8689

8070

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

ده،116ص.: مصور،نمودار

ص.ع.به فارسي و انگليسي

مرتضي اسماعيلي

20/1/93

علي زاغيان، مجتبي آقايي

رياضي

ID8070

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

LDPC Block and Convolutional Codes Based on Circulant Matrices Hamzeh Bahrami hamzeh bahrami@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Morteza Esmaeili emorteza@cc iut ac ir 2010 MSC 94B05 68P30 Keywords parity check matrix QC LDPC code LDPC convolutional code AbstractLow density parity check LDPC codes are considerable since these codes achieve near capacity per formance with iterative message passing decoding algorithms and there are methods to produce codeswith block lenght of adequate sizes Among the methods for constructing LDPC codes randomlyconstructed ones have weaknesses as far as storing and accessing a large parity check matrix encod ing data and analyzing code performance is concerned Designing these codes via algebraic structuressolves some of the aforementioned problems In recent years several algebraic methods have beenpresented for constructing LDPC codes Among them the structure of 155 64 20 code which is aquasi cyclic QC LDPC code designed by Tanner in refrence 25 is considered in this thesis Theparity check matrix of this code contains some blocks of circulant matrices so that it naturally inducesquasi cyclic property into the code and designs a suitable encoder In this dissertation based upon the structure of the parity check matrix of the 155 64 20 code a generalization of the method is provided in order to obtain a large class of QC regular LDPC codes In this method by using the structure of the multiplicative group of the integers modulo m therotation size for the circulant matrices within a parity check matrix is determined and regular QCLDPC block codes of various block lengths and various rates are obtained Moreover by modifyingthe parity check matrix of a regular QC LDPC code a class of irregular QC LDPC codes is introducedsuch that their thresholds are superior to those of the regular basic codes In the second chapter of thisthesis by using the close relationship between QC codes and convolutional codes a new method fordesigning LDPC convolutional codes via QC block codes is presented LDPC convolutional codes that

مرتضي اسماعيلي

علي زاغيان، مجتبي آقايي