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Considering high-order digital modulation schemes, the bottleneck in consumer products is the detector rather than the modulator. The complexity of the optimal a posteriori probability (APP) detector increases exponentially with respect to the number of modulated bits per data symbol. Thus, it is necessary to develop low-complexity detection algorithms with an APP-like performance, especially when performing iterative detection, for example in conjunction with bit interleaved coded modulation. We show that a special case of superposition modulation, dubbed Direct Superposition Modulation (DSM), is particularly suitable for complexity reduction at the receiver side. As opposed to square QAM, DSM achieves capacity without active signal shaping. The main contribution is a low-cost detection algorithm for DSM, which enables iterative detection by taking a priori information into account. This algorithm exploits the approximate piecewise linear behavior of the soft outputs of an APP detector over the entire range of detector input values. A theoretical analysis and simulation results demonstrate that at least max-log APP performance can be reached, while the complexity is significantly reduced compared to classical APP detection. Keywords: Digital modulation, Demodulation, Detection algorithms, Linear approximation