Bounds and observations on the transmission of data packets with minimum energy

Transmitting bursty data energy-efficiently is of interest in emerging wireless communication systems. We observe that in the AWGN channel a finite number of bits B cannot be transmitted with finite energy per bit epsiv_b as the error probability goes to zero. We show, however, that any sub-linear increase of B with the blocklength suffices. We derive structural properties of the behavior of epsiv_b with rate for fixed B and apply classical random coding error probability bounds to obtain numerical bounds. Implications are discussed for the design of practical systems where transmission energy is not the only component of energy consumption.