Non-Binary Error Control Coding for Wireless Communication and Data Storage - Carrasco, Rolando Antonio

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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