Course Content
Linear block codes : systematic linear codes and optimum decoding for the binary symmetric channel. The generator and parity check matrices, syndrome decoding on symmetric channels, Hamming codes, weight enumerators and the MacWilliams indentities, perfect codes. Introduction to finite fields and finite rings, factorization of Pn - l over a finite field. Cyclic Codes. BCH codes, idempotents and Mattson-Solomon polynomials, Reed-Solomon codes, Justeen codes, MDS codes, Alterant, Goppa and generalized BCH codes, spectral properties of cyclic codes. Decoding of BCH codes, Berlekamp"s decoding algorithm, Massey"s minimum shift register synthesis technique and its relation to Berlekamp"s algorithm. A fast Berlekamp Massey algorithm. Convolution codes, Wozencraft"s sequential decoding algorithm, Fann"s algorithm and other sequential decoding algorithms, Viterbi decoding algorithm.
Text / References
- 1 F.J. MacWilliams and N.J.A. Slone, The theory of error correcting codes, North Holland, 1977. R.E. Balahut, Theory and practice of error control codes, Addison Wesley, 1983.