5727

5342

كارشناسي ارشد

رياضي كاربردي﴿كد گذاري﴾

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1389

[ده]،97ص.: مصور،نمودار

ص.ع.به فارسي و انگليسي

مرتضي اسماعيلي

علي زاغيان

17/1/90

محمد حسام تدين، حميدرضا مرزبان

رياضي

ID5342

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Construction of LDPC Codes Based on Combinatorics Design and Finite Fields Mostafa Javedankherad m javedankherad@math iut ac ir 2011 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Morteza Esmaeili emorteza@cc iut ac ir Advisor Dr Ali Zagheian alizaghian 1338@gmail com 2000 MSC 68P30 Key words dispersion Base matrix Girth Balanced incomplete block design Di erence set Dif ference family LDPC code Abstract Low Density Parity Check LDPC codes were discovered rst in 1962 by Gallager and were rediscovered in 1996 by MacKay and Neal It is known that these codes have performance close to the Shannon limit Some methods for constructing LDPC codes are given The performance of a LDPC code with iterative sum product decoding algorithm depends on a number of code structural properties An important structural parameter is the girth of the code that is de ned as the length of shortest cycles in the code s Tanner graph Normally for a code to perform well with iterative decoding its Tanner graph needs to be free of short cycles The shortest cycles that e ect the code performance are cycles of length 4 Therefore in the code construction it is desirable to avoid having length 4 cycles Many experimental results show that the error oor of a LDPC code with iterative decoding greatly depends on the minimum distance of the code and hence it is necessary to keep the minimum distance of a LDPC code reasonably large The property that in a given Parity Check matrix H no two rows and no two columns are nonzero in more than one common coordinates is referred to as the Row Column RC constraint The RC constraint ensures that the Tanner graph of H is free of cycles of length 4 Construction of binary and q ary codes based on primitive eld elements additive and multiplicative subgroups of nite elds are studied Experimental results show that the constructed codes perform well over the Additive with Gaussian Noise AWGN channel with iterative sum product decoding algorithm Type I and Type II Bose Balanced incomplete block designs BIBD are presented These designs have an important property every two distinct points belong to the same number of blocks Using these designs two families

مرتضي اسماعيلي

علي زاغيان

محمد حسام تدين، حميدرضا مرزبان