Dr R Venkataramanan
Timing and Structure
Michaelmas Term. 16 lectures. Assessment: 100% exam
The aims of the course are to:
- To introduce students to the principles of information theory, data compression, and error-correction, which form the foundations of modern communication and information processing systems.
As specific objectives, by the end of the course students should be able to:
- Explain why entropy and channel capacity arise as fundamental limits for data compression and transmission, respectively
- Understand and implement basic compression algorithms such as Huffman coding and Arithmetic coding
- Encode and decode information using simple linear block codes
- Implement decoders for error-correcting codes such as LDPC codes
Information Theory and Data Compression (11L)
Probability fundamentals; Definitions of entropy, joint entropy, conditional entropy: interpretations as measures of uncertainty
Noiseless source coding theorem; Significance of entropy as the fundamental limit of compression
Bounds on code length for lossless data compression
Practical compression algorithms: Huffman coding, Arithmetic coding
Relative Entropy, Mutual Information: Properties and some applications
Discrete Memoryless Channels and Channel Capacity
The channel coding theorem: Random Coding and the direct coding theorem; Fano's inequality and the converse theorem
The additive white Gaussian noise (AWGN) channel and its capacity
Channel Coding (Error-correcting codes) (5L)
Introduction to block codes; Linear block codes
Representing a linear code using a factor graph; Sparse-graph codes
Message passing decoding of sparse-graph codes for binary erasure channels
The Belief-Propagation (BP) algorithm; BP decoding of sparse-graph codes for general binary input channels
This module will be of interest to anyone who wishes to understand how information can be mathematically modelled, measured, compressed, and transmitted. Though not a pre-requisite for 3F4, 3F7 provides a good foundation for further study of communication.
The following are useful references:
- T. Cover and J. Thomas, Elements of Information Theory, Wiley-Blackwell, 2006.
- D. MacKay, Information Theory, Inference and Learning Algorithms, Cambridge University Press, 2003 (free electronic copy available for download)
- T. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, 2008.
- R. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, 2012.
Please refer to Form & conduct of the examinations.
Last modified: 01/12/2016 10:07