پديد آورنده :
نجفيان، مهراب
عنوان :
زير گروه هاي دوري ميدان هاي متناهي و كدهاي شبه دوري LDPC
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
دوازده،90ص.: مصور،جدول،نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
مرتضي اسماعيلي
توصيفگر ها :
كدهاي LDPC-QC , هم مجموعه هاي دوري , مانريس پايه , ماتريس هاي جايگشتي دوري , ماتريس بررسي توازن , گراف تنر
تاريخ نمايه سازي :
10/4/92
استاد داور :
حميدرضا مرزبان، رضا مزروعي سبداني
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Abstract Quasi cyclic low density parity check QC LDPC codes are a class of linear block codes which was Discovered by R G Gallager in 1962 This class of codes has high capability of error correction In this thesis we study construction of QC LDPC codes by algebraic methods over finite field Fq These methods are based on constructing parity check matrices that are arrays of circulant permutation matrices We show that finite fields can be used effectively to construct of arrays of circulant permutation matrices and zero matrices as parity check matrices of QC LDPC codes The construction methods give codes without cycles of length four in their Tanner graphs The fact that these cycles are naturally eliminated in the constructions allows the code designer to concentrate more on improving the performance and lowering the error floor of the constructed codes The thesis is organized as fallows Chapter 1 gives a brief introduction of QC LDPC codes including the definitions of parity check and generator matrices in circulant forms and basic structure Chapter 2 contains several structured QC LDPC codes a construction is presented by multiplicative group of finite field Fq Corresponding to the cyclic subgroup of greatest prime factor of q 1 in Fq a method constructing a QC LDPC code is given and also for prime field Fq a method is given to construct binary LDPC codes In all these constructions it is shown that the base matrices satisfy the four cycle free property know as RC constraint We also introduce a method known as Masking method The Masking operation can be mathematically formulated as a special case of matrix product operation By Masking we present a class of asymptotically optimal LDPC codes for erasure burst correction with iterative decoding over binary erasure channel BEC In chapter 3 a class of quasi cyclic LDPC codes whose parity check matrices are arrays of circulant permutation matrices is introduced which are based on cyclic subgroups of finite fields If the order of these subgroups are relatively prime then the associated base matrix satisfies the RC constraint It is shown that if the order of one of the cyclic subgroups is 1 the order of the other cyclic subgroup is q 1 which are relatively prime and in this case the base matrix is a latin square This class of codes contains several known classes of algebraic quasi cyclic LDPC codes as subclasses In chapter 4 we give a new method to construct LDPC codes by q cyclotomic cosets of n where n is a prime number and gcd n q 1 This construction gives base matrices satisfying the RC constraint The elements in these matrices are then replaced by binary or non binary circulant to form parity check matrices of binary or non binary QC LDPC codes respectively This construction generate binary and q ary QC LDPC codes with high rates Experimental results show that the constructed codes perform very well overthe additive white Gaussian noise channel when decoded with iterative decoding based on sum product algorithm
استاد راهنما :
مرتضي اسماعيلي
استاد داور :
حميدرضا مرزبان، رضا مزروعي سبداني
