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In this paper we propose low complexity LDPC code design and decoding in Z4 which may be useful to combat phase ambiguities in wireless links affected by strong phase noise. We approximate messages exchanged on the Tanner graph using separable probability density functions. This allows a substantial reduction of decoder memory and complexity, with a negligible performance penalty, compared to ideal Z4 decoding. Furthermore, we show that the Density Evolution analysis of this suboptimal decoder leads to irregular LDPC designs matching the criteria of binary LDPC codes.