Limits on achievable dimensional and photon efficiencies with intensity-modulation and photon-counting due to non-ideal photon-counter behavior

Abstract

An ideal intensity-modulated photon-counting channel can achieve unbounded photon information efficiencies (PIEs). However, a number of limitations of a physical system limit the practically achievable PIE. In this paper, we discuss several of these limitations and illustrate their impact on the channel. We show that, for the Poisson channel, noise does not strictly bound PIE, although there is an effective limit, as the dimensional information efficiency goes as e¯ᵉᴾᴵᴱ beyond a threshold PIE. Since the Holevo limit is bounded in the presence of noise, this illustrates that the Poisson approximation is invalid at large PIE for any number of noise modes. We show that a nite transmitter extinction ratio bounds the achievable PIE to a maximum that is logarithmic in the extinction ratio. We show how detector jitter limits the ability to mitigate noise in the PPM signaling framework. We illustrate a method to model detector blocking when the number of detectors is large, and illustrate mitigation of blocking with spatial spreading and altering. Finally, we illustrate the design of a high photon efficiency system using state-of-the-art photo-detectors and taking all these effects into account.