Efficient Message-Passing Decoding of LDPC Codes using Vector-based Messages

In this paper we investigate reduced complexity decoders for LDPC codes over M-PSK modulation. Capacity calculations show only minor losses if only phase information is considered in the decoder. We device a decoder based on phase angle summation, which unfortunately does not work for codes over Galois fields (but shows promising results for codes over integer rings). For codes over Galois fields we construct table-based decoders which gives performance close to belief propagation decoders at substantially reduced complexity