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Algorithms for decoding the Reed-Solomon error control code
Tieftrunk, Tomáš ; Číž, Radim (referee) ; Šilhavý, Pavel (advisor)
Thesis discuss about effort to ensure from error, which may occur during transmission over noisy channel. There's used Reed Solomon code. It's block, cyclic and systematic code, which is symbol orientated. Computational process of decoding is mathematically time-consuming. In thesis is closely described Berlekamp-Masey algorithm, used in decoding to evaluate error polynomial. Process is illustrated in application in Matlab. Practical realization uses Reed Solomon code in communication over RS232. Communication is established between computer and microcomputer.
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Implementation of Self-Correcting Codes for 100 Gb/s Ethernet
Velecký, Jan ; Kučera, Jan (referee) ; Kekely, Lukáš (advisor)
The thesis deals with the design of entire RS-FEC layer for the 100 Gb/s Ethernet according to IEEE 802.3-2015 standard including Reed-Solomon encoder and decoder. Text clarifies mathematical basis of finite fields, linear block codes, cyclic codes and particularly Reed-Solomon codes used in design. Design of RS-FEC layer transmit side has been adjusted for implementation in COMBO network cards which use Xilinx Virtex-7 FPGA and realized in VHDL. Encoder has been optimized in several steps - as for FPGA resource usage and as for VHDL code synthesis duration. Reduction of resource usage has been achieved by using pipelining thanks to properties of cyclic codes. Synthesis duration then by creating logic of encoder on gate level on its own. Resulting implementation has been tested in simulation and it is optimized enough for usage in FPGA for Ethernet implementation. It is possible to adapt both design and implementation for 400Gb/s Ethernet which does not exist yet at the time of design.
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Data transmition security with BCH codes
Frolka, Jakub ; Tejkal, Vladimír (referee) ; Němec, Karel (advisor)
The bachelor thesis Data transmission security with BCH codes deals with class of random error correction cyclic codes which are able to protect data in binary form. BCH codes operate over algebraic structures called Galois fields. Encoding of these codes is same as encoding cyclic codes and can be used cyclic shift register, but decoding is more complex and can be done with many algorithms, in this thesis are mention three: Peterson algorithm, Matrix method and Berlekamp-Massey algorithm. In this thesis are described characteristics BCH codes, their usage in communication devices and their posibility implementation. An example BCH code which is able to correct four independent errors is created. This example is used for presentation of encoding and decoding methods. In the end is described implementation of data protection codec for FGPA devices.
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Protection of data transmission against long error bursts
Malach, Roman ; Lambertová, Petra (referee) ; Němec, Karel (advisor)
This Master´s thesis discuses the protection of data transmission against long error bursts. The data is transmited throught the channel with defined error rate. Parameters of the channel are error-free interval 2000 bits and length of burst error 250 bits. One of the aims of this work is to make a set of possible methods for the realization of a system for data correction. The basic selection is made from most known codes. These codes are divided into several categories and then the best one is chosen for higher selection. Of course interleaving is used too. Only one code from each category can pass on to the higher level of the best code selection. At the end the codes are compared and the best three are simulated using the Matlab program to check correct function. From these three options, one is chosen as optimal regarding practical realization. Two options exist, hardware or software realization. The second one would seem more useful. The real codec is created in validator language C. Nowadays, considering language C and from a computer architecture point of view the 8 bits size of element unit is convenient. That´s why the code RS(255, 191), which works with 8 bits symbols, is optimal. In the next step the codec of this code is created containing the coder and decoder of the code above. The simulation of error channel is ensured by last program. Finally the results are presented using several examples.
