كدگشايي جبري كدهاي دوري بدون چند جمله اي هاي خطاياب

چكيده انگليسي :

Algebraic Decoding of Cyclic Codes Without Error Locator Polynomials Omid Shafiei o shafiei@math iut ac ir Junuary 8 2019 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisors Dr Morteza Esmaeili emorteza@cc iut ac irDr Hamid Reza Marzban hmarzban@cc iut ac ir2010 MSC 94B35 94B15Keywords Decoding Cyclic Codes BCH Codes Berlekamp Massey Algorithm Known Syndrome Un known Syndrome Chien s SearchAbstract This M Sc thesis is based on the following paper Lin T C Lee C D Chen Y H and Truong T K Algebraic decoding of cyclic codes without error locator polynomials IEEE Trans Commun vol 64 no 7 pp 2719 2731 Jul 2016 Until 2016 all of which are presented for decoding BCH code associated with a polynomial to the error locator polynomial This dependency caused errors not to be correctly decoded as much as the error cor rection capacity of the BCH code In this M Sc thesis we propose a method for decoding cyclic codes with prime length in particular BCHcodes in which not used Error Locator polynomials for example the Berlekamp Massey BM algorithmand the Chien s search to identify errors in the received word Now a q ary cyclic code with length n n a prime number and the error correction capacity t is considered Suppose that a codeword of code Cis sent by a noisy channel in which only v t has occurred In the proposed method instead of usingthe Berlekamp Massey BM algorithm and Chien s search we suggest using a non square matrix of size v 1 v n whose entries in the first v columns are syndromes and the remaining entries are someelements of the field Fqm in which m is the smallest positive integer n q m 1 If every syndrome in theproposed matrix is known then Gaussian elimination method can be used to transform this matrix into arow echelon form which is v zero appearing in last n entries v 1 th of the matrix these zero entriescan only detect v of error position in a received word A main advantage of the proposed method is whenthe BCH bound is unequal to the minimum distance of the code Some cyclic codes which do not have2t consecutive known syndromes can be successfully decoded up to their minimum distance through thepresented non square matrix In fact if the minimum distance of a cyclic code equals the BCH bound thenthe BM algorithm is more efficient to decode it Sometimes it happens in the decoding process that the matrix cannot be expressed in such a way that thesyndromes in v of the first column are known First an efficient algorithm is provided to evaluate the truevalue of an unknown syndrome in a square matrix whose all entries are syndrome Second an efficientalgorithm is provided to evaluate the true value of an unknown syndrome in a square matrix with the lastcolumn whose entries are elements of finite filed Fqm and with the remaining columns whose entries arethe syndromes Third an efficient algorithm is provided to evaluate the true value of an unknown syndromein a square matrix with the last row and last column whose entries are elements of finite filed Fqm and withthe remaining rows and columns whose entries are the syndromes In the end for example the proposedmethod is described on the 47 23 15 ternary cyclic code

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كدگشايي جبري كدهاي دوري بدون چند جمله اي هاي خطاياب

كدگشايي , كد دوري , كدBCH , روش برليكمپ - مسي , شناسه معلوم , شناسه نامعلوم , جستجوي chien