MIT Department of Electrical Engineering & Computer Science

EECS Fall 1996 Catalogue Supplement

6.971 Error Correction Coding (H)

TR 11-12:30, 36-372
Prof. Mitchell Trott, 35-213, x2359
3-0-9
Prerequisites: A firm grasp of probability and linear algebra, together with mathematical maturity and familiarity with the basic concepts of digital communication

This advanced course covers both classical and recent results in the theory of error correction codes and decoding algorithms. All major categories of practical codes will be treated:

- cyclic redundancy check (CRC) codes
- BCH and Reed-Solomon codes
- convolutional codes
- trellis codes
- "turbo" codes and codes based on iterative decoding

Codes of these types are used, for example, in file transfer protocols, mobile radio communication, compact disc players, deep space communication, and modern high-speed modems.

While the emphasis is on codes that have practical applications, rather than on topics that advance the frontiers of mathematics, the course will include a significant dose of linear algebra, finite field arithmetic, and algebraic systems theory. The aim of the course is to illustrate which types of codes are appropriate for various communication scenarios, and to map out how the state of the art compares to theoretical limits.

Specific subtopics include: finite field Fourier transforms; efficient finite field arithmetic; linear systems over binary alphabets; probability of error calculation (without simulation); Hamming and Gilbert bounds; lattices; trellis complexity of block codes; trellis and Voronoi shaping; decoding methods based on graph search (Viterbi, Fano, stack, iterative decoding); and algebraic decoding (decoding via system identification, bounded distance decoding).

The course should be of interest if you plan to do research in communication, if you want to know how CD players really work, or if you want to learn about Galois Fields without taking a two semester class on modern algebra.