Symbol Message Passing Decoding of LDPC Codes for Orthogonal Modulations

Abstract

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.

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

“…In this work, we extend the results of [14]. First, we adapt the SMP decoder to Poisson channels with orthogonal (PPM) modulations where the field size q and the modulation order are equal.…”

“…We also observe from Tables I and II that the gap to the Shannon limit increases as n b increases, e.g., from 1.3 dB for n b = 0.002 to 1.8 dB for n b = 0.1 in case of q = 8 and SEMP. The complexity analysis of SMP was provided in [14] showing that SMP decoding might be a good choice when low-complexity decoding is targeted. Finally, DE on a surrogate QEC yields ensembles with similar thresholds as DE on the Poisson PPM channel for n b ∈ {0.002, 0.1}, confirming the validity of a surrogate QEC code design.…”

“…Messages in the decoder consist of the most reliable symbol only, but variable node (VN) processors are able to exploit soft information. In [14] additive white Gaussian noise (AWGN) channels with orthogonal modulations are considered, where the field size q matches the modulation order. Also a complexity discussion is provided in [14] showing favorable decoding complexity compared to binary LDPC codes with non-binary modulations.…”