Can analogue communication systems work better than digital systems and when?

Approaching the quality and power-bandwidth efficiency of the signals transmission to theoretical limits is considered now as the urgent task of communications and information theory. Nowadays, no analytical tools exist which allow its accurate solution and systematic design of (“ideal”) communication systems which work at these limits.
In the paper, we show that unlike digital communication systems, adaptive feedback communication systems (AFCS) with analogue signal transmission allow development of efficient analytical tools permitting to design the ideal AFCS whose performance attains upper theoretical boundaries. We also discuss the reasons which had hampered a development of optimal analogue AFCS theory, as well as the fields of more efficient application of analogue AFCS in comparison with digital AFCS and non-feedback digital communication systems.