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Addressing orthogonal frequency division multiplexing (OFDM) transmissions over frequency-selective Rayleigh fading channels, we propose a differential space-time-frequency (DSTF) coding scheme with maximum multipath diversity. Resorting to subcarrier grouping, we convert the system into a set of parallel DSTF systems, within which DSTF coding is considered. Through pairwise error probability (PEP) analysis, we prove that full diversity gain, which is the product of the number of transmit antennas, receive antennas, and the multipath channel length, can be achieved without channel state information (CSI) at the receiver. We analyze the performance of group DSTF coding over correlated fading channels and establish the design criteria for subcarrier selection and code selection. In addition to applying existing differential unitary diagonal codes, we propose a systematic approach to designing nondiagonal codes for DSTF systems, which are block diagonal (BD) and have the necessary unitary and full diversity properties. Based on permutation techniques, we have devised new excellent-performing BD DSTF codes, which significantly improve the coding gain as compared to their diagonal counterparts. Corroborating simulations confirm the merits of our approach.