On the capacity of a direct-detection photon channel with intertransition-constrained binary input

The classical directed detection photon channel is modeled by an output ν_t (observed signal) describing the photon-arrival Poisson (count) process with intensity (rate) λ_t+λ₀, where λ_t (photons/s) is the channel input (information carrying) intensity and λ₀ (photons/s) is the dark current intensity. Upper and lower bounds on the capacity of this channel are presented for two-level (binary) inputs taking on the extreme value λ_t ∈ {0,A}, where A denotes the peak power satisfying an average power constraint E(λ_t)⩽σ and having no level intertransition intervals shorter than Δ s. The upper bounds are derived by exploiting a known relation between mutual information rates for (d, ∞) coded inputs, where d is selected to satisfy the intertransition constraint and to optimize the bounds. In the case of no intertransition constraint, the lower and upper bounds coincide with the known exact capacity