It has been recognized that the impulsive noise (IN) generated by power devices poses significant challenges to wireless receivers. In this paper, we comprehensively assess the achievable information rate (AIR) for the well-established Markov-Middleton IN model with a phase-shift keying (PSK) input sequence across various channel conditions, including matched and mismatched decoding scenarios. Upon determining information-theoretic bounds, we propose an optimal turbo-DPSK-IN receiver design based on a commonly used commercial transmission setup consisting of a convolutional encoder, bit-level interleaver, and a differential PSK (DPSK) symbol mapper. We show that by incorporating the differential decoder into the maximum a-posteriori-based (MAP) IN detector, we can significantly enhance the receiver performance with a 4.5dB gain compared to the conventional MAP-based PSK-IN receiver and a gap of around 1dB to the theoretical bounds. We also propose a suboptimal separate receiver design that can be implemented with half the complexity of the joint design and near-optimal performance. We have evaluated the performance of the proposed receiver designs through extensive simulations, demonstrating their effectiveness in real-world scenarios with limited interleaver depth and mismatched state implementation.