PPM Poisson Channel

This report investigates the finite-length block error probability for the pulse position modulation (PPM) Poisson channel. Amongst, expressions for the Gallager random coding bound (RCB) and the Gaussian approximation of the converse theorem are derived (with a refinement of the third order term). Likewise, we introduce an erasure channel (EC) approximation that allows the application of known EC bounds to the PPM Poisson channel by matching the channel capacities. We show that the derived benchmarks are not only simple to compute, but also accurate. Moreover, an attempt to get a Dependence Testing (DT) bound is reported.