In this paper, we consider a distributed resource allocation problem with communication limitation. We propose a gradient-descent algorithm to solve the distributed resource allocation problem with quantization mechanism due to the communication limitations or in order to reduce the communication cost in the network. With carefully selected parameters, the convergence and correctness of the quantized algorithm can be obtained for fixed communication topologies and moreover, extended to switching jointly connected topologies. The exact optimal value can be obtained, which is different from some existing works, whose convergence accuracies were limited by the quantization bandwidth. In addition, the data rate of the proposed algorithm is also analyzed for both fixed and switching communication networks. Particularly, in the fixed topology case, we obtain that 1 bit is sufficient to solve the distributed problem with the proposed algorithm.
