11121

10237

كارشناسي ارشد

رياضي كاربردي(كد گزاري)

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1394

سيزده، 116ص.:نمودار

مرتضي اسماعيلي

به فارسي و انگليسي

حميدرضا مرزبان، محمدحسام تدين

1395/01/14

رياضي

ID10237

Array convolutional low density parity check codes Sayed Ahmad Khosravani Tavana ahmad khosravani@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Morteza Esmaeili emorteza@cc iut ac ir 2016 MSC 94B15 94B60 94B65 Keywords low density parity check code Array convolutional LDPC code Array LDPC code minimum hamming distance of code AbstractLow density parity check LDPC codes are an important family of linear codes which are introducedwith a parity check matrix having small number of non zero elements relative to the total entries ofthe matrix Theoretically LDPC codes can achieve remarkable performance very close to the Shannonlimit with iterative decoding In recent years it is proven that these codes have good error correctionand detection performance in communications systems Array LDPC codes are a special class of quasi cyclic LDPC codes constructed from a pair ofintegers q r0 where q is an odd prime and r0 q Two classes of array LDPC codes referred toas proper and improper codes are considered in this thesis An important parameters for a ectingthe error correction and detection capability of a code is its minimum Hamming distance Because nding the Hamming distance of a code by direct calculation is di cult the algebraic structures ofcode is used to determine the minimum Hamming distance In this thesis by using algebraic conceptssuch as codeword support and stopping set the minimum Hamming distance of array LDPC codesare calculated under certain conditions Then it is shown that the improper codes have a betterperformance compared to proper codes over the AWGN and binary erasure channels under thesum product decoding algorithm LDPC convolutional LDPCC codes are a subclass of LDPC codes In this thesis we study twoclasses of LDPCC codes known as Time Varying and time invariant codes LDPCC codes can beencoded through simple circuits based shift registers Their decoding can be performed by running a

مرتضي اسماعيلي

حميدرضا مرزبان، محمدحسام تدين