ECE 695C - Inference Methods for Codes on Graphs
Course Details
Lecture Hours: 3 Credits: 3
Counts as:
Experimental Course Offered:
Fall 2007
Catalog Description:
We will study the encoder/decoder structures, analysis and design tools for the graph-based error correcting codes, especially focusing on low-density parity-check (LDPC) codes. It will be explored step-by-step the frontier knowledge about achieving the channel capacity with efficient implementation. Many applications of the underlying principles will be discussed, including the LDPC source codes, the linear system detectors, and the turbo systems.
Course Objectives:
It is the holy grail of telecommunications to transmit messages at the rate of the channel capacity, which has been made possible by the modern error control codes in the last decade. A broad treatment of the latest progress of error control codes will be made from the inference perspective, and the underlying turbo principles can be adopted for other systems. The students will learn different techniques for code analysis and design, ranging from the factor graph analysis, convex optimization, to graph algorithms, which are essential to many communication/signal processing problems as well.
Required Text(s):
None.
Recommended Text(s):
- Information Theory, Inference and Learning Algorithms , D. J. C. MacKay
- Modern Coding Theory , T. Richardson and R. Urbanke
Lecture Outline:
| Lectures | Topics |
|---|---|
| 3 | Entropy and channel capacity from the detection perspective |
| 3 | Viterbi and BCJR decoders for convolution codes and trellis codes. |
| 3 | The turbo code |
| 3 | LDPC code encoding & different types of LDPC codes |
| 3 | Review and midterm exam #1 |
| 6 | Message-passing decoder as a distributed inference algorithm |
| 3 | Threshold-oriented code analysis & design: the density evolution |
| 3 | Iterative bounds, EXIT chart and the area theorem |
| 3 | Review and midterm exam #2 |
| 4 | Error-floor-oriented code analysis & design |
| 4 | Non-iterative decoders, including graph cover decoders, LP decoders, and the Maxwell decoders |
| 3 | Explicit LDPC code constructions |
| 3 | Other systems based on the turbo / extrinsic principle |
Assessment Method:
none