Differential Encoding for Quadrature-Amplitude Modulation

In this paper, we propose a novel differential encoder for QAM (quadrature-amplitude modulation), by a look-up table instead of a rule. Using a table for differential encoding has the advantages of both low complexity and good error performance. We propose algorithms to construct the table for maximizing the minimum noncoherent distance and minimizing the number of different data bits between two near codewords. For 16QAM, we show that the differential encoder obtained by the proposed algorithms is optimal in terms of minimum noncoherent distance.