Noncoherent multi-user detection schemes are attractive in massive MIMO uplink systems. In particular, sorted decision-feedback differential detection (DFDD) in combination with noncoherent decision-feedback equalization (nDFE) over the users has been shown to perform well, avoiding the need for channel estimation. So far, integrating channel coding in massive MIMO systems requires knowledge of the channel, where reliability information for the bits is calculated after combining a large number of symbol observations at the receiver. In this paper, we address one method to calculate reliability information by augmenting the sorted decision-feedback differential detection process. To this end, an equivalent trellis-encoder representation of bit-to-symbol mapping and differential encoding is established. Based on this, log-likelihood ratios for the differential symbols can be calculated. The performance of soft-decision decoding in noncoherent massive MIMO systems is assessed by means of numerical simulations and compared to that of a coherent scheme using channel estimation.
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