بهبود كران بالاي تعداد k-دسته يكتا با محاسبه‌ي تعداد متغيرهاي مستقل

One method for identifying the input sequences of a DNA data storage channel is the use of a profile vector, which refers to a vector that includes features of the subsequences of that sequence. The k-deck profile vector for a binary sequence is a profile vector that represents the frequency of occurrence of each of the possible subsequences of length k within sequences of length n , considering the order of symbols in the original sequence but not requiring them to be consecutive. It is known that if each sequence has it’s unique profile vector, it is possible to identify these sequences solely through the profile vector of each sequence. To achieve this, it is first necessary to calculate the number of unique profile vectors to determine the efficiency of using this method for identifying binary sequences in a data storage channel in DNA sequences. It is important to note that in this thesis, the mentioned channel is considered error-free. In this regard, researchers have sought to determine the lower an‎d upper bounds for the number of unique profile vectors. The approach used to improve the upper bound on the number of unique profile vectors compared to previous works involved calculating the number of independent variables by determining the number of independent governing equations between these variables an‎d counting the various possible arrangements of these variables. To this end, the governing equations for the members of the k-deck profile vector were derived under the assumption that the independent variables in the profile vectors of 1-deck to (k-1)-deck are fixed, for k=3,4,5,6. Then, the number of independent equations was calculated, an‎d by counting all values of the independent variable vector, the obtained upper bound was compared with the best previous upper bound. For k=3, no improvement in the upper bound was achieved, but for k=4,5,6, the upper bound was improved by 4, 14, an‎d 56 degrees, respectively.

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