Error Correcting Codes

Contents

Fields, vector spaces, linear block codes, error detection and correction, bounds on code parameters, maximum-likelihood decoding, dual codes, standard array decoding. Finite fields construction and properties, Reed-Solomon codes. Cyclic codes, BCH codes, Fourier transform characterization, encoding and decoding of BCH codes. Convolutional codes, trellis representation, Viterbi decoding, catastrophic encoders. Low density parity-check codes, message-passing decoding, density evolution. Other topics to be chosen from (time permitting): Polar codes, Reed-Muller codes, lattice codes.

Textbooks and references:
\begin{itemize}
\item R. Roth, Introduction to Coding Theory, Cambridge University Press, 2007
\item W.E. Ryan and S. Lin, Channel Codes: Classical and Modern, Cambridge University Press, 2009.
\item S. Lin and D.J. Costello, Error Control Coding, Pearson, 2011
\item R.E. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, 2003
\item F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland Publishing Company, 1977
\item W.C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003
\item J.G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 2008
\end{itemize}

References

1. R. Roth, Introduction to Coding Theory, Cambridge University Press, 2007
2. W.E. Ryan and S. Lin, Channel Codes: Classical and Modern, Cambridge University Press, 2009.
3. S. Lin and D.J. Costello, Error Control Coding, Pearson, 2011
4. R.E. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, 2003
5. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland Publishing Company, 1977
6.W.C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003
7. J.G. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 2008