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

Abstract

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 Fq. To improve performance, a second decoder with an extended message set {E ∪ Fq} is also investigated, where E denotes an erasure. Thresholds within 1.3 dB from the Shannon limit are obtained for low field orders.