1. Channel capacity: Basic example, capacity of the AWGN channel, the promise of channel capacity, basic facts of channel coding (threshold SNR, coding gain, bandwidth expansion), problems
2. Block-based coded transmission: HISO channel, Gaussian memoryless channel, HIHO channel, discrete memoryless channel, binary symmetric channel, optimum soft-input and hard-input block decoding (MAP, ML), optimum block decoding for the Gaussian memoryless channel and the discrete memoryless channel, problems
3. Fundamentals of block codes: Galois fields, Hamming weight and distance, Hamming spheres, repetition code, single parity check code, elementary modifications of block codes, minimum distance and bounded minimum distance decoding, error detection, erasure filling, burst errors, performance bounds (Singleton bound, Hamming bound, asymptotic performance bounds, capacity of the binary symmetric channel), problems
4. Linear block codes: Standard array, weight distribution and weight enumerator, error probability of the ML decoder, matrix description, dual code, syndrome, syndrome decoding, repetition code, single parity check code, Hamming codes, modifications and compositions of linear block codes (permutation, length and rate modifications, subfield-subcodes, product codes, interleaved codes, concatenated codes, turbo codes), problems
5. Fundamentals of cyclic block codes: Polynomials over GF(q), polynomial description, dual code, syndrome decoding, matrix description, shift-register circuits for encoding and decoding, problems
6. Primitive cyclic codes: Primitive elements and exponential representation, extension fields and splitting fields, primitive polynomials, defining set, cyclic redundancy check (CRC) codes, frequency-domain description, Reed-Solomon codes, BCH codes, problems
7. Convolutional codes: Elementary encoders, distance profile and free distance, weight distribution and weight enumerator, error probability of the ML decoder, truncation and termination, matrix description, syndrome, syndrome decoding, polynomial description, noncatastrophic encoders, trellis description, graph-searching decoders, Viterbi algorithm for hard-input and soft-input ML decoding, sequential decoding, trellis-coded modulation, problems
Lecture notes for this course are available at the "Graphischen Zentrum an der TU Wien", Wiedner Hauptstraße 8 - 10, 1040 Wien (EG, roter Bereich).
Shu Lin and D. J. Costello, Jr., Error Control Coding - Fundamentals and Applications. Pearson Prentice Hall, Upper Saddle River, NJ, 2004 R. E. Blahut, Algebraic Codes for Data Transmission. Cambridge University Press, Cambridge, UK, 2003 T. M. Cover and J. A. Thomas, Elements of Information Theory. Wiley, New York, 1991 R. G. Gallager, Information Theory and Reliable Communication. Wiley, New York, 1968
