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Burst error correction in digital transmissions using Berlekamp -Preparata codes
Pfudl, Tomáš ; Pfeifer, Václav (referee) ; Němec, Karel (advisor)
Bachelor's thesis discusses properties of the systematic convolution codes for error-bursts correction. Berlekamp-Preparata code is a member of this group. Thesis aims at detail description of this code and for picked code designs a codec. Properties discussed at the first part of thesis are used at the second part for picking the code and designing the codec. For designing there are used various methods (programming scripts, simulation model). Codec design is described from properties of communication channel to hardware realization. Each step is exactly interpreted. Whole theoretical design is made in Matlab and for designing the hardware there is used program Xilinx.
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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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Antierror systems with interleaving
Pacher, Jakub ; Zeman, Václav (referee) ; Němec, Karel (advisor)
This work involves in anti-error coding systems with interleaving. At first is given summary of high-frequency use error correction codes. Below there are described two basic techniques of interleaving and their confrontation. The next text is focusing on survey and characteristics of codes which conform to submission. After selection of optimal system is verified its function in MATLAB environment. Final step is creation of functional application in C++ environment. This application serves to transmission of error correction BMP pictures.
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An Encoder and Decoder of an Error-correction Code for Programmable Read-only Memories
Bareš, Jan ; Dvořák, Vojtěch (referee) ; Šťáva, Martin (advisor)
This work deals with theory of coding, analyses current groups of error correction codes and describes features and parametres of chosen representatives of these groups. By comparing these parametres along with given criteria it choses extended Hamming code as suitable code for securing read-only-memories (ROM). For this code it choses way of realization of synthetisable modules of coder and decoder and describes their design. The work describes design of synthetizable modules of coder and decoder in VHDL. Then it explains functionality of created application which is able to generate these synthetisable modules. For verification of generated modules it creates authentication environment. Part of this environment is also model of ROM allowing writing of any error value into the memory. In the end it automatically verifies generated modules of coder and decoder with various width of input information vector.
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Data transmition security with general linear block codes
Dzurenda, Petr ; Tejkal, Vladimír (referee) ; Němec, Karel (advisor)
This work deals with problematic basic characteristic common linear block codes, concretely with creation generating and controlling matrix and individual ways decoding common linear block codes and then are theoretic knowledge used in the next part bachelor’s thesis. Next part this work is bent on the concrete layout of common liner block code satisfactory specifications by submission. In this part it can by find way haw create generating matrix be able to correcting tree single errors then create control matrix for decoding and correct network for correcting errors. Programs are used in this work are explained there. In the end this part is example of coding and decoding. Lastly work is realization codec. In this part is description of coder and decoder realizations. This codec is simulating by program Matlab Simulink in part five. In last part are create boards of printed circuits by program Eagle for coder and decoder.
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Anti-Error Coding Systems with Block Codes
Pacher, Jakub ; Zezula, Radek (referee) ; Němec, Karel (advisor)
This work deals with selection and proven suitable error-correcting code securing aggregating errors. First we give analysis anti-error coding system and requirements rapid/fire at them. The next text is focusing on survey and characteristics often used codes, mainly Fire, Hamming and two BCHs codes. After an explanation of Hamming code use, the text describes verification of proper function anti-error system in the MathCad enviroment.
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Analysis of Computational Effort of Self-Correcting Codes
Bártů, Tomáš ; Drábek, Vladimír (referee) ; Bidlo, Michal (advisor)
The work deals with error-correcting codes, specifically encoding and decoding Reed-Solomon codes. An introduction to error-correcting codes is provided, followed by a description of the encoding and decoding principle of Reed-Solomon codes using the Petterson-Gorenstein-Zierler, Berlekamp-Massey, and Euclidean algorithms. Implementation is then described, which realizes some of the mentioned algorithms. This is followed by experiments with applications that compare the time and iteration complexity of the encoding and decoding processes.
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Projective geometry codes
Požárková, Zuzana ; Drápal, Aleš (advisor) ; Holub, Štěpán (referee)
In the presented work we define a class of error-correcting codes based on incidence vectors of projective geometries, including the necessary basis of coding theory and projective geometries. A detailed calculation is performed to show the dimension of these codes. In conclusion we concern ourselves with majority decoding. This work is a summary of the results of some known authors engaged in this field. We continue on some of these results and we present evidence of some of the statements, which have been proven differently by other authors.
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Expander codes
Calábková, Markéta ; Mareš, Martin (advisor) ; Hušek, Radek (referee)
Wherever information is transmitted we can find error-correcting codes. LDPC (low density parity check) codes are one of frequently used classes of codes and expander codes are promising members of this class. In this work, we explain what expander code are. We also show that expander codes simulta- neously have both asymptotically optimal parameters and linear-time encoding and decoding. Unfortunately, our constructions grant us codes, which are too big for regular use, for example for packet transmission. However, we believe that with better construction of expander graphs we will be able to construct short codes with significant practical applications. 1
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Projective geometry codes
Požárková, Zuzana ; Drápal, Aleš (advisor) ; Holub, Štěpán (referee)
In the presented work we define a class of error-correcting codes based on incidence vectors of projective geometries, including the necessary basis of coding theory and projective geometries. A detailed calculation is performed to show the dimension of these codes. In conclusion we concern ourselves with majority decoding. This work is a summary of the results of some known authors engaged in this field. We continue on some of these results and we present evidence of some of the statements, which have been proven differently by other authors.
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