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Mathematics of Communications


  • Credit value: 15 credits at Level 7
  • Assessment: a three-hour examination (80%) and short, problem-based coursework assignments (20%) 

Module description

This module introduces you to the mathematics underlying various aspects of communications technology, including coding theory and cryptography. It will give you an introduction to various communications applications and equip you with the mathematical background necessary for further exploration of these fields.

indicative module Syllabus

  • Information theory: uncertainty; Shannon entropy; conditional entropy; Shannon information; Shannon’s source coding theorem; Huffman coding; data compression
  • Error correcting codes: the binary symmetric channel; Hamming distance; Shannon’s noisy coding theorem; codes; bounds on the sizes of codes; linear codes; syndrome decoding; binary codes; Reed-Solomon codes
  • Cryptography and information security: perfect secrecy; the one-time pad; linear feedback shift registers; introduction to public-key cryptography; hash functions; secure pseudo-random number generation; secret-sharing schemes and perfectly secure message transmission

Learning objectives

By the end of this module, you will have:

  • knowledge and understanding of, and the ability to use, mathematical techniques
  • knowledge and understanding of a range of results in mathematics
  • a deeper understanding of several topics in mathematics
  • the ability to comprehend and evaluate conceptual and abstract material
  • the ability to devise rigorous mathematical proofs
  • the ability to understand and apply mathematical reasoning in several different areas of mathematics
  • problem-solving skills, including the ability to assess problems logically and to approach them analytically.

Recommended reading

  • Raymond Hill, A First Course in Coding Theory, Clarendon Press 1986.
  • D.R. Stinson, Cryptography: Theory and Practice (3rd edition), CRC Press 2005.