Σε μία εποχή όπου η ψηφιοποίηση δεδομένων έχει αυξηθεί ραγδαία η ανάγκη για τη βέλτιστη μετάδοσή τους είναι απαραίτητη. Από τα πλέον σημαντικά μέρη των προτύπων μετάδοσης είναι η κωδικοποίηση του καναλιού μέσω ειδικών αλγορίθμων ώστε να επιτευχθεί η εύρεση και διόρθωση τυχών λαθών. Οι κώδικες Bose, Chaudhuri και Hocquenghem (BCH) είναι τέτοιου είδους κώδικες που χρησιμοποιούνται ευρέως σε εφαρμογές όπως τα CD, DVD, σκληροί δίσκοι, δίσκοι στερεάς κατάστασης (SSD) και το πρότυπο δορυφορικής μετάδοσης τηλεόρασης υψηλής ανάλυσης (HDTV), DVB-S2. Στην παρούσα διπλωματική εργασία σχεδιάστηκε και υλοποιήθηκε κωδικοποιητής και αποκωδικοποιητής BCH για τις 11 περιπτώσεις κανονικού πλαισίου που προσφέρει το πρότυπο DVB-S2. Κύριος στόχος ήταν η όσο το δυνατόν καλύτερη υλοποίηση με γνώμονα το μέγεθος, με τη χρήση κοινών κυκλωμάτων και για τις 11 περιπτώσεις. Αποτέλεσμα αυτής της βελτιστοποίησης μεγέθους, ήταν κάποιες τεχνικές βελτιστοποίησης της ταχύτητας αποκωδικοποίησης, όπως το shortening, να μη χρησιμοποιηθούν καθώς θα είχαν ως αποτέλεσμα την αύξηση της επιφάνειας μερών του αποκωδικοποιητή κατά περίπου 11 φορές. Καθώς σκοπός της διπλωματικής ήταν η μελέτη της απόδοσης των κωδίκων BCH, μελετήθηκε ο ρυθμός λαθών σε διάφορες τιμές της αναλογίας ενέργειας – θορύβου (Eb / N0 ), αφού πρώτα υλοποιήθηκε σε FPGA. / The amount of digital information is growing rapidly the recent decades, making transmission optimization one of the top priorities in digital information systems. One of the main parts of every transmission standard is channel encoding, with the use of algorithms aimed at finding and correcting errors (Forward Error Correction – FEC). Such codes are Bose, Chaudhuri and Hocquenghem (BCH) code, which are widely used in applications like CDs, DVDs, Hard Drives, Solid State Drives (SSDs) and DVB-S2, a satellite transmission standard mostly used for High Definition Television (HDTV). This thesis sets out to account for the design and implementation of a BCH encoder and decoder for all 11 different code rates proposed by the DVB-S2 standard for normal frames. The design was area optimized in order for all 11 code rate encoders and decoders to work on the same FPGA. This lead to some optimization techniques being unused. Even though the codes are shortened, no shortening algorithms which aim at clock cycle optimization were used. Were they used, would lead parts of the decoder to be almost 11 times larger. The main goal of the thesis is to analyze the performance of the codes, so the error rate was measured under different values of the energy to noise ratio (Eb/ N0 ).

