Investigation of Bijections During the Conversion of a Digital Signal into a Continuous Signal and Inverse Conversion : with conversions carried out in the modulator and demodulator

The main attention in the article is paid to the conversion of a digital signal into a continuous one, which corresponds to the conversions carried out in the modulator and demodulator at the reception. This transformation can be characterized as Hamming-Euclid, when, under the influence of interference in the channel, distortions appear in the analog signal, which leads to errors in the discrete signal after demodulation. The article explores ways to compare the elements of the Euclidean space with the Hamming space after signal demodulation. In particular, the cases for natural code, Gray code and some random code are considered. The importance of carrying out similar studies for existing and future signal-code structures with various multiple methods of discrete modulation is shown.