D.Ing. / In this study we consider the application of Reed-Solomon codes on two distinct channels. The first channel is the packet erasure channel, where packets are either received errorfree,or packets are lost. The second channel is the power line channel where additive Gaussian noise,, impulsive noise and narrowband noise are encountered In this thesis we focus on M-FSK modulation for the power line channel. For the packet erasure channel,we develop two new erasures-only decoders .The distinction between the two decoders is that the one is optimized for burst erasure correction, while the second decoder is optimized for random erasure correction.It is found that for single burst erasures, or bursterasures contained within n - k elements (where n is the code length and k is the number of information elements to be encoded), the best performance is obtained with the burst erasure decoder. When used in conjunction with a modified interleaver found in the literature, the developed random erasure decoder yields the best all-round performance. The main contribution to the power line channel is the development of a combined demodulation and decoding strategy to detect narrowband interference When standard Reed-Solomon codes operate in a channel where narrowband interference is present, undetected errors result. With the proposed decoding strategy it is found that wideband noise (a generalization of impulsive noise) affects the performance more negatively than narrowband noise for M-FSK modulation. .

Reliable communication is an important part of everyday living. When transmitting a message over a physical channel, noise is introduced that causes errors in the message. These errors can be inversion errors or synchronization errors. The aim of this thesis is to investigate coding techniques to minimise the effect of synchronization errors that occurred in a transmitted message. Watermarks are inserted into the encoded sequence. A neural network system is implemented before the decoder to detect the watermark and regain synchronization. / Prof. H. C. Ferreira

Thesis discuss about effort to ensure from error, which may occur during transmission over noisy channel. There's used Reed Solomon code. It's block, cyclic and systematic code, which is symbol orientated. Computational process of decoding is mathematically time-consuming. In thesis is closely described Berlekamp-Masey algorithm, used in decoding to evaluate error polynomial. Process is illustrated in application in Matlab. Practical realization uses Reed Solomon code in communication over RS232. Communication is established between computer and microcomputer.

The theme of this thesis is simulation of DVB-C2 transmission. The first part of this thesis is focused mainly on theory, where it describes differences between digital and analog television transmission. The project also explains principle of operation DVB-C and DVB-C2 systems with focus on channel coding a modulation. Application for simulation of DVB-C2 transmission, which is developed in the MATLAB environment is described in the second part. The last part of this thesis includes results of simulations of DVB-C2 transmission and their comparison with measured values of DVB-C transmission.

This work presents an energy efficient adaptive error correction system utilizing the Reed-Solomon errors-and-erasures algorithm, targeted to an Altera Stratix FPGA device. The system adapts to changing channel conditions by reconfiguring the system with different decoders to allow for the lowest possible energy consumption rate that the current channel conditions will allow. A series of energy saving optimizations were applied to a set of previous designs, resulting in a reduction in the energy required to decode a megabit of data of more than 70%. In addition, a new channel model was used to assess the effects of differing reconfiguration rates on codeword error rate, energy consumption, and decoding speed.

Cellular Digital Packet Data (CDPD) is a new wireless packet data communications system which was developed by a consortium of U.S. cellular service providers to augment their voice communications systems. The main goal of the CDPD system design was to provide wireless packet data connectivity to mobile data communications customers. This thesis presents fundamental information required to successfully implement CDPD base station or mobile equipment. This information includes an introduction to the operation of data networks, a discussion of Gaussian Filtered Minimum Shift Keying (GMSK), and a detailed analysis of Reed-Solomon error correction codes. / Master of Science

Cellular digital packet data (CDPD) is a new service for wide-area data communication with wireless mobile users. CDPD system uses the existing infrastructure of the analog Advanced Mobile Phone Service (AMPS) cellular telephone network to transmit data with a channel hopping technique. The CDPD system employs Gaussian minimum shift keying (GMSK) as a modulation scheme and a Reed-Solomon code for error control to transmit high-quality data in the mobile and wireless environment. Most current CDPD receivers use errors only decoding of the Reed-Solomon code, although an improved errors and erasures decoding technique would also be possible. This thesis undertakes a performance evaluation of the CDPD system with an errors and erasures decoder for the Reed-Solomon coding. A thorough system simulation is conducted for both white Gaussian noise and flat Rayleigh fading channel environments. Results show that improved coding gains of 0.5 ~ 1 dB are possible for the additive white Gaussian noise channel and improved coding gains of 1.9 ~ 2.7 dB are possible for the fading channel. / Master of Science

