We consider a linear control system in which several signals are transmitted over communication channels with bit rate limitations. With the coding and medium access schemes of the communication system fixed, the achievable bit rates are determined by the allocation of communications resources such as transmit powers and bandwidths, to different communication channels. We model the effect of bit rate limited communication channels by uniform quantization and the quantization errors are modeled by additive white noises whose variances depend on the achievable bit rates. We optimize the stationary performance of the linear system by jointly allocating resources in the communication system and tuning parameters of the controller.