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An Introduction to Coding Theory

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Overview

Error control coding is an indispensible part of any digital communication system. In this introductory course, we will discuss theory of linear block codes and convolutional codes, their encoding and decoding techniques as well as their applications in real world scenarios. Starting from simple repetition codes, we will discuss among other codes: Hamming codes, Reed Muller codes, low density parity check codes, and turbo codes. We will also study how from simple codes by concatenation we can build more powerful error correcting codes.

Syllabus

Week 1:

Lecture 1: Introduction to error control coding

Lecture 2: Introduction to linear block codes, generator matrix and parity check matrix

Lecture 3: Properties of linear block codes: Syndrome, error detection

Week 2:

Lecture 4: Decoding of linear block codes

Lecture 5: Distance properties of linear block codes

Week 3:

Lecture 6: Some simple linear block codes: Repetition codes, Single parity check codes, Hamming codes, Reed Muller codes

Lecture 7: Bounds on size of codes: Hamming bound, Singleton bound, Plotkin bound, Gilbert-Varshamov bound

Week 4:

Lecture 8: Low density parity check codes

Lecture 9: Decoding of low density parity check codes-I: Belief propagation algorithm on BEC

Lecture 10: Decoding of low density parity check codes-I: Belief propagation algorithm on BSC and AWGN channels

Week 5:

Lecture 11: Introduction to convolutional codes-I: Encoding, state diagram, trellis diagram

Lecture 12: Introduction to convolutional codes-II: Classification, realization, distance properties

Lecture 13: Decoding of convolutional codes-I: Viterbi algorithm

Week 6:

Lecture 14: Decoding of convolutional codes-II: BCJR algorithm

Lecture 15: Performance bounds for convolutional codes

Week 7:

Lecture 16: Turbo codes

Lecture 17: Turbo decoding

Week 8:

Lecture 18: Distance properties of turbo codes

Lecture 19: Convergence of turbo codes

Lecture 20: Applications of linear codes

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