Channel capacity in bits per joule

Underwater acoustic telemetry has a total input energy constraint, since the energy is stored in the transmitter\´s batteries. This work is primarily rephrasing the work in channel capacity in terms of bit/J as compared to bit/s, to emphasize the energy efficiency and to deemphasize the speed of the telemetry. The energy channel capacity , for any waveform channel with well-defined capacity bit/s at signal power watts, is defined as bit/J. It is shown that for coherent binary frequency shift keying (BFSK) and waveform channels, the supremum of over is approached as approaches zero. For the Gaussian channel the best coding uses narrow bands with the highest S/N.