A new method of modulation and demodulation of a quasi-deterministic signal is investigated, which in the future opens up great opportunities for improving the efficiency of digital systems. The method contains new technical solutions for transforming a random signal, including the modulation of the characteristic function and the measurement of estimates of the real and imaginary parts of this function. The purpose of this work is the development of optimal algorithms and generalization of the theory of the new modulation and demodulation method by using new elements (algorithms) when transforming a random signal using the arcsine distribution law. Single-channel and dual-channel modems are considered for operation in a radio channel and in a wired channel respectively. The comparison of characteristics of the modems with optimal and non-optimal modulation algorithms is performed, wherein the characteristics of the first modem turn out to be an order of magnitude better than the second modem. It has been established that the modems have different noise immunity in a channel with «white» noise and in this indicator surpass the known modems by at least ten orders of magnitude. The energy efficiency of the modems is high and exceeds the efficiency of QPSK (Quadrature Phase Shift Keying) signal modems by 10 dB at the error probability level of 1∙10-10.