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BCH codes
Frolka, Jakub ; Šilhavý, Pavel (referee) ; Šedý, Jakub (advisor)
The work deals with data security using BCH codes. In the work are described BCH codes in binary and non-binary form, and their most important subclass RS codes. Furthermore, this work describes the method of decoding Peterson-Gorenstein-Zierl, Berlekamp- Massey and Euclidean algorithm. For the presentation of encoding and decoding process, the application was created in Matlab, which has two parts – Learning BCH codes and Simulation of BCH codes. Using the generated application performance of BCH codes was compared at the last part of the work.
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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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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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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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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 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.
|
|
|
BCH codes
Frolka, Jakub ; Šilhavý, Pavel (referee) ; Šedý, Jakub (advisor)
The work deals with data security using BCH codes. In the work are described BCH codes in binary and non-binary form, and their most important subclass RS codes. Furthermore, this work describes the method of decoding Peterson-Gorenstein-Zierl, Berlekamp- Massey and Euclidean algorithm. For the presentation of encoding and decoding process, the application was created in Matlab, which has two parts – Learning BCH codes and Simulation of BCH codes. Using the generated application performance of BCH codes was compared at the last part of the work.
|
|
|
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.
|
|
|
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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