 Course Co-ordinated by IIT Kanpur
 Coordinators IIT Kanpur

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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.
 Week Topics 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 2. Lecture 4: Decoding of linear block codes Lecture 5: Distance properties of linear block codes 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 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 5. Lecture 11: Decoding of convolutional codes-II: BCJR algorithm Lecture 12: Performance bounds for convolutional codes 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 7. Lecture 15: Turbo codes Lecture 16: Turbo decoding 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

An exposure to linear algebra and probability theory as well as a course in digital communications

1. âError Control Codingâ, by Shu Lin and Daniel J. Costello, Jr., second edition, Prentice Hall, 2004.
2. Todd K. Moon, âError Correction Codingâ, 1st Edition, Wiley-Interscience, 2006.Â
3. F. J. MacWilliams, N. J. A. Sloane, âThe Theory of Error-Correcting Codesâ, North-Holland, Amsterdam, 1977
4. R. E. Blahut, âAlgebraic Codes for Data Transmissionâ, 1st Edition, Cambridge University Press 2003.
5. Cary W. Huffman, Vera Pless, âFundamentals of Error-Correcting Codesâ, 1st Edition, Cambridge University Press, 2003.
6. Rolf Johannesson and Kamil Sh. Zigangirov, ``Fundamentals of Convolutional Codingââ, IEEE Press, 1999.

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