12967

11856

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

۱۳۹۶

ده، ۱۰۹ص.:‌ مصور، جدول، نمودار

مرتضي اسماعيلي

محمد حسام تدين، محمدرضا درفشه

1396/08/13

كتابنامه

علوم رياضي

رياضي

ID11856

Algebraic Spatially Coupled Quasi Cyclic LDPC Codes Sajjad Kave s kave@math iut ac ir september 13 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Morteza Esmaeli emorteza@cc iut ac ir 2010 MSC 05C80 05C90 Keywords Spatially Coupled Quasi Cyclic LDPC Code convolutional code window decoding PEG algorithm rate compatible codes threshold saturation unwrapping replicate and mask method AbstractIn this thesis we present a class of convolutional codes defined by a low density parity check matrixthat is named Spatially coupled low density parity check SC LDPC codes These codes have receivedmuch attention due to their excellent thresholds such as threshold saturation phenomenon Due to theproperty of both QC LDPC codes and SC LDPC codes in this thesis we addressed the construction ofSC LDPC codes with a QC structure over arbitrary finite fields these codes are called SC QC LDPCcodes A natural method of constructing SC QC LDPC codes is to unwrap a QC LDPC block code The unwrapping construction can preserve many structural properties of the underlying block code such as the girth and the minimum distance however unwrapped SC QC LDPC block codes couldstart to show error floors at a block error rate BLER of 10 2 which is the operating BLER of manywireless communication systems So this is undesirable for practical applications since the throughputof many communication systems is determined by the BLER For solving this problem the replicate and mask R M construction of finite length spatially coupled LDPC codes is proposed The cruxof the R M construction is replicating the parity check matrix of an LDPC block code and maskingit with a designed masking matrix this construction generalizes the conventional matrix unwrappingconstruction and contains it as a special case and results in a much larger class of SC QC LDPC codeswith a more flexible parameter selection Compared to the conventional unwrapping approach theproposed R M construction provides more flexibility in the selection of the code parameters such asthe rate and degree distributions and the optimization of the constructed codes The R M SC LDPC

مرتضي اسماعيلي

محمد حسام تدين، محمدرضا درفشه