. Moreover, this unique book introduces computer simulations integrally to help you master key concepts. Including a companion DVD with MATLAB programs and supported with over 540 equations, this hands-on reference provides you with an in-depth treatment of a wide range of practical implementation issues. DVD Included! Contains carefully designed MATLAB programs that you can apply to your projects in the field.

Offers engineers with a comprehensive understanding of error control coding, an essential and widely applied area in modern digital communications. This book includes such codes as: block, Reed Solomon, convolutional, turbo, and LDPC codes. Error control in digital communications and storage Brief introduction to abstract algebra Binary block codes Reed-Solomon codes Convolutional codes Modern codes. Some online versions lack accompanying media packaged with the printed version.