Course Details
Contents
Motivation for Error Control Codes: A brief introduction to Information Theory - Channel Coding Theorem
Basics of binary codes: block length, Hamming weight, minimum distance, rate
Mathematical Preliminaries: Groups, Rings, Fields, Vector Spaces
Linear block codes: generator and parity check matrices, dual code
Bounds on code sizes: Hamming, Gilbert-Varshamov, Singleton bounds
Decoding Linear Block Codes: Standard Array, ML, MAP Decoder
MDS codes: Reed Solomon (RS) Codes, Dual of RS codes,Systematic Encoding of RS codes
Berlekamp-Welch decoding, Shamir's Secret Sharing
Applications to Learning: Straggler Mitigation in Distributed Computing
Applications in Post-Quantum Cryptography: McElice Cryptosystem
Reed Muller Codes, Polar codes
Semi-Rings and Generalized Distributive Law
LDPC Codes: Belief Propagation/ Message Passing decoder
Convolutional Codes and Viterbi Decoding
Finite Fields, Cyclic Codes (BCH codes)
References
Ron. M. Roth, Introduction to Coding Theory, Cambridge University Press, 2006. (An excellent textbook primarily covering block codes)
S. Lin and D.J. Costello, Error Control Coding (2nd edition), Prentice-Hall, 2004. (A good introduction from the engineering perspective.)
T. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, 2008. (Focuses on LDPC and related codes)
R. Johanneson and K.Sh. Zigangirov, Fundamentals of Convolutional Coding, IEEE Press, 1999.
F. J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North-Holland, 1977.
R. E. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, 2002.
R. J. McEliece, Theory of Information and Coding (2nd edition), Cambridge University Press, 2002.
Video Lectures by Prof. Mary Wootters, Stanford University
Video Lectures by Prof. P. Vijay Kumar, IISc Bengaluru
Video Lectures by Prof. Andrew Thangaraj, IIT Madras