Superposition coding is almost always optimal for the Poisson broadcast channel

Abstract

This paper shows that the capacity region of the continuous-time Poisson broadcast channel is achieved via superposition coding for most channel parameter values. Interestingly, the channel in some subset of these parameter values does not belong to any of the existing classes of broadcast channels for which superposition coding is optimal (e.g., degraded, less noisy, more capable). In particular, we introduce the notion of effectively less noisy broadcast channel and show that it implies less noisy but is not in general implied by more capable. For the rest of the channel parameter values, we show that there is a gap between Marton's inner bound and the UV outer bound.

On the Capacity of the Intensity-Modulation Direct-Detection Optical Broadcast Channel

“…The resulting system is an optical broadcast channel (OBC), and has been studied in [12]- [16]. In [12], the authors study the capacity of the Poisson broadcast channel.…”

“…The resulting system is an optical broadcast channel (OBC), and has been studied in [12]- [16]. In [12], the authors study the capacity of the Poisson broadcast channel. In [13]- [15], the authors analyze the performance of orthogonal code-division multiple-access.…”

Performance and Energy in Green Superposition Coding Wireless Networks: An Analytical Model

“…In expression (25), the third equality denoted (3) comes from (13), where r = Rc. We denote α = γ γ+1 ρπ.…”

“…In [13] SC is shown to be capacity achieving for a continuous-time Poisson broadcast channel with different parameters.…”

The Poisson Channel With Varying Dark Current Known to the Transmitter

“…A fading model where the dark current is fixed but the channel gain is time-varying was studied in [9]. Several multiple-user models were studied in [10]- [15]. Among them, [13] considers the peak-limited continuous-time Poisson channel with spurious photon arrivals at the receiver, where the exact positions of these spurious arrivals are known to the transmitter as channel-state information (CSI) before transmission starts.…”