🤖 AI Summary
This work investigates the asymptotic channel capacity of Gaussian and Poisson optical intensity channels under an average optical intensity constraint in the extremely low signal-to-noise ratio (SNR) regime. Addressing a longstanding theoretical gap—namely, the absence of rigorous asymptotic characterizations—the authors employ a combination of information-theoretic analysis, asymptotic expansion techniques, extreme-value distribution modeling, and entropy bounding methods. They derive, for the first time, tight asymptotic expressions for the capacity of both channels as the average intensity ℰ tends to zero from above: ℰ√(½ log(1/ℰ)) for the Gaussian channel and ℰ log log(1/ℰ) for the Poisson channel. These results precisely characterize the scaling laws governing capacity decay with diminishing input intensity. The findings substantially enhance the accuracy of capacity prediction and provide stronger theoretical foundations for ultra-low-power optical communication systems operating under vanishingly weak illumination.
📝 Abstract
In this paper, we study two types of optical wireless channels under average-intensity constraints. One is called the Gaussian optical intensity channel, where the channel output models the converted electrical current corrupted by the additive white Gaussian noise. The other one is the Poisson optical intensity channel, where the channel output models the number of received photons corrupted by the positive dark current. When the average input intensity $mathcal{E}$ is small, the capacity of the Gaussian optical intensity channel is shown to scale as $mathcal{E}sqrt{frac{logfrac{1}{mathcal{E}}}{2}}$, and the capacity of the Poisson optical intensity channel as $mathcal{E}loglogfrac{1}{mathcal{E}}$, which close the existing capacity gaps in these two channels.