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

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 Kötter-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