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 "mandatory problems" to the teaching assistant before the respective exercise unit. Students are required to personally participate in the exercise units.

First class: Mon., October 3, 2022, 10:45 - 12:00. The course will take place in presence mode in seminar room 389 (CG0118).

Exercise section: There will be 6-8 exercise units per semester taking place at the lecture’s scheduled time and place. The dates of the exercise units will be announced in TISS at least one week in advance. Attendance of the exercise units is mandatory (one no-show allowed).

At the beginning of each exercise unit, the solutions for two mandatory problems have to be handed in. By presenting solutions on the blackboard, students can earn up to 20 credits during the entire semester. The number of credits earned for a presentation depends on the difficulty of the problem and the quality of the presentation and solution. A collection of possible exercise problems can be found in the lecture notes. The specific problems (including the mandatory problems) for each exercise unit will be announced on in TISS at least one week in advance.

Admittance to the written exam:

In order to be admitted to the written exam, the following conditions must be fulfilled:  

– At least 10 credits have been earned by presenting problems to the class.

– All mandatory problems have been handed in (2 incomplete mandatory problems and 1 “no-show” are permitted).

Written exam:

At the written exam, which consists of 4 problems, up to 80 credits can be earned. A calculator and a collection of mathematical formulas are permitted to be used in the exam. Lecture notes will be provided by the exam supervisors. To check for dates and register for an exam use TISS.

Admittance to the oral exam:

To be admitted to the oral exam, at least 40 credits must be earned at the written exam. Under this condition, the credits of the written exam are added to those of the exercise units, and an intermediate grade is obtained as follows:

The final grade depends on the intermediate grade and the oral exam.

The exam consists of written and oral parts. Active participation in the Exercise section 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