Information Theory and Coding

Course aim

The first part of this course is about information theory. The course aims at answering two fundamental questions in data communications: What is the ultimate data compression? What is the ultimate transmission rate of a communication channel? To answer these questions, the basic tools and concepts in information theory are introduced. Practical coding schemes for data compression and transmission over noisy channels are introduced in the second part of this course.

Course content

Review of Mathematical Background and Basic Concepts in Probability Theory.



Introduction of Information Measures and their Properties: Entropy; Mutual Information; Conditional Entropy; Conditional Mutual Information; Kullback-Leibler Divergence; Log-sum inequality; Data Processing Inequality; Fano’s inequality.



Asymptotic Equipartition Property (AEP): Law of Large Numbers; Types and Typicality.

Lossless source coding theorem and algorithms.



Noisy Channel Models and Shannon’s Channel Coding Theorem.



Fundamentals of Linear Codes: Introduction to Error Detection and Correction; Types of Codes; Minimum Distance.



Block Coding Principles: Generator Matrix Description, Systematic Codes, Detection and Correction Bounds.



Convolutional Codes (Encoding): encoders; generator polynomials; constraint length; state diagrams; tree and trellis diagrams; distance measures.



Convolutional Codes (Decoding): Viterbi algorithm; Soft-Decision Decoding; MAP Decoding.



LDPC Codes: Code Density, Tanner Graphs, Belief Propagation.



Special topics: Network Coding and Digital Fountain.

Textbook(s)

Cover, Thomas M. 2006, Elements of Information Theory, 2nd, Wiley-Interscience

Lin, Shu; Costello, D. J. 2004, Error Control Coding, 2nd, Prentice-Hall, New Jersey

Prerequisite(s)

A good understanding of probability theory is required. Knowledge of communication theory would be advantageous.

Corequisite(s)

Nil

Teaching method

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Assessment

Assignment in 2 parts, Computer modelling project - code design, Examination

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
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Fee-paying program for domestic and international students
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* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.