Course Code: MTH351
Synopsis
MTH351 Coding Theory introduces students to mathematics behind successful transmission of data through a noisy channel and correcting errors in corrupted messages. The topics covered are of central importance for many applications in computer science and engineering. The course gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. The issues of bounds and decoding essential to the design of good codes will be featured prominently.
Level: 3
Credit Units: 5
Presentation Pattern: EVERY JULY
Topics
- Groups
- Cosets
- Polynomial Rings
- Fields
- Finite Fields
- Linear Codes
- Hamming Distances and Hamming Codes
- Cyclic Codes
- BCH Codes
- Reed-Solomon Codes
- Goppa Codes
- Turbo Codes
Learning Outcome
- Show the existence/non-existence of certain codes with certain parameters.
- Demonstrate the decoding of BCH codes, Reed-Solomon codes and Quadratic-residue codes.
- Calculate generator matrix and parity-check matrix of a given linear code.
- Construct certain linear codes from other given linear code.
- Determine the generator polynomial of a given cyclic code.
- Compute the capacity of a discrete memoryless communications channel.