A robust pulse position coded modulation scheme for the Poisson channel

A coded modulation scheme for the Poisson channel is investigated. The scheme relies on the serial concatenation of an outer low-density parity-check (LDPC) code over an order-q finite field and q-ary pulse position modulation (PPM). Due to the matching between code and modulation symbols, no iterative message exchange between the decoder and the modulator is required. The PPM capacity limit serves as a reference to evaluate the efficiency of the proposed scheme in the asymptotic setting via density evolution. A simplified form of the Gallager random coding bound (RCB) is also developed and used as a reference for the finite-length performance of the coded modulation scheme. The optimization via density evolution is performed on a surrogate (erasure) channel, yielding excellent iterative decoding thresholds for a wide range of channel parameters. The proposed coded modulation technique performs close to the theoretical bounds not only asymptotically, but also for moderate block lengths. It turns to represent a viable solution for deep-space direct detection optical links, for which the Poisson channel is adopted as a model.