Non-Binary Error Control Coding for Wireless Communication and Data Storage

Professor Rolando A. Carrasco, Newcastle, UK has carried out research and given lectures in the area of channel coding, signal processing and mobile communication for over 20 years. He has published over 200 papers, and much of his research relates to the design and construction of non-binary coding schemes for wireless communications, in particular Ring-TCM codes, Reed-Solomon codes and Algebraic-Geometric codes.

Comprehensive introduction to non-binary error-correction coding techniques

Acknowledgements Preface Chapter 1 - Information, Channel Capacity and Channel Modelling * Introduction 1.2. Measure of Information 1.3. Channel Capacity 1.4 Channel Modelling 1.5. Definition of a communications channel and its parameters 1.6. Multiple Input Multiple Output (MIMO) Channel 1.8. Magnetic Storage Channel Modelling 1.9. Summary References Chapter 2 - Basic Principles of Non-Binary Codes 2.1. Introduction to Algebraic Concepts 2.2. Algebraic Geometry 2.3. Conclusions Chapter 3 - Non-Binary Block Codes 3.1. Introduction 3.2. Fundamentals of Block Codes 3.3. Bose-Chaudhuri-Hocquenghem (BCH) Codes Example 3.3. Constructing a non-binary BCH code over GF(4) of length n = 15 symbols 3.4. Reed-Solomon Codes Example 3.4: Constructing a non-binary BCH code over GF(16) of length n = 15 symbols 3.5. Decoding Reed-Solomon Codes 3.6. Coded Modulation 3.7. Conclusions References Chapter 4 - Algebraic-Geometric Codes 4.1. Introduction 4.2. Construction of Algebraic-Geometric Codes 4.3. Decoding Algebraic-Geometric Codes 4.4. Majority Voting 4.5. Calculating the Error Magnitudes. 4.6. Complete Hard-Decision Decoding Algorithm for Hermitian Codes. 4.8. Simulation Results 4.9. Conclusions References Chapter 5 - List Decoding 5.1. Introduction 5.2. List Decoding of Reed-Solomon Codes using the Guruswami-Sudan algorithm 5.3. Soft-Decision List Decoding of Reed-Solomon codes using the Kotter-Vardy Algorithm. 5.4. List Decoding of Algebraic-Geometric Codes 5.5. Determining the Corresponding Coefficients 5.6. Complexity reduction Interpolation 5.7. General Factorisation 5.8. Soft-Decision List Decoding of Hermitian Codes 5.9. Conclusions References Chapter 6 - Non-Binary Low Density Parity Check Codes 6.1. Introduction 6.2. Construction of Binary LDPC Codes - Random and Structured Methods 6.3. Decoding of Binary LDPC Codes using the Belief Propagation Algorithm. 6.4. Construction of Non-Binary LDPC Codes defined over Finite Fields 6.5. Decoding Non-Binary LDPC Codes with the Sum Product Algorithm 6.6.Conclusions References Chapter 7 - Non-Binary Convolutional Codes References Chapter 8 - Non-binary Turbo codes 8.1. Introduction 8.2. The turbo encoder 8.3. The Turbo Decoder 8.4. Non-Binary Turbo Codes 8.5. Conclusion References