Course Title | ## Coding Theory | ||

Course Code | ## MH4310 | ||

Offered | Study Year 4, Semester 2 | ||

Course Coordinators | Xing Chaoping (Prof) | xingcp@ntu.edu.sg | 6513 7473 |

Frederique Elise Oggier (Assoc Prof) | frederique@ntu.edu.sg | 6513 2026 | |

Pre-requisites | MH1301 and MH2200 | ||

AU | 4 | ||

Contact hours | Lectures: 39, Tutorials: 12 | ||

Approved for delivery from | AY 2020/21 semester 2 | ||

Last revised | 18 Mar 2020, 11:31 |

This course aims to introduce the topic of coding theory, which studies the design of mechanisms to ensure reliability of data transmission (or storage) in the presence of perturbance. In this course, you will learn what are linear codes, their properties, how to construct them, and how to use them to ensure data reliability.

Upon successfully completing this course, you should be able to:

- Define what is a linear code.
- Give examples of linear codes.
- Compute the minimum distance of a linear code.
- Encode and decode a linear code.
- Explain where coding theory is being used.
- Weigh the trade-offs involving code parameters.

The definition of a linear code, its dimension and its length.

The definition of generator matrix, parity check matrix and dual code.

The definition of Hamming distance/weight, and how to compute it.

How to encode and decode.

Hamming codes

Perfect codes

Golay codes

Maximum distance separable (MDS) codes

Reed-Mueller codes

BCH codes

Reed-Solomon codes

Bounds on code parameters

Component | Course ILOs tested | SPMS-MAS Graduate Attributes tested | Weighting | Team / Individual | Assessment Rubrics |
---|---|---|---|---|---|

Continuous Assessment | |||||

Mid-semester Quiz | |||||

Short Answer Questions | 1, 2, 3, 4, 5, 6 | 1. a, b | 20 | individual | See Appendix for rubric |

Short Answer Questions 1 | 1, 2, 3, 4, 5, 6 | 1. a, b | 20 | individual | See Appendix for rubric |

Examination (2 hours) | |||||

Short Answer Questions | 1, 2, 3, 4, 5, 6 | 1. a, b, c | 60 | individual | See Appendix for rubric |

Total | 100% |

These are the relevant SPMS-MAS Graduate Attributes.

## 1. Competence

a. Independently process and interpret mathematical theories and methodologies, and apply them to solve problems

b. Formulate mathematical statements precisely using rigorous mathematical language

c. Discover patterns by abstraction from examples

Feedback will be given after the CA, so that you know where you stand, and what are the weakest points to be improved upon.

Since the class size for this class is not very large, you are welcome to ask for personal consultation should you want or need a more personalized feedback.

After the final exam, the Examiner's Report will be available on NTUlearn.

Lectures (39 hours) | During the lecture, the new concepts are introduced and explained to you. In order to improve the effectiveness of learning, the following steps are taken: |

Tutorials (12 hours) | In tutorials, you will mostly be asked to compute codes and their properties, and to use them in different application scenarios. |

C. Xing and X. Ling, ``Coding Theory: A First Course"

ISBN-13: 978-0521529235

ISBN-10: 0521529239W. Cary Huffman and Vera Pless, ``Fundamentals of Error Correcting Codes", Cambridge

Online ISBN: 9780511807077

DOI: https://doi.org/10.1017/CBO9780511807077

As for any class you attend, it is your responsibility to learn the material, whether you decide to attend the class or to read the material, as well as to try out the tutorial questions.

Good academic work depends on honesty and ethical behaviour. The quality of your work as a student relies on adhering to the principles of academic integrity and to the NTU Honour Code, a set of values shared by the whole university community. Truth, Trust and Justice are at the core of NTUâ€™s shared values.

As a student, it is important that you recognize your responsibilities in understanding and applying the principles of academic integrity in all the work you do at NTU. Not knowing what is involved in maintaining academic integrity does not excuse academic dishonesty. You need to actively equip yourself with strategies to avoid all forms of academic dishonesty, including plagiarism, academic fraud, collusion and cheating. If you are uncertain of the definitions of any of these terms, you should go to the Academic Integrity website for more information. Consult your instructor(s) if you need any clarification about the requirements of academic integrity in the course.

Instructor | Office Location | Phone | |
---|---|---|---|

Frederique Elise Oggier (Assoc Prof) | MAS05-13 | 6513 2026 | frederique@ntu.edu.sg |

Xing Chaoping (Prof) | SPMS-MAS-05-27 | 6513 7473 | xingcp@ntu.edu.sg |

Week | Topic | Course ILO | Readings/ Activities |
---|---|---|---|

1 | Definition of coding theory, what it is and where it is used. Definition of encoding, linear code, generator matrix, parity check matrix | 1, 2, 4, 5 | introduction of chapter 1, 1.1 and 1.2 (Huffman and Pless) |

2 | Dual codes, Hamming distance | 1, 2, 3 | 1.3, 1.4 (Huffman and Pless) |

3 | Error correction, Hamming spheres. | 4 | 1.11 (Huffman and Pless) |

4 | Syndrome decoding | 4 | 1.11 (Huffman and Pless) |

5 | Rate, Sphere Packing Bound, Hamming codes | 2, 3, 6 | 1.12 and 1.8 (Huffman and Pless) |

6 | Golay codes, puncturing and extending | 2, 3, 6 | 1.9 and 1.5.2, 1.5.3 (Huffman and Pless) |

7 | Reed-Mueller codes | 2, 3, 6 | 1.10 (Huffman and Pless) |

8 | Bounds | 6 | section 2 (Huffman and Pless) |

9 | Finite fields | 6 | section 3 (Huffman and Pless) |

10 | Reed-Solomon codes | 2, 3 | section 5.2 (Huffman and Pless) |

11 | Cyclic codes | 2, 3, 6 | section 4(Huffman and Pless) |

12 | BCH codes: introduction | 2, 3, 6 | section 5(Huffman and Pless) |

13 | More on BCH codes and Reed-Solomon codes | 2, 3 | section 5 (Huffman and Pless) |