5123

4813

كارشناسي ارشد

رياضي كاربردي﴿نظريه كد گذاري﴾

اصفهان: دانشگاه صنعتي اصفهان،دانشكده علوم رياضي

1388

[نه]،97ص.:مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

مرتضي اسماعيلي

علي زاغيان

89/1/29

محمدحسام تدين،غلامرضا اميدي

رياضي

ID4813

به فارسي و انگليسي:قابل رويت در نسخه ديجيتالي

Several construction methods of LDPC codes Mokhtar Salahian m salahian@math iut ac ir January 27 2010 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iransupervisor Dr Morteza Esmaeili2000 MSC 94B60Key words Dispersion Euclidean geometry incidence vector location vector low density parity check code quasi cyclic code superposition Abstract In this thesis we presents an expanded account of construction of low densityparity check LDPC codes based on two articles L Q Zeng 2008 This thesis presents ten algebraic methods for constructing non binary low densityparity check LDPC codes based on nite elds and nite geometries These codeshave Tanner graphs with girth at least 6 Simulations show that these codes per form well under iterative decoding algorithms The parity check matrices of thecodes constructed by nite elds usually have nearly full row rank hence the encod ing complexity is low In general the construction methods based on nite eldsare suitable for generating high rate codes with parity check matrices having smallcolumn weight The parity check matrices of the codes constructed by the nite ge ometries usually have large column weights hence these codes may show a very lowerror oor In this thesis we give three new algebraic code construction methods The constructed codes compete with the previously reported codes from rate andgirth perspectives The performance of an LDPC code with iterative decoding dependes on a numberof code structural properties One such structural property is the girth of the codethat is de ned as the length of the shortest cycle in the codes Tanner graph Fora code to perform well with iterative decoding its Tanner graph must not containtoo many short cycles The shortest cycles that a ect code performance the mostare cycles of length 4 Therefore in code construction cycles of length 4 must beprevented Many experimental results show that the error oor of an LDPC codewith iterative decoding very much depends on the minimum distance of the code andhence it is necessary to keep the minimum distance of an LDPC code reasonably large For an irregular code with iterative decoding its error performance also depends onthe degree distribution of the variable and check nodes of its Tanner graph

مرتضي اسماعيلي

علي زاغيان

محمدحسام تدين،غلامرضا اميدي