We have demonstrated error-free operations of slow-light via stimulated Brillouin scattering (SBS) in optical fiber for 10-Gb/s signals with different modulation formats, including non-return-to-zero (NRZ), phase-shaped binary transmission (PSBT) and differential phase-shiftkeying (DPSK). The SBS gain bandwidth is broadened by using current noise modulation of the pump laser diode. The gain shape is simply controlled by the noise density function. Super-Gaussian noise modulation of the Brillouin pump allows a flat-top and sharp-edge SBS gain spectrum, which can reduce slow-light induced distortion in case of 10-Gb/s NRZ signal. The corresponding maximal delay-time with error-free operation is 35 ps. Then we propose the PSBT format to minimize distortions resulting from SBS filtering effect and dispersion accompanied with slow light because of its high spectral efficiency and strong dispersion tolerance. The sensitivity of the 10-Gb/s PSBT signal is 5.2 dB better than the NRZ case with a same 35-ps delay. The maximal delay of 51 ps with error-free operation has been achieved. Futhermore, the DPSK format is directly demodulated through a Gaussian-shaped SBS gain, which is achieved using Gaussian-noise modulation of the Brillouin pump. The maximal error-free time delay after demodulation of a 10-Gb/s DPSK signal is as high as 81.5 ps, which is the best demonstrated result for 10-Gb/s slow-light.