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We present a loadable and erasable all-optical fiber storage buffer based on parametric gain and cross-phase modulation (XPM) loading. The gain is provided by a phase-sensitive amplifier (PSA), implemented as a Sagnac interferometer, and relies on the nonlinear interaction within standard dispersion-shifted fiber. PSAs inherently have the property of stabilizing ones and zeros and thus eliminate the need to use optical filters within the buffer, or the need for any other kind of intensity discriminator. The action of the PSA is then twofold. It provides the gain and also achieves bistability of the buffer, which gives it an advantage over a linear amplifier such as erbium-doped fiber amplifier for our experimental configuration. External data are written into the buffer using wavelength-induced XPM. This method is insensitive to the optical phase of the incoming data and thus does not require tracking of its phase. The buffer is erased by employing a nonlinear optical loop mirror as a switch. We demonstrate storage of picosecond pulse packets at bit rates of 1 Gb/s for periods of time up to 1 ms.