M.Yu. Aliev − Head of Department,

JSC «Typhoon» (Kaluga)

E-mail: aris@mail.ru

A.M. Donetskov − Ph.D. (Eng), Associate Professor, 

«Information Systems and Networks» Department, Kaluga Branch of Bauman MSTU

E-mail: dam1358@mail.ru

A.S. Nikolaev – Ph.D.(Eng.), Associate Professor, 

«Information Systems and Networks» Department, Kaluga Branch of Bauman MSTU

E-mail: nikolanta@yandex.ru

Formulation of the problem. Often when using correction codes in data transmission systems, the choice of one or another redundant code is limited not by the code's ability to detect and correct errors, but by the complexity of the encoder scheme, and especially the decoder, when implementing these devices. Therefore, it is necessary to pay attention not only to the creation of codes with the best corrective properties, but also to the development of algorithms and schemes for encoders and decoders for these codes.

One of the algorithms is the majority decoding method. In its implementation, shift registers, adders modulo two, and majority elements are used. The main problem in creating the decoder circuit is the complexity of the majority element. It increases sharply with the increase in the number of its inputs. And to fight the code with multiple errors, multi-input majority elements are needed. Increasing the multiplicity of the error corrected by one adds two inputs to the scheme of the major element. Therefore, the problem of minimizing the circuit of this element becomes relevant.

Purpose of work: To create a method for minimizing the functions of the majority and threshold functions, which gives a good result with a simple minimization algorithm.

Results. The article discusses methods of minimizing the function of the majority element, allowing to obtain a function with the least number of elementary logical operations included in it. An algorithm has been developed for representing the function of the major and threshold elements in the form of a system of equations for elements having an arbitrary number of inputs. The created system of equations does not require minimization. The algorithm is unambiguous. By the example of the eleventh-majoritarian majority element, the effectiveness of the method is shown.

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