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
CORE/ELECTIVE: Elective
UG/PG: Both UG and PG
PREREQUISITES: An exposure to linear algebra and probability theory as well as a course in digital communications
INDUSTRY SUPPORT: Telecommunication Companies
5686 students have enrolled already!!
ABOUT THE INSTRUCTOR:
Prof. Adrish Banerjee received his Bachelors degree from Indian Institute of Technology, Kharagpur and Masters and Ph.D. degree from University of Notre Dame, Indiana. He is currently an Associate Professor in the Department of Electrical Engineering at Indian Institute of Technology, Kanpur. He is a recipient of Microsoft Research India young faculty award, Institute of Engineers India young engineer award, and IETE Prof. K. Sreenivasan memorial award. His research interests are in the physical layer aspects of wireless communications, particularly green communications, error control coding, and cognitive radio.
COURSE LAYOUT:
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: Introduction to convolutional codes-I: Encoding, state diagram, trellis diagram
Lecture 9: Introduction to convolutional codes-II: Classification, realization, distance properties
Lecture 10: Decoding of convolutional codes-I: Viterbi algorithm
Week 5-
Lecture 11: Decoding of convolutional codes-II: BCJR algorithm
Lecture 12: Performance bounds for convolutional codes
Week 6-
Lecture 13: Low density parity check codes
Lecture 14: Decoding of low density parity check codes: Belief propagation algorithm on BSC and AWGN channels
Week 7-
Lecture 15: Turbo codes
Lecture 16: Turbo decoding
Week 8-
Lecture 17: Distance properties of turbo codes
Lecture 18: Convergence of turbo codes
Lecture 19: Automatic repeat request schemes
Lecture 20: Applications of linear codes
SUGGESTED READING MATERIALS:
1. “Error Control Coding”, by Shu Lin and Daniel J. Costello, Jr., second edition, Prentice Hall, 2004.
3. F. J. MacWilliams, N. J. A. Sloane, “The Theory of Error-Correcting Codes”, North-Holland, Amsterdam, 1977
4. R. E. Blahut, “Algebraic Codes for Data Transmission”, 1st Edition, Cambridge University Press 2003.
5. Cary W. Huffman, Vera Pless, “Fundamentals of Error-Correcting Codes”, 1st Edition, Cambridge University Press, 2003.
6. Rolf Johannesson and Kamil Sh. Zigangirov, ``Fundamentals of Convolutional Coding’’, IEEE Press, 1999.
CERTIFICATION EXAM :
The exam is optional for a fee.
Date and Time of Exams: April 28 (Saturday) and April 29 (Sunday) : Morning session 9am to 12 noon;
Exam for this course will be available in one session on both 28 and 29 April.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.
CERTIFICATION:
Final score will be calculated as : 25% assignment score + 75% final exam score
25% assignment score is calculated as 25% of average of Best 6 out of 8 assignments
E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur.It will be e-verifiable at nptel.ac.in/noc.
