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We propose and experimentally demonstrate the use of an incoherent spectrally sliced amplified spontaneous emission (ASE) source as the pump for broadband stimulated Brillouin scattering-based slow light. Both 2.5-Gb/s on-off-keyed and differential-phase-shift-keyed signals are continuously delayed by as much as 170 ps, with less than 4-dB power penalty at 10-9 bit error rate. A 2-GHz and a 4-GHz spectrally sliced pump are compared, emphasizing the need of optimizing the slow-light spectral-width according to the signal bandwidth. Furthermore, independent and simultaneous delay on multiple data channels with different modulation formats within a single slow-light medium is proposed and experimentally demonstrated by using a periodically spectrally sliced ASE source. Our approach might be useful in future heterogeneous multiformat, multibit-rate, and multichannel fiber-optic communication systems and networks.