Cooperation in a cellular network is seen as a key technique in managing other cell interference to observe a gain in achievable rate. In this paper, we present the achievable rates for a cloud radio network using a zero forcing (ZF) equalizer with dirty paper precoding (DPC). We show that when complete channel state information is available at the cloud, rates close to those achievable with total interference cancellation can be achieved. With mean capacity gains, of up to 200% over the conventional cellular network in the downlink, this precoding scheme shows great promise for implementation in a cloud radio network. To simplify the analysis, we use a stochastic geometric framework based on Poisson point processes instead of the traditional grid based cellular network model. We study the impact of limiting the channel state information on the achievable rate. Bounds are developed on the achievable rate with limited feedback. These bounds are shown to be tight while permitting analytical tractability. Specifically, we show that with a limited feedback of about 5-6 channel states from each user, we obtain significant gain compared to conventional systems.