ECE Course Outline

ECE6606

Coding Theory and Applications (3-0-3)

Prerequisites
ECE 3075
Corequisites
None
Catalog Description
To introduce the theory and practice of error control coding, with emphasis on linear, cyclic, convolutional, and parallel concatenated codes
Textbook(s)
Wicker, Error Control Coding for Digital Communication and Storage, Prentice Hall, 1995. ISBN 9780132008099 (required)

Topical Outline
Introduction to Linear Block Codes
-Linear Vector spaces
-Generator and parity check matrices
-Syndrome decoding, standard arrays

Finite field fundamentals
-Groups, fields, rings, elementary Galois fields
-Irreducible, minimal and primitive polynomials
-Extension fields
-Conjugacy classes, minimal polynomials, factorization of 
-Ideals and generator polynomials

General Cyclic codes
-General theory of linear cyclic codes
-Shift register encoders and decoders

BCH and Reed-Solomon codes
-Generator polynomial approach to encoding BCH codes
-The BCH bound
-Basic properties of Reed Solomon Codes
-Decoding BCH codes:  Peterson's algorithm
-Decoding BCH codes:  Berlekamp's algorithm
-Decoding RS codes:  Berlekamp-Massey algorithm
-Decoding RS codes:  Euclid's algorithm

Convolutional Codes
-Shift register encoding
-Viterbi decoding

Serial Concatenated Codes

Parallel Concatenated Codes
-Parallel Concatenation Encoder
-Interleaving
-MAP Decoding, SOVA
-Turbo Decoding