Analysis of Symbol Message Passing LDPC Decoder for the Poisson PPM Channel

A simple decoding algorithm, dubbed symbol message passing decoder, is studied for q-ary low-density parity-check codes over the q-ary Poisson pulse-position modulation channel. The messages in the decoder are symbols from the finite field ${\mathbb{F}_q}$. To improve performance, a second decoder with an extended message set $\left\{ {{\text{E}} \cup {\mathbb{F}_q}} \right\}$ is also investigated, where E denotes an erasure. Thresholds within 1.3 dB from the Shannon limit are obtained for low field orders.