As one of the most powerful error-correcting codes, Low-density parity check codes are widely used in digital communications. Because of the performance of LDPC codes are capable to close the shannon limited extraordinarily, LDPC codes are to be used in the new Digital Video Broadcast-Satellite-Second Generation(DVB-S2) and it is the first time that LDPC codes are included in the broadcast standard in 2003. In this thesis, a restructured parity-check matrices which can be divided into sub-matrices for LDPC code in DVB-S2 is provided. Corresponded to this restructured parity-check matrix, a reconstructed decoding table is invented. The encoding table of DVB-S2 standard only could obtain the unknown check nodes from known variable nodes, while the decoding table this thesis provided could obtain the unknown variable nodes from known check nodes what is exactly the Layered-massage passing algorithm needed. Layered-message passing algorithm which also known as "Turbo-decoding message passing" is used to reduce the decoding iterations and memory storage for messages. The thesis also investigate Bp algorithm, lambda-min algorithm, Min-sum algorithm and SISO-s algorithm, meanwhile, simulation results of these algorithms and schedules are also presented.

No description available.

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.