Time-division multiplexing for green broadcasting

The problem of minimizing the total (transmit and decoding) energy required for communicating over a two-receiver Gaussian broadcast channel is investigated. For achieving a specified rate-tuple, joint broadcast schemes (e.g. superposition coding) require smaller transmit energy per-bit than the conceptually simpler time-division multiplexing (TDM) based schemes. However, for short distance communication, the energy expended in the decoding can be comparable to that required in the transmission. Two technical advances are introduced to understand these energy costs: (a) an improvement on the best known outer bounds on the error exponents for the Gaussian broadcast problem, and (b) a finer analysis to have these bounds hold for neighborhood sizes instead of block-lengths. Using these results, it is then shown that in some typical short and moderate distance communication scenarios, time-division multiplexing saves on the decoding energy, thereby likely requiring smaller total energy than any joint broadcasting scheme for achieving the target rate and error probabilities. Further, we observe that TDM outperforms joint schemes by larger margins when the ratio of the distances of the receivers from the transmitter is closer to 1.