In this paper we investigate reduced complexitydecoders for LDPC codes over M-PSK modulation. Capacitycalculations show only minor losses if only phase informationis considered in the decoder. We device a decoder based onphase angle summation, which unfortunately does not work forcodes over Galois fields (but shows promising results for codesover integer rings). For codes over Galois Fields we constructtable-based decoders which gives performance close to BeliefPropagation decoders at substantially reduced complexity.