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This is an introductory course on coding theory with an emphasis on algebraic codes. I assume that you have a basic knowledge of linear algebra, and probability. I will be covering a selection of topics from Chapters 1-7, 11-12 and 17. Some homework assignments will require you to code in matlab. There will be two course projects. You are assumed to have familiarity with matlab or some other programming language. Course details are given below.

Textbook: Error Control Coding by Shu Lin and Daniel Costello Jr.

Course topics. Detailed outline.

• Introduction to coding
• Linear block codes
• Algebra for coding
• Cyclic codes
• BCH and Reed Solomon codes
• Performance of block codes
• Convolutional codes
• LDPC codes and other advanced topics (time permitting)

Grading policy (Tentative)
20% Homework, 20% Miniquizzes, 35% Projects, 25% Finals.

Lectures

15 Jan Introduction

17 Jan First look at error correcting codes

20 Jan Algebra (Groups)

21 Jan Algebra (Fields, vector spaces)

22 Jan Linear codes

27 Jan Decoding linear code

28 Jan Standard array decoder

29 Jan Performance of standard array decoder; First look at GF(4)

31 Jan Finite fields, basic properties

03 Feb Structure of finite fields

04 Feb Structure of finite fields

05 Feb Structure of finite fields

07 Feb Polynomials over finite fields and factorization

10 Feb Polynomials over finite fields, Miniquiz-1

11 Feb (Nonbinary) Linear codes and code constructions

12 Feb Product codes and bounds on codes

17 Feb Cyclic codes, basic properties

18 Feb Cyclic codes, Miniquiz-2

19 Feb Encoding and decoding cyclic codes

24 Feb Introduction to BCH Codes

25 Feb BCH Codes, Miniquiz-3

26 Feb Decoding BCH codes, Peterson-Gorenstein-Zierler method

28 Feb No class

03 Mar Decoding BCH codes, Berlekamp-Massey algorithm

04 Mar Decoding BCH codes, Berlekamp-Massey algorithm continued

07 Mar Performance of block codes

10 Mar Problem session

11 Mar Problem session, Miniquiz-4

12 Mar Introduction to convolutional codes

14 Mar Convolutional codes-various formulations

17 Mar No class

18 Mar Feedforward/feedback realizations of convolutional codes

19 Mar Strucutural properties of convolutional codes

21 Mar Structural properties of convolutional codes

24 Mar Decoding convolutional codes

25 Mar Viterbi's algorithm

26 Mar Performance analysis of convolutional codes

28 Mar Performance analysis of convolutional codes

01 Apr Construction of convolutional codes

04 Apr LDPC codes

07 Apr Decoding LDPC codes

08 Apr Decoding LDPC codes, sum product algorithm, variations