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

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. Dr. Martin Johnston, Newcastle, UK is a Research Associate at the University of Newcastle and is working on the construction of algebraic-geometric codes and LDPC codes suitable for future data storage devices.

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
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