The PPM Poisson Channel: Finite-Length Bounds and Code Design

Abstract

This work 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. 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. Additionally, the design of protograph-based non-binary low-density parity-check (LDPC) codes for the (PPM) Poisson channel is addressed. The order q of the finite field is directly matched to the PPM order, so that no iterative message exchange between the decoder and the demodulator is required. The suggested design turns out to be robust w.r.t. different channel parameters, yielding performances within 0.5 dB from the theoretical benchmarks.