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# Error control coding: An introduction to linear block code

## 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, 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 capacity approaching low density parity check codes. We will also discuss bounds on number of codewords given codeword length and minimum distance of code.

## 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, error correction

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: Belief propagation algorithm
Lecture 10: Applications of linear block codes