MAS3714
Coding Theory
- Offered for Year: 2025/26
- Module Leader(s): Dr William Rushworth
- Owning School: School of Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
| Semester 2 Credit Value: | 10 |
| ECTS Credits: | 5.0 |
Aims
To explain the necessity for error correcting codes, to establish their general properties, to show how to construct linear and cyclic codes and to gain practice in their use.
Module Summary
Error-correcting codes are at the heart of the digital revolution. They are used to store music on CD's and video on DVD's; to send data across telecommunications networks; and to broadcast digital television. In practice, a digital signal may be degraded in transit by many factors - cosmic rays, fluctuations in power supplies, even (in the case of a CD) dust and scratches - so that some 0s are changed to 1s and vice versa; error-correcting codes are designed to rectify this. We work with words, binary strings of some standard length n. Certain words are designated as codewords, and the signal is converted to a sequence of codewords before transmission. At the receiving end, each word is examined as it arrives, and, if it turns out to be a non-codeword (indicating that the signal has been degraded), it is replaced by the nearest codeword. This explains why small imperfections on a CD do not affect the quality of the sound that you hear. We shall concentrate on a particularly nice class of codes called linear codes, a beautiful application of elementary linear algebra. Here errors can be corrected automatically by simple matrix operations. In particular, we shall investigate cyclic codes, linear codes based on polynomials.
Outline Of Syllabus
General properties of codes. Perfect codes. Linear codes. Parity-check matrices and syndrome decoding. Hamming codes. Extensions of codes. Cyclic codes.
Learning Outcomes
Intended Knowledge Outcomes
Students will understand and be able to use the language of coding theory. They will understand how small errors in transmitted digital data can be automatically corrected.
Intended Skill Outcomes
Students will be able to produce generator and parity-check matrices (for linear codes). They will be able to use polynomials to construct cyclic codes. They will be able to use syndrome decoding to correct small errors in received data.
Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
| Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
| Totals | 100 |
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work.
Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.
Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work.
In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.
Assessment Methods
The format of resits will be determined by the Board of Examiners.
Exams
| Component | Length (mins) | Semester | When set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination 1 | 120 | 2 | A | 85 | N/A |
Other Assessments
| Component | Semester | When set | Percentage | Comment |
|---|---|---|---|---|
| Problem solving exercises 1 | 2 | M | 5 | Coursework assignments |
| Problem solving exercises 2 | 2 | M | 5 | Coursework assignments |
| Problem solving exercises 3 | 2 | M | 5 | Coursework assignments |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments are expected to consist of three written assignments of equal weight: the exact nature of assessment will be explained at the start of the module. These allow the students to develop their problem solving techniques, to practice the methods learnt in the module, to assess their progress and to receive feedback; this assessment has a secondary formative purpose as well as its primary summative purpose. The coursework assignments may be written assignments, computer based assessments or a combination of the two, and in the case of combined assessments, the deadlines for the two parts will not necessarily be the same.
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/