Hyperphase modulation - the optimal method for transmitting messages in the Gaussian communication channels

The monograph is devoted to topical issues related to the choice for the designed communication systems of multidimensional signals that allow transmitting messages by communication with the maximum possible speed (maximum spectral efficiency), as well as with maximum energy efficiency, the theoretical limit of which was established by the creator of the theory of information theory by Claude Shannon.
It has an analytical overview of the main modern methods of building noise -resistant codes designed to transmit messages in discrete communication channels, and two -dimensional and multidimensional signals with which the messages are transmitted in continuous communication channels.
A number of new results are presented in the monograph. New methods of determining the probability of error when receiving multidimensional signals that allowed to summarize the Shannon theorem about the throughput of the continuous communication channel in case the signals have a limited duration and the required probability of an error arising from the demodulation of the accepted signals is known. The book develops constructive methods for constructing multidimensional ensembles of volumetric and surface-spherical signals, which, as shown by Shannon, are optimal for transmitting messages in the communication channel with white Gaussian noise. A method of assessing the energy efficiency of communication systems is proposed. This method is used to compare communication systems, which use different modulation methods and different noiseless codes. It is shown that in communication systems that use multidimensional signal ensembles, the use of noise -resistant codes is inappropriate.
The book is addressed to scientists and engineers to specialists in the development and design of new ground, satellite telecommunication communication systems, mobile and digital broadcasting systems. It can be used as a training manual for graduate students and students of information and radio engineering specialties