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Barcode recognition system
Pribula, Wojciech ; Richter, Miloslav (referee) ; Petyovský, Petr (advisor)
This thesis describes barcodes which are used in postal services. Specifically, it is concerned with Intelligent Mail Barcode, the GS1-128 code, the C128 code of Ceska posta (Czech Postal Services) and the QR code. The thesis attempts to analyze methods of encoding information into barcodes and error detection algorithms used for error correction during the decoding processes. Most importantly, there is described Reed-Solomon error correction in the QR code. There are presented and evaluated different methods of code detecting which are suggested by authors of various academic articles. The thesis also describes the method of creating test sets of images and proposed appearances of the scanning scene. Additionally, there are described algorithms for detection and decoding barcodes GS1-128, C128 and IMB in the image which was created during the work on this thesis. Finally, there is the evaluation of the percentage success of algorithms.
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User Interface for Efficient Corrections of OCR Output
Szepsi, Pavol ; Kapinus, Michal (referee) ; Hradiš, Michal (advisor)
The aim of the present bachelor thesis was to design and implement a web user interface for checking and correcting OCR outputs which will be suitable for mobile and touchscreen devices. The user interface uses the OCR output variants that the user can use to modify the recognized text. The interface is implemented in JavaScript using the Vue JS framework. XAMPP package is used for the server part. The tool Axios is used for communication between the user interface and the server. The created interface allows users to quickly and easily correct the OCR outputs, either on a computer or on a mobile device.
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Error protection of data transmission using BCH Codes
Kašpar, Jaroslav ; Křivánek, Vítězslav (referee) ; Němec, Karel (advisor)
The thesis Data transmission error-protection with BCH codes deals with a large class of random-error correcting cyclic codes which are able to protect binary data and can be used for example in data storages, high speed modems. Bose, Chaudhuri and Hocquenghem (BCH) codes operate over algebraic structures called Galois fields. The BCH encoding is the same as cyclic encoding and can be done with linear feedback shift register but decoding is more complex and can be done with different algorithms - in this thesis there are two algorithms for decoding Peterson and Berlekam-Massey mentioned. The aim of this thesis is to find BCH code which is able to correct t = 6 independent errors in up to data sequence n = 150 bits, then peruse possible realizations of the codecs and set criteria for the best realization, then design and test this realization. This thesis is split into three main parts. In the first part there are encoding and decoding methods of the BCH code generally described. The second part deals with selecting of the right code and realization. There was chosen BCH (63,30) code and realization with FPGA chip. In the last part is described design of BCH encoder and decoder and compilation in the Altera design software.
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Determinants of the Residential Real Estate Prices in Selected EU Countries
Rákosníková, Andrea ; Hlaváček, Michal (advisor) ; Schwarz, Jiří (referee)
This thesis aims to identify the determinants of real housing prices in the 13 newest EU member states. Determinants were identified using individual time series and aggregate panel analyses to ensure the best results. Cointegrating relationships were confirmed through testing and factored into the choice of estimation methods. The time series regression was done using the VECM, and the same method was used to test the theory that the capitals are the price leaders in housing markets. Results revealed that this effect is limited to only some markets, particularly affecting Czechia and Slovakia. Panel analyses, done using the PDOLS and ECM, were used to examine determinants and the speed of convergence of variables to equilibrium. The results of the aggregate panel regression showed that numerous determinants, namely the construction prices, GDP, number of housing permits, rents, and population, affect housing prices significantly. However, area-specific panels and time series models highlighted significant variations in results across countries. For example, GDP is not a significant determinant in V4 countries, while its effect is vital for the Balkans. The most surprising results were observed for Cyprus and Malta, where the relationships between the prices and determinants seem to be distorted by...
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User Interface for Efficient Corrections of OCR Output
Szepsi, Pavol ; Kapinus, Michal (referee) ; Hradiš, Michal (advisor)
The aim of the present bachelor thesis was to design and implement a web user interface for checking and correcting OCR outputs which will be suitable for mobile and touchscreen devices. The user interface uses the OCR output variants that the user can use to modify the recognized text. The interface is implemented in JavaScript using the Vue JS framework. XAMPP package is used for the server part. The tool Axios is used for communication between the user interface and the server. The created interface allows users to quickly and easily correct the OCR outputs, either on a computer or on a mobile device.
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