Submitted by JOSIANE SANTOS DE OLIVEIRA (josianeso) on 2017-05-25T12:10:45Z No. of bitstreams: 1 Elcio Kondo_.pdf: 2605139 bytes, checksum: bc6eb6e69a381723f69fbce90af22fab (MD5) / Made available in DSpace on 2017-05-25T12:10:45Z (GMT). No. of bitstreams: 1 Elcio Kondo_.pdf: 2605139 bytes, checksum: bc6eb6e69a381723f69fbce90af22fab (MD5) Previous issue date: 2017-01-11 / Nenhuma / Atualmente vários equipamentos eletrônicos são equipados com memórias NAND Flash para armazenar dados. Essas memórias são controladas através de um circuito integrado com um controlador de memória, que internamente possui um sistema para garantir a integridade das informações armazenadas, os quais são conhecidos por Error Correction Codes (ECC). Os ECCs são códigos capazes de detectar e corrigir erros através de bits redundantes adicionados à informação. Normalmente, os códigos ECC são implementados em hardware dentro do controlador de memória NAND Flash. Neste trabalho comparou-se alguns códigos de ECC utilizados pela indústria, para as comparações utilizou-se os códigos ECC: Hamming, BCH (Bose-Chaudhuri-Hocquenghem) e Reed- Solomon. Sistematicamente realizou-se comparações entre os ECCs selecionados e escolheu-se os dois mais apropriados (BCH e Hamming), os quais foram implementados em linguagem VHDL, o que possibilitou identificar o código com melhor vantagem econômica no uso em memórias NAND Flash. / Nowadays several electronic equipment are using NAND Flash memories to store data. These memories are controlled by an integrated circuit with an memory controller embedded that internally has a system to ensure the integrity of the stored information, that are known as Error Correction Codes (ECC). The ECCs are codes that can detect and correct errors by redundant bits added to information. Usually the ECC codes are implemented on NAND Flash memory controller as a hardware block. On this text ECC codes used by industry, the Hamming code, BCH (Bose-Chaudhuri-Hocquenghem) and Reed-solomon codes were compared.Systemically compare between selected ECCs were done and selected two codes (BCH and Hamming), which were described in VHDL language and allowed to identify the best code with better economical advantage for NAND Flash memories.

Solutions to the problem of large peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems are proposed. Although the design of PAPR reduction codewords has been extensively studied and the existence of asymptotically good codes with low PAPR has been proved, still no reduced PAPR capacity achieving code has been constructed. This is the topic of the current thesis.This goal is achieved by implementing a time-frequency turbo block coded OFDM. In this scheme, we design the frequency domain component code to have a PAPR bounded by a small number. The time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity. Through comparative numerical evaluation we show that our method achieves considerable improvement in terms of PAPR with slight performance degradation compared to capacity achieving codes with similar block lengths. For the frequency domain component code, we used the realization of Golay sequences as cosets of the fi rst order Reed-Muller code and the modi cation of dual BCH code. A simple MAP decoding algorithm for the modi ed dual BCH code is also provided. Finally, we provide a flexible and practical scheme based on probabilistic approach to a PAPR problem. This approach decreases the PAPR without any signi cant performance loss and without any adverse impact or required change to the system. / Engineering and Applied Sciences

This thesis deals with the most recent passive optical network standard NG-PON2, describes the sublayer model which includes error correction coding during propagation in optical fibres. Assesses the impact of split ratios using the simulation environment created from defined model and compares various scenarios. Discusses possible sources of errors of simulation model in compare to real deployment.

No description available.

The Motorola Inc. paging protocol FLEX is discussed. The design and construction of a FLEX paging protocol decoder is discussed in detail. It proposes a decoding solution that includes a radio frequency (RF) receiver and a decoder board. The RF receiver will be briefly discussed. The decoder design is the main focus of this thesis as it transforms the RF frequency modulated (FM) data from the receiver and converts it to FLEX data words. The decoder is designed to handle bit sampling, bit clock synchronization, FLEX packet detection, and FLEX data word collection. The FLEX data words are then sent by the decoder to an external computer through a serial link for bit processing and storage. A FLEX transmitter will send randomly generated data so that a bit error rate (BER) calculation can be made at a PC. Each receiver'9s noise power and noise bandwidth will be measured so that noise spectral density may be calculated. A complete measurement set-up will be shown on how these noise measurements are made. The BER at a known power level is recorded. This enables Eb/No curves to be generated so that results of the decoding algorithm may be compared. This is performed on two different receivers. / Master of Science

