This paper considers stabilization of parametrically uncertain systems via lossy and data-rate-constrained channels. We propose a quantization scheme which helps to reduce the required data rate for the stabilization compared with the case using the uniform quantizer; the existing works tackling the control of uncertain systems over communication channels commonly use the uniform quantizer. For systems utilizing the new quantizer, a necessary condition and a sufficient condition are derived. The conditions demonstrate limitations and tradeoffs among data rate, packet loss probability, and uncertainty bounds on plant parameters for stabilization.