Special Aspects of Errors Definition via Sum Codes within Embedded Control Schemas Being Realized by Means of Boolean Complement Method

Within present article characteristics of errors definition are being analyzed within coded words of conventional sum codes (Berger Codes). Unrevealed features of earlier unknown errors detection based on self-multiplicity and forms (unidirectional, symmetrical either asymmetrical), were discovered by us, which may be helpful while synthesis of embedded control schemas, for example, by means of Boolean Complement Method. Here we demonstrated, that while implementation of Berger Codes, certain amount of symmetrical as well as asymmetrical plus unidirectional faults within coded words are not being spotted, which considered as a difference compares to prior defined characteristics of malfunction identification within data vectors of Berger Codes only (regarding our abovementioned case, any symmetrical errors are not the matter of identification, but at the same time, any of unidirectional or asymmetrical mistakes are being found, which is useful while errors definition systems synthesis). The share of not traced errors from the entire quantity per Berger Codes with data vectors dimensions <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r=4\ldots 7$</tex> is composed of less than 2%, as for Berger Codes with vectors lengths <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r=8\ldots 15$</tex> , it is even less than 0.5%. The abovementioned factor has significant influence on probabilistic characteristics of errors detection into coded words of Berger Codes: for instance, within prospect of failure absence in single digit order number <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p=0.9$</tex> , chance of error identification in coded words Pm is above the value of 0.99 for total noted lengths of data vectors. Application of conventional codes with summation is well thought-out as effective case for embedded control systems synthesis including via Boolean Complement Method, where, data and check digits of coded words are being evaluated by means of diagnostic object itself.

Перевод пока недоступен