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Coded interleaved differential M-ary phase-shift keying (M-DPSK) with iterative decoding, the so-called "Turbo DPSK," is known as a power-efficient transmission format. Due to the rotational invariance of DPSK, it particularly enables detection without channel state information (CSI). However, the soft-input soft-output (SISO) component decoder for DPSK is the computational bottleneck if performance close to the ideal case of perfect CSI is desired. In this paper, we take a fresh look at SISO decoding without CSI and apply sphere decoding (SD) to reduce complexity. In particular, we devise a maximum a posteriori probability (MAP) multiple-symbol differential sphere decoder (MSDSD) which efficiently solves the high-dimensional search problem inherent to detection without CSI. Together with a soft-output generation device the MAP-MSDSD algorithm forms a new SISO-MSDSD module for iterative decoding. We analyze the extrinsic information transfer (EXIT) characteristic of the novel module, by means of which we are able to design powerful encoder and decoder structures. For, respectively, the additive white Gaussian noise (AWGN) and the continuously time-varying Rayleigh-fading channel without CSI these designs operate within 1.7-1.9 and 2.3-2.5 dB of channel capacity assuming perfect CSI. These figures compare favorably with results available in the literature, especially for reasonably high data rates of 1-2 bit/channel use. Simulation studies of the average and the maximum complexity required by SISO-MSDSD demonstrate the advantageous performance versus complexity tradeoff of our approach.