Capacity Bounds and High-SNR Capacity of the Additive Exponential Noise Channel With Additive Exponential Interference

Communication in the presence of a priori known interference at the encoder has gained great interest because of its many practical applications. In this paper, additive exponential noise channel with additive exponential interference (AENC-AEI) known noncausally at the transmitter is introduced as a new variant of such communication scenarios. First, it is shown that the additive Gaussian channel with a priori known interference at the encoder when the transmitter suffers from a fast-varying phase noise can be modeled by the AENC-AEI. Then, capacity bounds for this channel under a non-negativity constraint as well as a mean value constraint on input are derived. Finally, it is shown both analytically and numerically that the upper and lower bounds coincide at high signal to noise ratios (SNRs), and therefore, the capacity of the AENC-AEI at high SNRs is obtained. Interestingly, this high SNR-capacity has a simple closed-form expression and is independent of the interference mean, analogous to its Gaussian counterpart.