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LDPC codes
Hrouza, Ondřej ; Šedý, Jakub (referee) ; Šilhavý, Pavel (advisor)
The aim of this thesis are problematics about LDPC codes. There are described metods to create parity check matrix, where are important structured metods using finite geometry: Euclidean geometry and projectice geometry. Next area in this thesis is decoding LDPC codes. There are presented four metods: Hard-Decision algorithm, Bit-Flipping algorithm, The Sum-Product algorithm and Log Likelihood algorithm, where is mainly focused on iterative decoding methods. Practical output of this work is program LDPC codes created in environment Matlab. The program is divided to two parts -- Practise LDPC codes and Simulation LDPC codes. The result reached by program Simulation LDPC codes is used to create a comparison of creating and decoding methods LDPC codes. For comparison of decoding methods LDPC codes were used BER characteristics and time dependence each method on various parameters LDPC code (number of iteration or size of parity matrix).
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Parametric Geometry Sketch Tool
Vala, Jan ; Zahrádka, Jiří (referee) ; Zemčík, Pavel (advisor)
Purpose of this Bachelor's thesis is the design and implementation of Parametric geometry sketch tool. This thesis also includes basic terms of dynamic geometry. Summary of the state of the art, description of existing tools, followed by evaluation of their features. Results and possibilites of future expansion are summarized in the last chapter.
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Non-Euclidean geometry for secondary schools
Miháliková, Lucia ; Dvořák, Petr (advisor) ; Zhouf, Jaroslav (referee)
The aim is appropriate elaboration of the subject non-Euclidean geometry to high school. The work includes historical introduction that de- scribes the path to the discovery of non-Euclidean geometry. Introduction is focused on failed proof attempts of the fifth Euclidean postulate, as well as errors in them which mathematicians committed. Work continues with list of sentences that are equivalent to the fifth postulate and focuses on different ways of partitioning the geometry in the literature, and clarifying the place of non-Euclidean geometry in these distributions. The work also demonstra- tes the use of non-Euclidean geometry in everyday life. The important part is the introduction of the primary notion of non-Euclidean geometry using three-dimensional models of this geometry. Aim of thesis is to show the rea- der which ways we can use to approach geometry, what are the advantages and disadvantages of these methods. The last section is devoted to practical work with non-Euclidean geometry. For this purpose, appropriate mathemati- cal model of this geometry was chosen, easy to operate even with the help of mathematical software often used for teaching in high school. Keywords: Non-Euclidean geometry, geometry of Lobachevsky, Euclidean geometry, 5. axiom of Euclid, Beltrami-Klein model 1
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Non-Euclidean geometry for secondary schools
Miháliková, Lucia ; Dvořák, Petr (advisor) ; Zhouf, Jaroslav (referee)
The aim is appropriate elaboration of the subject non-Euclidean geometry to high school. The work includes historical introduction that de- scribes the path to the discovery of non-Euclidean geometry. Introduction is focused on failed proof attempts of the fifth Euclidean postulate, as well as errors in them which mathematicians committed. Work continues with list of sentences that are equivalent to the fifth postulate and focuses on different ways of partitioning the geometry in the literature, and clarifying the place of non-Euclidean geometry in these distributions. The work also demonstra- tes the use of non-Euclidean geometry in everyday life. The important part is the introduction of the primary notion of non-Euclidean geometry using three-dimensional models of this geometry. Aim of thesis is to show the rea- der which ways we can use to approach geometry, what are the advantages and disadvantages of these methods. The last section is devoted to practical work with non-Euclidean geometry. For this purpose, appropriate mathemati- cal model of this geometry was chosen, easy to operate even with the help of mathematical software often used for teaching in high school. Keywords: Non-Euclidean geometry, geometry of Lobachevsky, Euclidean geometry, 5. axiom of Euclid, Beltrami-Klein model 1
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Parametric Geometry Sketch Tool
Vala, Jan ; Zahrádka, Jiří (referee) ; Zemčík, Pavel (advisor)
Purpose of this Bachelor's thesis is the design and implementation of Parametric geometry sketch tool. This thesis also includes basic terms of dynamic geometry. Summary of the state of the art, description of existing tools, followed by evaluation of their features. Results and possibilites of future expansion are summarized in the last chapter.
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LDPC codes
Hrouza, Ondřej ; Šedý, Jakub (referee) ; Šilhavý, Pavel (advisor)
The aim of this thesis are problematics about LDPC codes. There are described metods to create parity check matrix, where are important structured metods using finite geometry: Euclidean geometry and projectice geometry. Next area in this thesis is decoding LDPC codes. There are presented four metods: Hard-Decision algorithm, Bit-Flipping algorithm, The Sum-Product algorithm and Log Likelihood algorithm, where is mainly focused on iterative decoding methods. Practical output of this work is program LDPC codes created in environment Matlab. The program is divided to two parts -- Practise LDPC codes and Simulation LDPC codes. The result reached by program Simulation LDPC codes is used to create a comparison of creating and decoding methods LDPC codes. For comparison of decoding methods LDPC codes were used BER characteristics and time dependence each method on various parameters LDPC code (number of iteration or size of parity matrix).
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