An Introduction to Coding Theory

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.

INTENDED AUDIENCE: 3rd/4th year UG students, PG students & faculty in electronics and communications engineering
PREREQUISITES: An exposure to linear algebra and probability theory as well as a course in digital communications
INDUSTRY SUPPORT: Telecommunication Companies

COURSE LAYOUT

Week 1-Lecture 1: Introduction to error control codingLecture 2: Introduction to linear block codes, generator matrix and parity check matrixLecture 3: Properties of linear block codes: Syndrome, error detection
Week 2-Lecture 4: Decoding of linear block codesLecture 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 codesLecture 7: Bounds on size of codes: Hamming bound, Singleton bound, Plotkin bound, Gilbert-Varshamov bound
Week 4-Lecture 8: Introduction to convolutional codes-I: Encoding, state diagram, trellis diagramLecture 9: Introduction to convolutional codes-II: Classification, realization, distance propertiesLecture 10: Decoding of convolutional codes-I: Viterbi algorithm
Week 5-Lecture 11: Decoding of convolutional codes-II: BCJR algorithmLecture 12: Performance bounds for convolutional codes
Week 6-Lecture 13: Low density parity check codesLecture 14: Decoding of low density parity check codes: Belief propagation algorithm on BSC and AWGN channels
Week 7-Lecture 15: Turbo codesLecture 16: Turbo decoding
Week 8-Lecture 17: Distance properties of turbo codesLecture 18: Convergence of turbo codesLecture 19: Automatic repeat request schemesLecture 20: Applications of linear codes