5122

4812

كارشناسي ارشد

رياضي كاربردي﴿نظريه اطلاعات و كد گذاري﴾

اصفهان: دانشگاه صنعتي اصفهان،دانشكده رياضي

1388

[نه]،89ص.:مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

مرتضي اسماعيلي

علي زاغيان

29/1/89

محمدحسام تدين،حميدرضا مرزبان

رياضي

ID4812

به فارسي و انگليسي:قابل رويت در نسخه ديجيتالي

Stopping distance and stopping redundancy of nite geometry LDPC codes zohreh Hooshmand Jazi z hooshmand@math iut ac ir January 27 2010 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisors Dr Morteza Esmaeili emorteza@cc iut ac ir2000 MSC Primary 68P30 Secondary 05B25 Key words Euclidean geometry iterative decoding low density parity check codes projective geometry stopping distance stopping redundancy stopping set AbstractThis thesis presents a geometric approach to the construction of low density parity check LDPC codes Four classes of LDPC codes are constructed based on the lines and points ofEuclidean and projective geometries over nite elds Codes of these four classes have good minimum distances and their Tanner graphs havegirth 6 Furthermore they can be put in either cyclic or quasi cyclic forms A stopping set S in a parity check matrix H is a subset of the variable nodes in theTanner graph for H such that all the neighbors of S are connected to S at least twice Givena parity check matrix H the size of the smallest nonempty stopping set is called the stoppingdistance of H The stopping redundancy C of a code C is the minimum number of rows in any parity check matrix H for C such that s H d C It is always possible to nd a parity checkmatrix H for C such that s H d C In fact the parity check matrix consisting of allthe nonzero codewords of the dual code C has this property Unlike the stopping distance which depends on the speci c choice of H the stopping redundancy is a property of the codeitself The stopping distance and stopping redundancy of a linear code are important conceptsin the analysis of the performance and complexity of the code under iterative decoding ona binary erasure channel In this thesis the stopping sets and stopping distance of nitegeometry LDPC FG LDPC codes are studied It is shown that the lower bound on theminimum distance of FG LDPC codes is also a lower bound on the stopping distance of FG LDPC codes which implies that this codes have considerably large stopping distance ThusFG LDPC codes have a good performance under iterative decoding Finally stopping distance of FG LDPC codes constructed based on the points and linesof Euclidean or projective geometry are obtained and an upper bound on the stoppingredundancy of these codes is provided 1

مرتضي اسماعيلي

علي زاغيان

محمدحسام تدين،حميدرضا مرزبان