Features of Converting Signals to Binary and Minimizing Distortion

A well-known complex of methods for converting signals into binary digital form is shown, potential theoretically achievable boundaries of such conversions are determined. Values are calculated that indicate the value of the code distance between the original values and those obtained after transformation. Euclidean space metric. A correspondence is established between these messages and binary code combinations in the Hamming space. It is proved that in some cases the values that determine the distance between messages and the metric are quite general and should be clarified for specific situations. Distortion minimization is suitable for cases where the minimum code distances of the primary metric space are related to the minimum code distances of the secondary metric space. And also in the article the admissible limits of such minimization are found.