MINIMIZING SIGNAL DISTORTIONS AT THE MOST OPTIMAL CHOICE OF DIGITAL CONVERSION METHOD
DOI: 10.36724/2072-8735-2020-14-5-27-34
Anastasiya Yu. Kudryashova, Moscow Technical University of Communications and Informatics, Moscow, Russia, asykka@bk.ru
Abstract
When converting various signals into digital form, certain distortions (errors) appear in them, associated with the discretization and quantization. This circumstance is taken into account when developing appropriate methods for analog-to-digital conversion in order to ensure established quality requirements. As a rule, this is either the maximum permissible absolute error or the standard error. However, in addition to this, distortion also occurs due to the random influence of interference introducing errors into the digital signal. As a result, the quality of the signal obtained during transmission and during further restoration of the signal may not correspond to the originally established requirements. To minimize distortion due to errors in the digital signal, it is necessary to study the influence of these random factors on the transmitted signal. As will be shown below, in this article, one of the factors affecting noise immunity is the method of rational choice of methods for digital representation of the original signal as a sequence of code combinations of a binary code. This method takes into account transformations from one metric space (in which the original signal was presented) to another (the Hamming space used to describe the binary signal). It is proposed to use the error matrix to describe the arising distortions in the reconstructed signal (as a result of errors in the binary digital signal), the elements of which will be the distortion values for all possible cases of incorrect recovery of binary code combinations. The article analyzes the error matrix and the code distance matrix of the binary code, calculates the total number of distortions in the transformations of various metric spaces. The values are calculated that determine the distance between the original messages and the given Euclidean space metric. This distance will allow you to establish a correspondence between these messages and code combinations of the binary code, for which the distance is already set in another space (Hamming space). Also, the article proposes minimization of distortions if the minimum distances of one metric space are associated with the minimum distances of another metric space. In addition, limitations on this minimization were identified.
Keywords: digital signal, distortion matrix, error matrix, code distance, total distortion.
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