Coding Theory and Applications
(3-0-0-3)
CMPE Degree: This course is Not Applicable for the CMPE degree.
EE Degree: This course is Not Applicable for the EE degree.
Lab Hours: 0 supervised lab hours and 0 unsupervised lab hours.
Technical Interest Group(s) / Course Type(s): Telecommunications
Course Coordinator:
Prerequisites: ECE 3075
Catalog Description
To introduce the theory and practice of error control coding, with emphasison linear, cyclic, convolutional, and parallel concatenated codes
Course Outcomes
Not Applicable
Strategic Performance Indicators (SPIs)
Not Applicable
Topical Outline
1. Introduction to Linear Block Codes
a. -Linear vector spaces
b. -Generator and parity-check matrices
c. -Syndrome decoding, standard arrays
2. Finite field fundamentals
a. -Groups, fields, rings, elementary Galois fields
b. -Irreducible, minimal and primitive polynomials
c. -Extension fields
d. -Conjugacy classes, minimal polynomials, factorization of
e. -Ideals and generator polynomials
3. General Cyclic codes
a. -General theory of linear cyclic codes
b. -Shift register encoders and decoders
4. BCH and Reed-Solomon codes
a. -Generator polynomial approach to encoding BCH codes
b. -The BCH bound
c. -Basic properties of Reed Solomon Codes
d. -Decoding BCH codes: Peterson's and Berlekamp’s algorithms
e. -Decoding RS codes: Berlekamp-Massey and Euclid’s algorithm
5. Convolutional Codes
a. -Shift register encoding
b. -Viterbi decoding
6. Turbo Codes
a. Serial- vs parallel-concatenated codes
b. -Parallel concatenation encoder
c. -Interleaving
d. APP decoding, SOVA
e. -Turbo decoding
f. EXIT charts
7. Low-Density Parity-Check codes
a. Gallager A algorithm
b. Belief propagation algorithm
c. Density evolution
8. Polar codes
a. Polar transform
b. Construction of polar codes
c. Decoding of polar codes