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The performance of future ultralong-haul communication systems exploiting phase-encoded signals is likely to be compromised by nonlinear phase noise generated during signal transmission. One potential way to mitigate against nonlinear phase noise is to use phase-sensitive amplifiers (PSAs) that have been demonstrated to help remove such phase noise as well as to provide simultaneous signal amplitude noise suppression when operated in saturation. Recently, we have shown that a PSA-based signal regenerator based on degenerate four-wave mixing could be implemented in a network-compatible manner in which only the (noisy) signal is present at the device input (black-box operation). However, this scheme was tested only with relatively high-frequency deterministic perturbations applied to the signal. Here, we address both theoretically and experimentally the important issue of how such a regenerator works with more realistic random broadband amplitude/phase noise distributions. Good regenerative performance is demonstrated and our study also illustrates an additional unique feature of PSA-based regenerators-namely error correction for differentially encoded signals when placed in front of a DPSK receiver. Furthermore, we present a simplified regenerator implementation providing highly stable operation and representing a significant further step toward a practical device.