• Introductory Concepts: Noisy channels, block codes, encoding and decoding, maximum-likelihood decoding, minimum-distance decoding, error detection and correction. Shannon's noisy-channel coding theorem.

• Linear codes: Minimum distance, generator and parity-check matrices, dual codes, standard array decoding, syndrome decoding. Repetition codes, Hamming codes.

• Bounds on Code Parameters: Hamming bound, Singleton bound, Gilbert-Varshamov bound, Plotkin bound.

• Basic Finite Field Theory: Definitions, prime fields, construction of prime power fields via irreducible polynomials, existence of primitive elements, minimal polynomials.

• Algebraic Codes: Bose-Choudhury-Hocquenghem (BCH) codes, Reed-Solomon codes, and alternant codes as instances of generalized Reed-Solomon (GRS) codes. Decoding algorithms for GRS codes.

• Cyclic codes: Definition, characterization as ideals of polynomial rings. BCH codes viewed as cyclic codes.

• Convolutional Codes: Definitions, encoders, state and trellis diagrams, Viterbi decoder.

• The Generalized Distributive Law: As expounded in the paper
  S.M. Aji and R.J. McEliece, "The generalized distributive law", IEEE Transactions on Information Theory, vol. 46, no. 2, pp. 325-343, March 2000.

• Low-Density Parity-Check (LDPC) Codes: Definitions, Tanner graph, iterative message-passing decoding algorithms. Material largely based on the paper
  T. Richardson and R.L. Urbanke, "The capacity of low-density parity-check codes under message-passing decoding", IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 599-618, Feb. 2001.

• Other topics to be selected from, as time permits: Polar codes and Reed-Muller codes, erasure codes for distributed storage

The following books are recommended as references:

• R.M. Roth, Introduction to Coding Theory, Cambridge University Press, 2006. (An excellent textbook primarily covering block codes. Access to e-book is available courtesy of the IISc library.)

• T. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, 2008. (Focuses on LDPC and related codes. Access to e-book is available courtesy of the IISc library.)

• R. Johanneson and K.Sh. Zigangirov, Fundamentals of Convolutional Coding, IEEE Press, 1999. (Covers exactly what the title says.)

• S. Lin and D.J. Costello, Error Control Coding (2nd edition), Prentice-Hall, 2004. (A good introduction from the engineering perspective.)

• R.E. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, 2002. (This is an updated version of the original classic, now out of print, Theory and Practice of Error-Control Codes, Addison-Wesley, 1983.)

• F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North-Holland, 1977. (All you wanted to know about classical coding theory but were afraid to ask. An encyclopaedic reference.)

• E.R. Berlekamp, Algebraic coding theory, McGraw-Hill, 1968. Revised edition published by Aegean Park Press in 1984.

• W.C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003. (A good book from which to learn the basics. Written at an undergraduate level, assuming only knowledge of linear algebra.)

• R.J. McEliece, Theory of Information and Coding (2nd edition), Cambridge University Press, 2002. (A concise and well-written introduction to information and coding theory.)

• Vera Pless, Introduction to the Theory of Error-Correcting Codes (3rd edition), Wiley-Interscience, 1998. (A classic undergraduate text.)

• J.H. van Lint, Introduction to Coding Theory (3rd edition), Springer-Verlag (Graduate Texts in Mathematics), 1999. (Not really the most accessible introduction to the subject, but if you are comfortable with elementary abstract algebra and combinatorics, then it's a great book to read. Written for advanced undergraduates and graduate students in mathematics.)

The following online resources are likely to be useful:

• A video course on error-correcting codes taught by Prof. P. Vijay Kumar as part of the National Programme on Technology Enhanced Learning (NPTEL).
  [Lecture notes from the course]

• Another video course on coding theory taught by Prof. Andrew Thangaraj (IIT Madras), also on NPTEL.