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Next generation high data rate applications such as High-Definition (HD) video transmission place a heavy load on wireless network resources. To achieve the strict quality of service requirements of HD video in a multi-user network requires efficient resource allocation. Rate-distortion theory provides an appropriate basis for this. The Nash Bargaining Solution (NBS) is proven to generate an optimal solution to a rate-distortion based convex resource allocation problem. Particle Swarm Optimization (PSO) is a meta-heuristic optimizer capable of generating near-optimal solutions. PSO, however, is not constrained to convex optimization problems. The motivation of this work is to demonstrate a PSO implementation capable of achieving an optimal solution to the resource allocation problem. The capability of the PSO approach to reach an optimal solution suggests its potential for resource allocation in a network of heterogeneous applications where convex optimization methods do not apply.