Detta arbete är ett examensarbete i matematik på kandidatnivå vid Växjö universitet. Det är en studie av kodningsteori i allmänhet med fokusering på cykliska koder och Reed-Solomon-koder i synnerhet. Reed-Solomon-koderna används för att skapa McElieces kryptosystem. En kortfattad analys av McElieces kryptosystems säkerhet görs tillsammans med en genomgång av kända sätt att forcera denna typ av kryptosystem. Här visar det sig att användning av Reed-Solomon-kod försvagar kryptosystemet i förhållande till om den ursprungligt föreslagna Goppa-koden används. För att kunna göra denna säkerhetsanalys görs också en kortfattad genomgång av komplexitetsteori och vad det innebär att ett problem är NP-fullständigt. Nyckelord: Kodningsteori, Kodteori, Cykliska koder, BCH-koder, Reed-Solomon-koder, McElieces kryptosystem, Kryptering, Kodforcering, Komplexitetsteori, NP-fullständigt / This work is produced on bachelor level in mathematics at University of Växjö. It is a study of coding theory with focus on cyclic codes in general and Reed-Solomon codes in detail. Reed-Solomon codes are used for implementing McEliece's crypto system. A short analysis of McEliece's crypto system security is also made together with a description of some known ways to break this type of cryptosystem. It is shown that using Reed-Solomon codes weaken this cryptosystem compared to using the original supposed Goppa codes. The security analyse also need a short summary of complexity theory and what it means that a problem is NP-complete. Keywords: Coding theory, Cyclic codes, BCH codes, Reed-Solomon codes, McEliece's cryptography system, Cryptography, Code breaking, Complexity theory, NP-complete

<p>Detta arbete är ett examensarbete i matematik på kandidatnivå vid Växjö universitet. Det är en studie av kodningsteori i allmänhet med fokusering på cykliska koder och Reed-Solomon-koder i synnerhet. Reed-Solomon-koderna används för att skapa McElieces kryptosystem. En kortfattad analys av McElieces kryptosystems säkerhet görs tillsammans med en genomgång av kända sätt att forcera denna typ av kryptosystem. Här visar det sig att användning av Reed-Solomon-kod försvagar kryptosystemet i förhållande till om den ursprungligt föreslagna Goppa-koden används. För att kunna göra denna säkerhetsanalys görs också en kortfattad genomgång av komplexitetsteori och vad det innebär att ett problem är NP-fullständigt.</p><p><strong>Nyckelord: </strong>Kodningsteori, Kodteori, Cykliska koder, BCH-koder, Reed-Solomon-koder, McElieces kryptosystem, Kryptering, Kodforcering, Komplexitetsteori, NP-fullständigt</p> / <p>This work is produced on bachelor level in mathematics at University of Växjö. It is a study of coding theory with focus on cyclic codes in general and Reed-Solomon codes in detail. Reed-Solomon codes are used for implementing McEliece's crypto system. A short analysis of McEliece's crypto system security is also made together with a description of some known ways to break this type of cryptosystem. It is shown that using Reed-Solomon codes weaken this cryptosystem compared to using the original supposed Goppa codes. The security analyse also need a short summary of complexity theory and what it means that a problem is NP-complete.</p><p><strong>Keywords:</strong> Coding theory, Cyclic codes, BCH codes, Reed-Solomon codes, McEliece's cryptography system, Cryptography, Code breaking, Complexity theory, NP-complete</p>

Today’s society requires that transformation of information is done effectively and correctly. In other words, the received message must correspond to the message being sent. There are a lot of decoding methods to locate and correct errors. The main purpose in this degree project is to study one of these methods based on the Euclidean algorithm. Thereafter an example will be illustrated showing how the method is used when decoding a three - error correcting BCH code. To begin with, fundamental concepts about coding theory are introduced. Secondly, linear codes, cyclic codes and BCH codes - in that specific order - are explained before advancing to the decoding process. The results show that correcting one or two errors is relatively simple, but when three or more errors occur it becomes much more complicated. In that case, a specific method is required. / Dagens samhälle kräver att informationsöverföring sker på ett effektivt och korrekt sätt, det vill säga att den information som når mottagaren motsvarar den som skickades från början. Det finns många avkodningsmetoder för att lokalisera och rätta fel. Syftet i denna uppsats är att studera en av dessa, en som baseras på Euklides algoritm och därefter illustrera ett exempel på hur metoden används vid avkodning av en tre - rättande BCH - kod. Först ges en presentation av grunderna inom kodningsteorin. Sedan introduceras linjära koder, cykliska koder och BCH - koder i nämnd ordning, för att till sist presentera avkodningsprocessen. Det visar sig att det är relativt enkelt att rätta ett eller två fel, men när tre eller fler fel uppstår blir det betydligt mer komplicerat. Då krävs någon speciell metod.

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.