Error-Control Coding for Data Networks

The purpose of Error-Control Coding for Data Networks is to provide an accessible and comprehensive overview of the fundamental techniques and practical applications of the error-control coding needed by students and engineers. An additional purpose of the book is to acquaint the reader with the analytical techniques used to design an error-control coding system for many new applications in data networks. Error~control coding is a field in which elegant theory was motivated by practical problems so that it often leads to important useful advances. Claude Shannon in 1948 proved the existence of error-control codes that, under suitable conditions and at rates less than channel capacity, would transmit error-free information for all practical applications. The first practical binary codes were introduced by Richard Hamming and Marcel Golay from which the drama and excitement have infused researchers and engineers in digital communication and error-control coding for more than fifty years. Nowadays, error-control codes are being used in almost all modem digital electronic systems and data networks. Not only is coding equipment being implemented to increase the energy and bandwidth efficiency of communication systems, but coding also provides innovative solutions to many related data-networking problems.

1 Error-Control Mechanisms. - 1. 1 Introduction. - 1. 2 Error-Handling Processes in Communication Systems. - 1. 3 Examples of Error-Control Strategies. - 1. 4 Basic Principles of Error-Control Codes. - 1. 5 Noisy Channel Coding Theorem. - 1. 6 Decoding Complexity and Coding Performance. - 1. 7 Channel Bandwidth and Signal Power. - 1. 8 Approaching Shannon Capacity. - Problems. - 2 Elements of Algebra. - 2. 1 Groups. - 2. 2 Rings. - 2. 3 Basic Structures of Fields. - 2. 4 Vector Spaces. - 2. 5 Finite Fields. - 2. 6 Euclid s Algorithm. - 2. 7 Binary Field Arithmetic. - 2. 8 Arithmetic Operations in GF(q). - Problems. - 3 Linear Block Codes. - 3. 1 Error-Control Block Codes. - 3. 2 Definition of (n, k) Linear Codes over GF(q). - 3. 3 Decoding of Linear Block Codes. - 3. 4 Performance of Algebraic Decoding. - 3. 5 Hamming Codes. - 3. 6 Reed-Muller Codes. - 3. 7 Linear Block Codes for Burst-Error Correction. - 3. 8 Product Code. - Problems. - 4 Linear Cyclic Codes. - 4. 1 Description of Linear Cyclic Codes. - 4. 2 Shift-Register Encoders and Decoders of Cyclic Codes. - 4. 3 Binary Quadratic Residue Codes and Golay Code. - 4. 4 Error Detection with Cyclic and Shortened Cyclic Codes. - 4. 4. 1 Error Detection with Cyclic Codes. - 4. 4. 2 Applications of CRC in Industry Standards. - Problems. - 5 BCH Codes. - 5. 1 Definition of the BCH Codes. - 5. 2 The BCH Bound on the Minimum Distance dmin. - 5. 3 Decoding Procedures for BCH Codes. - 5. 4 Algebraic Decoding of Quadratic Residue Codes. - 5. 5 BCH Codes as Industry Standards. - Problems. - 6 Reed-Solomon Codes. - 6. 1 The State of RS Coding. - 6. 2 Construction of RS Codes. - 6. 3 Encoding of RS codes. - 6. 4. Decoding of (n, k) RS Codes. - Problems. - 7 Implementation Architectures and Applications of RS Codes. - 7. 1 Implementation of RS Codes. - 7. 2 RS codes in industry standards. - 8 Fundamentals of ConvolutionalCodes. - 8. 1 Convolutional Encoder. - 8. 2 State and Trellis-Diagram Description of Convolutional Codes. - 8. 3 Nonsystematic Encoder and Its Systematic Feedback Encoder. - 8. 4 Distance Properties of Convolutional Codes. - 8. 5 Decoding of Convolutional Codes. - 8. 6 Performance Bounds. - 8. 7 Punctured Convolutional Codes of Rate (n-1) /n and Simplified Maximum-Likelihood Decoding. - Problems. - 9 ARQ and Interleaving Techniques. - 9. 1 Automatic Repeat Request. - 9. 2 Interleaves. - Problems. - 10 Applications of Convolutional Codes in Mobile Communications. - 10. 1 Convolutional Codes used in the GSM systems. - 10. 2 Convolutional Codes Specified in CDMA Cellular Systems. - 11 Trellis-Coded Modulation. - 11. 1 M-ary Modulation, Spectral Efficiency and Power Efficiency. - 11. 2 TCM Schemes. - 11. 3 Set Partitioning and Construction of Codes. - 11. 4 Rotational Invariance. - 11. 5 Unequal Error Protection(UEP) Codes and the Pragmatic Approach to TCM Systems. - Problems. - 12 Concatenated Coding Systems and Turbo Codes. - 12. 1 Concept of Concatenated Coding System. - 12. 2 Concatenated Coding Systems with Convolutional (or Trellis) Codes and RS Codes. - 12. 3 Turbo Codes. - Appendix A Some Basics of Communication Theory. - A. 1 Vector Communication Channels. - A. 2 Optimal Receivers. - A. 3 Message Sequences. - Appendix B C-programs of Some Coding Algorithms. - B. 1 Encoding and Decoding for Hamming Codes. - B. 2 Compute Metric Tables for A Soft-Decision Viterbi Decoder. - About the Authors.