The fast ignitor scheme in inertial confined fusion requires ultrashort laser pulse with high signal-to-noise ratio (SNR). The amplified spontaneous emission (ASE) noise modulations in pump pulse are transferred onto the signal spectrum and these modulations of signal spectrum generate the time-pedestal before and after this main pulse, which degrades the signal-to-noise ratio. The restrictions of the SNR by the random ASE noise and the duration of its pedestal are numerically modeled. A number of ways that can reduce the noise level and increase the signal-to-noise ratio are discussed.