Information Theory and Biodiversity

Overview

Introduction to information theory. Basic modular arithmetic and factoring. Finite-field arithmetic. Random variables and some concepts of probabilities. RSA cryptography and factorisation. Uniquely decipherable and instantaneous codes. Optimal codes and Huffman coding. Code extensions. Entropy, conditional entropy, joint entropy and mutual information. Shannon noiseless coding theorem. Noisy information channels. Binary symmetric channel. Decision rules. The fundamental theorem of information theory. Basic coding theory. Linear codes. A brief introduction to low-density parity-check codes.

Learning Objectives

On completion of the module, it is intended that students will be able to: explain the security of and put in use the RSA protocol; understand how to quantify information and mutual information; motivate the use of uniquely decipherable and instantaneous codes; use Huffman encoding scheme for optical coding; use source extension to improve coding efficiency; prove Shannon noiseless coding theorem; understand the relation between mutual information and channel capacity; calculate the capacity of some basic channels; use basic error correction techniques for reliable transmission over noisy channels.

Skills

Problem solving skills; report writing skills; computing skills

Assessment

None