On the Capacity of a Direct-Detection Photon Channel with IntertransitionConstrained Binary Input

The classical direct detection photon channel is modeled by an output v_t(observed signal) describing the photon-arrival Poisson (count) procèss with intensity (rate) λ _t + λ₀, where λ_t (photons/sec) is the channel input (information carrying) intensity and λ₀ (photons/sec) 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 values 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 sec. The upper bounds are derived by exploiting a known relation between mutual information and optimal nonlinear filtering in the Poisson regime. The lower bounds are based on bounding the achievable information rates for (d,∞) coded inputs, commonly used for magnetic recording, 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 capacitv.