Differential amplitude phase shift keying (DAPSK) is a promising modulation technique for use in high-mobility environments, as it does not require channel estimation. In this paper, a novel reduced complexity soft demodulator for high-order DAPSK constellations is proposed. The main idea relies on a two-step approximation of the sum-log demapper. In the first step, a parallel factor analysis (PARAFAC) decomposition is used to approximate log-likelihood ratios. Next, the basis functions obtained through the first step are approximated by piecewise-linear curves. Numerical optimization techniques are employed for the PARAFAC decomposition and its piecewise-linear approximation whose parameters are then stored in a lookup table. It has been verified through computer simulations that the proposed scheme clearly outperforms the scheme proposed in the paper “Reduced-complexity noncoherent soft-decision-aided DAPSK dispensing with channel estimation,” (IEEE Trans. Veh. Technol., vol. 62, pp. 2633-2643, 2013.), while also having lower computational cost. Moreover, it is shown that the performance of the exact sum-log demapper and the proposed demapper is very close for 2 × 4 and 4 × 16 DAPSK constellations.