Info
Lecturer: Boris Kudryashov
Language: English
Lecture: Delta, 1025, Monday 14:15 - 16:00, weeks 24-35, 37-39
Practice session: Delta, 2035, Tuesday 16:15 - 18:00, weeks 24-39
Office hours for homework discussions: Delta, 3089, Friday, 11:15 - 13:00, weeks 24-39
Books for the course:
Djordjevic, Ivan, William Ryan, and Bane Vasic. Coding for optical channels. Springer Science & Business Media, 2010.
Declercq D, Fossorier M, Biglieri E. Channel Coding: Theory, Algorithms, and Applications: Academic Press Library in Mobile and Wireless Communications. Academic Press; 2014 Jul 29.
Contact:
Boris Kudryashov (boriskud@ut.ee)
Vitaly Skachek
General information
This course is primarily intended for Bachelor's level students and is recommended for Master's students with an interest in modern data communications.
In the course, we will answer the questions
- why do the data rates in communications systems grow so fast?
- why, nevertheless. huge amounts of data are delivered so reliably?
The progress in the technology of generating signals in the optic range of frequencies and in manufacturing the delivering media is an important necessary condition for providing huge data rates. However, the less time/space resources allocated for each bit of information, the higher probability that unavoidable channel noise will destroy some parts of sent messages. Thus, the larger the bit rate, the larger the portion of erroneously received signals at the channel output.
Information Theory and the Theory of Error-correcting codes provide a solid background for developing reliable communication systems. Shannon's information theory theorems show theoretical limits of achievable performance, and the theory of error-correcting codes suggests a wide choice of efficient practical encoding and decoding schemes. The goal of the course is to study the theory and methods suitable for the specific case of super-fast communications.
The following restrictions should be taken into account:
- specific restrictions on the signal sets suitable for fiber-optic channels
- efficiency of using channel resources (energy and bandwidth) should be close to the theoretical limits
- complexity (delays and amount of computations per transmitted data bit) for high-speed communication cannot be large.
Thus, we are targeting very efficient and very simple coding schemes.
Contents
Lectures and practice sessions?
| N | Lecture | Practice session |
|---|---|---|
| 1 | Physical media. Limitations: signal-to-noise-ratio, bandwidth, etc. | Performances of uncoded transmission |
| 2 | From symbols to signals: Modulation techniques. | Arithmetics over finite alphabets. Hamming distance vs Euclidean distance |
| 3 | Linear space and its dual space. Linear codes. | Generator and parity-check matrices. Code examples |
| 4 | Basics of optimal decoding. Graph representations of linear codes. | Simulation of maximum-likelihood (ML) decoding. Trellis representation examples. Viterbi algorithm. |
| 5 | SISO decoding. BCJR algorithm. Suboptimal decoding | Examples and implementation issues. Simulations. |
| 6 | Convolutional codes. | Free distance and weight enumerators |
| 7 | Connections between the block and convolutional codes. Tailbiting codes. | Optimal decoding of terminated convolutional codes |
| 8 | Approaching the Shannon limits: Coding gain, bounds on error correcting performance | Computing theoretical limits. Estimating performances of error-correcting codes. |
| 9 | Concatenated codes | Concatenated codes constructions |
| 10 | Turbo-codes | Examples. Simulations |
| 11 | Low-density parity-check codes (LDPC) | Tanner graph, girth, lifting |
| 12 | Belief-propagation decoding | Implementation, simulations |
| 13 | Nonbinary and generalized LDPC codes | Implementation of arithmetic over finite field |
| 14 | Shaping | Implementation issues |
| 15 | Inter-symbol interference (ISI). Analysis. Mitigation | Example solutions for ISI channels |
| 16 | Communication standards: DVB, ATSC, 5G, etc. | Simulations. Demos. |
| Topic | Content | Start (Date) | Deadline (Date) |
| Coded modulation | Combine QAM modulation with a simple linear code. Compare efficiency with uncoded transmission | 01.03.2023 | 03.04.2023 |
| ML and MAP decoding | Choose a code with low trellis complexity. Simulate the Viterbi and the BCJR algorithms. Apply to concatenated construction. | 04.04.2023 | 02.05.2023 |
| LDPC codes with BP decoding | For predetermined restrictions on the code length and the code rate simulate LDPC coding with BP decoding and compare with previously considered scenarios. | 03.05.2023 | 21.05.2023 |
Schedule:
Lecture Monday 14.15 - 16.00 weeks (24-39), Delta, 1004
Practical session Monday 16.15 - 18.00 week (24-39) Delta, 1004
Office hours, Friday 11:15, week (24-39) Delta, 3089