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 ofC_{J}bit/J as compared toCbit/s, to emphasize the energy efficiency and to deemphasize the speed of the telemetry. The energy channel capacityC_{J}, for any waveform channel with well-defined capacityCbit/s at signal powerSwatts, is defined asC/Sbit/J. It is shown that for coherent binary frequency shift keying (BFSK) and waveform channels, the supremum ofC_{J}overSis approached asSapproaches zero. For the Gaussian channel the best coding uses narrow bands with the highest S/N.