  Radio communication over interstellar distances is studied, accounting for
noise, dispersion, scattering and motion. Large transmitted powers suggest
maximizing power efficiency (ratio of information rate to average signal power)
as opposed to restricting bandwidth. The fundamental limit to reliable
communication is determined, and is not affected by carrier frequency,
dispersion, scattering, or motion. The available efficiency is limited by noise
alone, and the available information rate is limited by noise and available
average power. A set of five design principles (well within our own
technological capability) can asymptotically approach the fundamental limit; no
other civilization can achieve greater efficiency. Bandwidth can be expanded in
a way that avoids invoking impairment by dispersion or scattering. The
resulting power-efficient signals have characteristics very different from
current SETI targets, with wide bandwidth relative to the information rate and
a sparse distribution of energy in both time and frequency. Information-free
beacons achieving the lowest average power consistent with a given receiver
observation time are studied. They need not have wide bandwidth, but do
distribute energy more sparsely in time as average power is reduced. The
discovery of both beacons and information-bearing signals is analyzed, and most
closely resembles approaches that have been employed in optical SETI. No
processing is needed to account for impairments other than noise. A direct
statistical tradeoff between a larger number of observations and a lower
average power (including due to lower information rate) is established. The
"false alarms" in current searches are characteristic signatures of these
signals. Joint searches for beacons and information-bearing signals require
straightforward modifications to current SETI pattern recognition approaches.
