Symbol Message Passing Decoding of LDPC Codes for Orthogonal Modulations

A simple decoder for q-ary low-density parity-check codes is studied, termed symbol message passing. The decoder passes hard decisions from a q-ary alphabet. For orthogonal modulations over the additive white Gaussian channel for which the modulation order and the field order q are equal, it is shown that the extrinsic messages can be modelled as observations of a q-ary symmetric channel, allowing to work out density evolution equations. A stability analysis is provided which emphasizes the influence of degree-3 variable nodes. Simulation results show performance gains for increasing q w.r.t. binary low-density parity-check codes with bit-interleaved coded modulation, and potential savings in decoding complexity.