ECE 556
CODING THEORY
ECE 556, TTh 12:30-13:50pm, 3020 ECEB. ECE 556 is also cross-listed as CS 577 and MATH 579.
Catalog description: We will start by covering the mathematical concepts needed to understand algebraic coding theory and the concepts of cyclic codes and in particular, Reed-Solomon codes.
These will heavily focus on finite fields, combinatorics and number theory.
In the second part of the course we will turn our attention to codes on graphs (LDPC codes), polar codes, codes for distributed storage, coded computing and learning and coding for synthetic biology (i.e., coding for DNA- and polymer-based data storage). Our treatment of these subjects will rely on some basic and some not-so-basic notions from combinatorics and graph theory, optimization and machine learning and rudimentary molecular biology.
Due to time limitations we will not discuss convolutional codes.
LECTURE NOTES (Scribed)
Hamming codes, linear codes, dual codes
Extended coverage of MacWilliams identities
Finite fields - basic treatment
Finite fields - more advanced treatment
Finite fields - more advanced treatment with examples
Double error-correcting BCH codes
Decoding of RS codes: The PGZ algorithm
Decoding of RS codes: Euclid's algorithm (McEliece notes)
List decoding of RS codes: Sudan's algorithm
Polar Codes (Prof. Arikan's slides)
Single-deletion-correcting codes (article by Prof. Sloan)
String correlation and avoiding forbidden substrings
Shannon Channel: Joao Ribeiro's talk on Coded Trace Reconstruction
Prof. Atri Rudra's Tutorial on Group Testing
Prof. Arya Mazumdar's Lecture Notes on Group Testing
Tutorial on LDPC codes by Prof. Siegel
Recommended Text I: The Theory of Error-Correcting Codes (Mac Williams and Sloane, a classic for algebraic coding theory).
Recommended Text II: Algebraic Codes for Data Transmission (Blahut, an engineering-oriented approach to coding theory).
Recommended Text III: Introduction to Coding Theory (Roth, contains a number of topics not covered in the above cited texts).
Course Directors : Professor Olgica Milenkovic (milenkov@illinois.edu)
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