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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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Possibilities of Error Controls in Frequency hopping Stations
Pust, Radim ; Kovář, Pavel (referee) ; Wieser,, Vladimír (referee) ; Burda, Karel (advisor)
The doctoral thesis deals with design of coding for frequency hopping stations in band with intensive jamming. In digital modulations erroneous determination of the modulation state occurs due to jam at the receiver side. The result is erroneously transferred symbols of the message. Errors created during the transmission can be eliminated by using error control systems. It is also possible to prevent these errors by using algorithms (techniques) of frequency hopping which select the appropriate channel. Appropriate communication channel is a channel with a lower probability of erroneous symbol in the message. The main contribution of this thesis is to design a new frequency hopping technique with collision avoidance (FH/CA). The station with FH/CA technique measures signal levels in the considered several channels before every jump. Based on the measurements the most appropriate channel with the lowest value of measured signal level is selected. Therefore, it is more probable that a jump to an unoccupied channel with a transmission will occur. Using a mathematical model, the performance of the newly proposed FH/CA technique is compared with the currently used techniques FH and AFH. Comparison criteria are the probability of a collision between an FH/CA communication system and a static (device transmitting continuously at a fixed frequency) or dynamic jammer (i.e. other FH or AFH systems). By comparing the values of the probability of jammed transmission, indisputable theoretical advantages of the new FH/CA technique were found, compared to the currently used FH and AFH techniques. The FH/CA technique always has better or equal results compared with the FH technique in the case of interference by static and dynamic jammers. The FH/CA technique in a band with static and dynamic jammers usually has better results than the AFH technique. A significant contribution of the FH/CA technique can be seen in the case of dynamic jammers. On the other hand, in the case of static jammers the FH/CA technique is in certain situations worse than the AFH technique. The accuracy of the mathematical models were successfully verified on a simulation model that was created as a part of this thesis in the MATLAB environment. Based on the obtained data from the model there was designed coding for frequency hopping stations with the new technique of frequency hopping FH/CA which is designed for small-volume data transfer in a band with intensive jamming.
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Continued fractions in coding theory
Fišer, Jan ; Šťovíček, Jan (advisor) ; Holub, Štěpán (referee)
The first part of the thesis acquaints us with the Reed-Solomon codes, methods of their construction and encoding. At the same time we provide the evi- dence of their most important properties including the relevant theoretical basis. In the second chapter we introduce the theory of continued fractions over a field and examine their structure. Applying the executed general ob- servations on the specific case of the formal Laurent series we get to efficient Reed-Solomon decoding algorithm. Without complete proofs we also men- tion other two decoding algorithms that are based on solving the key equation as well, namely Berlekamp-Massey and Euclidean algorithm. In the end we show the equivalence of these three algorithms.
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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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Continued fractions in coding theory
Fišer, Jan ; Šťovíček, Jan (advisor) ; Holub, Štěpán (referee)
The first part of the thesis acquaints us with the Reed-Solomon codes, methods of their construction and encoding. At the same time we provide the evi- dence of their most important properties including the relevant theoretical basis. In the second chapter we introduce the theory of continued fractions over a field and examine their structure. Applying the executed general ob- servations on the specific case of the formal Laurent series we get to efficient Reed-Solomon decoding algorithm. Without complete proofs we also men- tion other two decoding algorithms that are based on solving the key equation as well, namely Berlekamp-Massey and Euclidean algorithm. In the end we show the equivalence of these three algorithms.
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|
|
Possibilities of Error Controls in Frequency hopping Stations
Pust, Radim ; Kovář, Pavel (referee) ; Wieser,, Vladimír (referee) ; Burda, Karel (advisor)
The doctoral thesis deals with design of coding for frequency hopping stations in band with intensive jamming. In digital modulations erroneous determination of the modulation state occurs due to jam at the receiver side. The result is erroneously transferred symbols of the message. Errors created during the transmission can be eliminated by using error control systems. It is also possible to prevent these errors by using algorithms (techniques) of frequency hopping which select the appropriate channel. Appropriate communication channel is a channel with a lower probability of erroneous symbol in the message. The main contribution of this thesis is to design a new frequency hopping technique with collision avoidance (FH/CA). The station with FH/CA technique measures signal levels in the considered several channels before every jump. Based on the measurements the most appropriate channel with the lowest value of measured signal level is selected. Therefore, it is more probable that a jump to an unoccupied channel with a transmission will occur. Using a mathematical model, the performance of the newly proposed FH/CA technique is compared with the currently used techniques FH and AFH. Comparison criteria are the probability of a collision between an FH/CA communication system and a static (device transmitting continuously at a fixed frequency) or dynamic jammer (i.e. other FH or AFH systems). By comparing the values of the probability of jammed transmission, indisputable theoretical advantages of the new FH/CA technique were found, compared to the currently used FH and AFH techniques. The FH/CA technique always has better or equal results compared with the FH technique in the case of interference by static and dynamic jammers. The FH/CA technique in a band with static and dynamic jammers usually has better results than the AFH technique. A significant contribution of the FH/CA technique can be seen in the case of dynamic jammers. On the other hand, in the case of static jammers the FH/CA technique is in certain situations worse than the AFH technique. The accuracy of the mathematical models were successfully verified on a simulation model that was created as a part of this thesis in the MATLAB environment. Based on the obtained data from the model there was designed coding for frequency hopping stations with the new technique of frequency hopping FH/CA which is designed for small-volume data transfer in a band with intensive jamming.
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