Reducing Distortion when Applying the Rational Choice of the Digital Conversion Method

When converting signals into digital form, certain distortions (errors) appear in these signals associated with 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. 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 received during transmission and recovery may not meet the established requirements. In order to minimize distortions arising due to errors in the digital signal, it is necessary to study the influence of these random factors on the transmitted signal, to explore ways to rationally choose digital display methods taking into account transformations in various metric spaces. 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 that determine the distance between the original messages and the given metric of the Euclidean space are calculated. These values will allow you to establish a correspondence between messages and code combinations of the binary code, for which the distance is already set in another space (Hamming). Also, the article suggests minimizing distortions if the minimum distances of one metric space are associated with the minimum distances of another metric space. In addition, the study revealed limitations on this minimization.