After successful completion of the course, students are able to: (1) know and understand the most important techniques for channel coding, especially regarding their properties, advantages, and limitations; (2) solve relevant problems.

1. Fundamentals of block codes:  Galois fields, 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

2. Linear block codes:  Linearity, minimal distance, 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, serially concatenated codes, turbo codes), problems

3. Cyclic block codes:  Polynomial description, dual code, syndrome decoding, matrix description, shift-register circuits for encoding and decoding, primitive cyclic codes, defining set, cyclic redundancy check (CRC) codes, frequency-domain description, Reed-Solomon codes, BCH codes, problems

4. 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

5. Turbo codes:  Encoder, elementary parameters, BER performance, weight distribution and spectral thinning, interleaver, L-values, iterative turbo decoding algorithm, BCJR algorithm, max-log-MAP algorithm, EXIT chart, problems 

6. LDPC codes:  Definition and properties of LDPC codes, regular and irregular LDPC codes, Tanner graph, encoding, some constructions of LDPC codes, repeat-accumulate codes, iterative decoding (bit-flipping algorithm, factor graph, belief propagation-based algorithms), problems

Appendix:  Mathematical fundamentals:  Galois fields, Hamming weight and Hamming distance, Hamming spheres, standard array, polynomials over GF(q), primitive elements and exponential representation, extension fields and splitting fields, primitive polynomials, DFT over GF(q), problems

The prof (Hlawatsch) verbally presents the class material, discusses the material with his students, and answers the students' questions. For this, he uses a blackboard, on which he writes certain characters and draws simple figures with of a piece of chalk (also using different colors if helpful). He also uses a tablecloth to erase the board every now and then. Finally, he uses an overhead projector to project more complicated figures and tables on a screen. The prof's presentation is supported by detailed lecture notes. In the exercise section, students present and explain relevant exercise problems to the audience; in addition, they have to hand in their own solutions of "compulsory problems" to the teaching assistant before the respective exercise unit. Students are required to personally participate in the exercise units.

First class: Mon., October 5, 2020, 10:45 - 12:00, EI 6 Eckert

Because of the limited capacity of the classroom, the first class (on October 5) will be additionally offered in distance mode. The subsequent classes will be held only in presence mode (if possible). The exercises will be held in distance mode.

Exam consists of written and oral parts. Active participation in the Exercise section is required. Grading mode and previous exam problems: see https://www.nt.tuwien.ac.at/teaching/courses-winter-term/digital-communications-2/

Registration for the Exercises is required --> during the first exercise unit. Personal attendance during the exercise units is required.

Early October, lecture notes for this course will become available at Grafisches Zentrum der TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna. For complementary literature see the lecture notes for Digital Communications 1.

A sound knowledge of random variables and random vectors is an absolute prerequisite