Subject Code:  EC6L029

Name:  Advanced Coding Theory

L-T-P: 3-0-0

Credit: 3

Binary symmetric channels, erasure channel, introduction to linear codes and error correcting codes. Encoding and decoding of a linear code, dual codes, hard decision decoding, syndrome decoding. Gaussian channels, soft decision decoding, bitwise map decoder. Convolutional codes, Trellis representation, Viterbi decoder, recursive convolutional codes, Turbo Codes, Turbo Decoders, EXIT charts. Low Density Parity Check (LDPC) Codes, Definition and construction, degree distributions, regular and irregular ensembles, Hard and soft message-passing decoders, density evolution, Protograph LDPC Codes, Minsum iterative message passing decoder, Layered message passing decoder. Polar Codes, Definition and construction, Encoding of polar codes, Successive cancellation decoder, Upper bound on probability of error, List decoding, Capacity-approaching property of polar codes, Error exponent, finite length scaling, non-binary codes. Fountain Codes, Definition and construction of LT codes. and Raptor codes, systematic Raptor codes, Gaussian-elimination decoding, ~elief-propagation decoding, inactivation decoding, standardized Raptor codes.

Text Books:
  1. T. Richardson and R. Urbanke, "Modern Coding Theory", Cambridge University Press 2008, ISBN-13: 978-0-521-16576-1
  2. S. Lin and D. J. Costello, "Error Control Coding," 2nd Ed., Pearson Prentice Hall, 200.ยข, ISBN13: 978-0130426727.
  3. R. Johannesen and K. Sh. Zigangirov, "Fundamentals of Convolutional Coding", Wiley-IEEE Press, 1999, Print ISBN: 9780780334830
  4. E. Sasoglu, "Polarization and Polar codes", Foundations and Trends in Communications and Information Theory Vol:8, No:4, pp. 259-381, 2012, ISBN: 978-1-60198-596-5
  5. W. Ryan and S. Lin, "Channel codes, Classical and Modern", Cambridge University Press 2009, ISBN-13 978-0-521-84868-8.
  6. R.M. Roth, "Introduction to Coding Theory", Cambridge University Press, 2006, ISBN-13 978-0521-84868-8

Reference Books:

  1. Robert G. Gallager "Low Density Parity-Check Codes", MIT Press, 2003, ISBN: 9780262571777.
  2. E. Arikan, "Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels," IEEE Tr
  3. F.J. MacWilliams and N.J.A. Sloane, "The Theory of Error-Correcting Codes", Elsevier/NorthHolland, 1977, Hardcover ISBN: 9780444851932.
  4. Ian F. Blake, Ronald C. Mullin, "The Mathematical Theory of Coding", Academic Press Inc., 1975, ISBN: 01210355006.~
  5. D. J. C. MacKay, "Fountain codes," in lEE Proceedings- Communications, vol. 152, no. 6, pp. 1062-1068,2005, doi: 10.1049/ip-com:20050237.
  6. M. Luby, "LT codes," The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proc., Vancouver, BC, 2002, pp. 271-280, doi: 10.1109/SFCS.2002.1181950.