Este trabalho investiga a decodificação turbo de códigos produto construídos a partir de códigos de Reed-Solomon sobre constelações QAM. Por meio da geometria euclidiana da constelação utilizada e das relações dos elementos de campo de Galois utilizados na codificação Reed-Solomon com os símbolos pertencentes ao alfabeto de modulação, é proposto um algoritmo de decodificação que utiliza a localização geométrica dos símbolos recebidos no processo de decodificação turbo. Tanto a primeira etapa da decodificação SISO baseada no algoritmo de Chase, como a extração da informação extrínseca baseada no algoritmo proposto por Pyndiah, são tratadas pelo uso de uma abordagem geométrica sobre o espaço euclidiano. Os resultados de simulação utilizando o algoritmo proposto coincidem com aqueles usando a decomposição e análise pragmática binária, sendo que a abordagem apresentada conduz a simplificações e otimizações em relação à metodologia binária no que ser refere à implementação dos possíveis esquemas de decodificação. / This work investigates the turbo decoding of product codes built using Reed- Solomon codes in QAM constellations. Using the euclidian geometry of the constellation and the relations of the Galois field elements used in the Reed-Solomon code and the modulation alphabet, a decoding algorithm for the turbo decoding process is proposed using the geometric localization of the received symbol. Both the first stage of the SISO decoding based on the Chase algorithm, as the calculation of the extrinsic information based on the Pyndiah algorithm, are treated using the geometric approach in the euclidian space. The simulations show that this algorithm gives similar performance results as the pragmatic binary decomposition approach, and leads to simplifications and optimizations in decoding implementations schemes compared to the former.

Η εργασία αφορά ένα ειδικό είδος κωδικοποίησης εντοπισμού και διόρθωσης λαθών, την κωδικοποίση Reed-Solomon. Οι κώδικες αυτού του είδους χρησιμοποιούνται σε τηλεπικοινωνιακές εφαρμογές (ενσύρματη τηλεφωνία, ψηφιακή τηλεόραση, ευρυζωνικές ασύρματες επικοινωνίες) και σε συστήματα ψηφιακής αποθήκευσης (οπτικοί, μαγνητικοί δίσκοι). Η κωδικοποίηση Reed-Solomon βασίζεται σε μία ειδική κατηγορία αριθμητικών πεδίων τα πεδία Galois (Galois Field). Στα πλαίσια της εργασίας πραγματοποιήθηκε μελέτη των ιδιοτήτων των πεδίων Galois. και σχεδιάστηκε κωδικοποιητής-αποκωδικοποιητής για κώδικες Reed Solomon. Η σχεδίαση υλοποιήθηκε σε υλικό (hardware) σε γλώσσα Verilog HDL. Η σύνθεση των κυκλωμάτων πραγματοποιήθηκε με τεχνολογία Πεδίων Προγραμματιζόμενων Πινάκων Πυλών (τεχνολογία FPGA) και τεχνολογία Ολοκληρωμένων Κυκλωμάτων Ειδικού Σκοπού (τεχνολογία ASIC). Ακολουθήθηκε η μεθοδολογία σχεδιασμού Μονάδων Διανοητικής Ιδιοκτησίας για ολοκληρωμένα κυκλώματα (IP core), σύμφωνα με την οποία η σχεδίαση είναι ανεξάρτητη της πλατφόμας υλοποίησης και μπορεί να υλοποιηθεί με καθόλου ή ελάχιστες αλλαγές σε διαφορετικές τεχνολογίες. Η έννοια των IP core βρίσκει ιδιαίτερη εφαρμογή σε Συστήματα σε Ολοκληρωμένα Κυκλώματα (System on Chip). / The present work is about a specific group of error detection and correction codes, the Reed-Solomon codes. Such codes are used in telecommunications applications (wire telephony, digital television, broadband wireless communications) and digital storage systems (optical, magnetic disks). The Reed Solomon codes are based on a specific category of numerical fields, called Galois Fields. The Work consists of the study of the properties of Galois fields and of the design of an codec for Reed Solomon codes. The design was implemented in hardware with the use of Verilog HDL language. The synthesis of the circuit targets Field programmable Gate Array (FPGA) and Applications Specific Integrated Circuit (ASIC) technologies. The design methodology for Intellectual Property Units for integrated circuits (IP cores) was used. According to that methodology the design is platform independent and consequently the implementation can be achieved with minimal or no changes in different technologies. The IP cores model is widely applied in Systems on Integrated Circuits (System on Chips).

Mass., Massachusetts Inst. of Technology, Diss.--Cambridge, 2001. / Literaturverz. S. [337] - 347.