▶Japanese
Post to SNS
- Home
- > School of Engineering
- > Undergraduate major in Information and Communications Engineering
- > Algebraic Systems and Coding Theory
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Information and Communications Engineering
- Instructor(s)
- Kasai Kenta
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(W631) Thr3-4(W631)
- Group
- -
- Course number
- ICT.C209
- Credits
- 2
- Academic year
- 2019
- Offered quarter
- 3Q
- Syllabus updated
- 2019/9/25
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
Starting from some mathematical basic concepts of algebraic structure: group, ring and fields, this course lectures linear codes which are subspace whose scalar is finite fields, and their algebraic decoding.
Student learning outcomes
Goal: Understand the groups, rings, fields, field and its properties forming the basis of algebra, and learn the theory system on the method of constructing code space with high error correction capability. Learn systematically about the algebra and its application necessary for the construction method and decoding method of the code, centering on the Reed-Solomon code which is the most widely used error correction code.
Keywords
Error correction code, encoding and decoding, algebra, group, ring, finite field, minimum distance, linear code, Hamming code, RS code, BCH code
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Each week consists of two lectures.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | code space, channels, Hamming distance, minimum distance, bounded-distance decoding, MAP decoding, ML decoding | Explain code space, channels, Hamming distance, minimum distance, bounded-distance decoding, MAP decoding, ML decoding |
| Class 2 | generator matrix, parity-check matrix, dimension, Singleton bound | Explain generator matrix, parity-check matrix, dimension, Singleton bound |
| Class 3 | parity-check matrix and minimum distance, Hamming code | Explain parity-check matrix and minimum distance, Hamming code |
| Class 4 | coset, syndrome, syndrome decoder | Explain coset, syndrome, syndrome decoder |
| Class 5 | bounds on codes, weight distribution, MacWilliams identity | Explain |
| Class 6 | group, cyclic group, sub-group, coset, quotient ring | Explain group, cyclic group, sub-group, coset, quotient ring |
| Class 7 | ring, homomorphism, isomorphism, ideal, integer ring, Euclidean algorithm, uniqueness of prime factorizations | Explain ring, isomorphism, ideal, integer ring, Euclidean algorithm, uniqueness of prime factorizations |
| Class 8 | finite field, polynomial ring, primitive element, order | Explain finite field, polynomial ring, primitive element, order |
| Class 9 | construction of finite fields, structure of finite fields, minimum polynomial | Explain construction of finite fields, structure of finite fields, minimum polynomial |
| Class 10 | construction of RS codes | Explain construction of RS codes |
| Class 11 | Vandermonde's matrices, generator and parity-check matrix of RS codes | Explain Vandermonde's matrices, generator and parity-check matrix of RS codes |
| Class 12 | decoding of RS codes | Explain decoding of RS codes |
| Class 13 | cyclic codes, generator and parity-check matrices | Explain cyclic codes, generator and parity-check matrices |
| Class 14 | construction of BCH codes, minimum distance of BCH codes, cyclic RS codes | Explain construction of BCH codes, minimum distance of BCH codes, cyclic RS codes |
| Class 15 | relation on RS codes an BCH codes, | Explain relation on RS codes an BCH codes |
Textbook(s)
Handouts are provided at each class.
Reference books, course materials, etc.
坂庭好一、渋谷智治、代数系と符号理論入門、コロナ社、2010年
植松友彦、代数系と符号理論、オーム社、2010年
Assessment criteria and methods
Grade are based on exercise, homework, mid-term and final exams.
Related courses
- ICT.C205 ： Communication Theory (ICT)
- ICT.C201 ： Introduction to Information and Communications Engineering
- ICT.E218 ： Experiments of Information and Communications Engineering II
- ICT.C214 ： Communication Systems
Prerequisites (i.e., required knowledge, skills, courses, etc.)
nothing
