Energy-Efficient Communication in the Presence of Synchronization Errors

Communication systems are traditionally designed to have tight transmitter-receiver synchronization. This requirement has negligible overhead in the high-signal-to-noise ratio (SNR) regime. However, in many applications, such as wireless sensor networks, communication needs to happen primarily in the energy-efficient regime of low SNR, where requiring tight synchronization can be highly suboptimal. In this paper, we model the noisy channel with synchronization errors as a duplication/deletion/substitution channel. For this channel, we propose a new communication scheme that requires only loose transmitter-receiver synchronization. We show that the proposed scheme is asymptotically optimal for the Gaussian channel with synchronization errors in terms of energy efficiency as measured by the rate per unit energy. In the process, we also establish that the lack of synchronization causes negligible loss in energy efficiency. We further show that, for a general discrete memoryless channel with synchronization errors and a general input cost function admitting a zero-cost symbol, the rate per unit cost achieved by the proposed scheme is within a factor two of the information-theoretic optimum.