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When multiple video streams are present in an ad hoc network, they share and compete for the common network resources. A rate allocation algorithm must balance the available resources among the video streams in a fair and efficient manner. In addition, it is desirable to have a distributed solution so that nodes do not need to collect global information of the network and that the computational burden can be shared. We propose a distributed rate allocation algorithm which minimizes the total distortion of all video streams. Based on the subgradient method, the proposed scheme only requires link price updates at each relay node based on local observations and rate adaptations at each source node derived from rate-distortion (RD) models of the video. Simulation results show that the proposed scheme can achieve the same optimal rate allocation as that obtained from exhaustive search.