We investigate design and performance of communications over the bandlimited Gaussian channel with one-bit output quantization. A transceiver structure is proposed, which generates the channel input using a finite set of time-limited and approximately bandlimited waveforms, and performs oversampling on the channel output by an integrate-and-dump filter preceding the one-bit quantizer. The waveform set is constructed based on a specific bandlimited random process with certain zero-crossing properties which can be utilized to convey information. In the presence of the additive white Gaussian noise, a discrete memoryless channel model of our transceiver is derived. Consequently, we determine a closed-form expression for the high signal-to-noise-ratio (SNR) asymptotic information rate of the transceiver, which can be achieved by independent and identically distributed input symbols. By evaluating the fractional power containment bandwidth, we further show that at high SNR, the achievable spectral efficiency grows roughly logarithmically with the oversampling factor, coinciding with a notable result in the absence of noise [19]. Moreover, the error performance of our transceiver is evaluated by low density parity check coded modulation. Numerical results demonstrate that reliable communication at rates exceeding one bit per Nyquist interval can be achieved at moderate SNR.