Polar codes with a stepped boundary

We consider explicit polar constructions of blocklength $n\rightarrow\infty$ for the two extreme cases of code rates $R\rightarrow1$ and $R\rightarrow0.$ For code rates $R\rightarrow1,$ we design codes with complexity order of $n\log n$ in code construction, encoding, and decoding. These codes achieve the vanishing output bit error rates on the binary symmetric channels with any transition error probability $p\rightarrow 0$ and perform this task with a substantially smaller redundancy $(1-R)n$ than do other known high-rate codes, such as BCH codes or Reed-Muller (RM). We then extend our design to the low-rate codes that achieve the vanishing output error rates with the same complexity order of $n\log n$ and an asymptotically optimal code rate $R\rightarrow0$ for the case of $p\rightarrow1/2.$Comment: This article has been submitted to ISIT 201

CoCalc as a Learning Tool for Neural Network Simulation in the Special Course "Foundations of Mathematic Informatics"

The role of neural network modeling in the learning content of the special course "Foundations of Mathematical Informatics" was discussed. The course was developed for the students of technical universities - future IT-specialists and directed to breaking the gap between theoretic computer science and it's applied applications: software, system and computing engineering. CoCalc was justified as a learning tool of mathematical informatics in general and neural network modeling in particular. The elements of technique of using CoCalc at studying topic "Neural network and pattern recognition" of the special course "Foundations of Mathematic Informatics" are shown. The program code was presented in a CoffeeScript language, which implements the basic components of artificial neural network: neurons, synaptic connections, functions of activations (tangential, sigmoid, stepped) and their derivatives, methods of calculating the network's weights, etc. The features of the Kolmogorov-Arnold representation theorem application were discussed for determination the architecture of multilayer neural networks. The implementation of the disjunctive logical element and approximation of an arbitrary function using a three-layer neural network were given as an examples. According to the simulation results, a conclusion was made as for the limits of the use of constructed networks, in which they retain their adequacy. The framework topics of individual research of the artificial neural networks is proposed.Comment: 16 pages, 3 figures, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer (ICTERI, 2018

Fast Polarization for Processes with Memory

Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. Namely, previous works have not addressed fast polarization of the high entropy set under memory. We consider polar codes for processes with memory that are characterized by an underlying ergodic finite-state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both for the high and for the low entropy sets.Comment: 17 pages, 3 figures. Submitted to IEEE Transactions on Information Theor

CoCalc як засіб навчання нейромережевого моделювання в спецкурсі «Основи математичної інформатики»

Обговорено роль нейромережевого моделювання у змісті навчання спецкурсу «Основи математичної інформатики» для студентів технічних університетів – майбутніх фахівців з інформаційних технологій, спрямованого на подолання розриву між теоретичною інформатикою та її прикладними застосуваннями: програмною, системною та комп’ютерною інженерією. Обґрунтовано вибір CoCalc як засобу навчання основи математичної інформатики у цілому та нейромережевого моделювання зокрема. Наведено елементи методики використання CoCalc у навчанні теми «Нейронні мережі та розпізнавання образів» спецкурсу «Основи математичної інформатики». Наведено програмний код мовою CoffeeScript, що реалізує основні компоненти штучної нейронної мережі: нейрони, синаптичні з’єднання, функції активації (тангенціальна, сигмоїдальна, ступінчаста) та їх похідні, методи обчислення вагових коефіцієнтів мережі та ін. Обговорено особливості застосування теореми Колмогорова для визначення архітектури багатошарових нейронних мереж. Подано приклади реалізації диз’юнктивного логічного елементу та апроксимації довільної функції з використанням тришарової нейронної мережі. За результатами моделювання зроблено висновок про межі застосування побудованих мереж, в яких вони зберігають адекватність. Запропоновано рамкову тематику індивідуальних навчально-дослідних проектів із побудови штучних нейронних мереж.The role of neural network modeling in the learning сontent of special course “Foundations of Mathematic Informatics” was discussed. The course was developed for the students of technical universities – future IT-specialists and directed to breaking the gap between theoretic computer science and it’s applied applications: software, system and computing engineering. CoCalc was justified as a learning tool of mathematical informatics in general and neural network modeling in particular. The elements of technique of using CoCalc at studying topic “Neural network and pattern recognition” of the special course “Foundations of Mathematic Informatics” are shown. The program code was presented in a CofeeScript language, which implements the basic components of artificial neural network: neurons, synaptic connections, functions of activations (tangential, sigmoid, stepped) and their derivatives, methods of calculating the network`s weights, etc. The features of the Kolmogorov–Arnold representation theorem application were discussed for determination the architecture of multilayer neural networks. The implementation of the disjunctive logical element and approximation of an arbitrary function using a three-layer neural network were given as an examples. According to the simulation results, a conclusion was made as for the limits of the use of constructed networks, in which they retain their adequacy. The framework topics of individual research of the artificial neural networks is proposed

Conceptual mechanization studies for a horizon definition spacecraft communications and data handling subsystem

Conceptual mechanization for horizon definition spacecraft communications and data handling subsyste

Space programs summary no. 37-62, volume 2 for the period 1 January - 28 February 1970. The Deep Space Network

Deep Space Network operations revie

High Speed S-band Communications System for Nanosatellites

3Cat-3 is a nanosatellite based on the 6 unit cubesat standard. Its payload is an optical multispectral imager that imposes stringent downlink requirements for a nanosatellite. This TFG is based on the experience gained in 3Cat-1 and 3Cat-2 communications systems to develop a "high speed" (goal >= 5 Mbps) downlink for nanosatellites based on the TI CC3200.In order to accomplish the objectives of the next generation of nanosatellites high-speed downlinks have to be designed. This goal faces stringent design constraints as nanosatellites are limit in power, processing capabilities and dimensions. In the quest for higher bit rates the widely used VHF band has to be replaced for higher frequency bands and the link budged margin tightened, decreasing the SNR at reception. The proposed solution uses COTS 2.4 GHz WiFi adapters as transceivers. Range limitations imposed by the default 802.11 mode of operation are bypassed by using packet forging and injection at transmission jointly with monitor mode at reception. A loss-resilient unidirectional downlink is achieved by using application-layer encoding by means of LPDC-Staircase codes. This solution has been already implemented in 3CAT-2, a 6 unit cubesat GNSS-R mission to be launched in July 2016. In addition, bursts of errors are combated by using Reed-Solomon. The system has been tested under Doppler shift and scintillation effects, and a 188Km link between Barcelona and Mallorca has been performed, showing satisfactory results

Sequence codes

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