In this paper, we propose a limited rate feedback scheme for decode-and-forward (DF) relay-assisted networks. It is assumed that the cellular user is far from the base station such that the direct communication is impossible and communication is performed with the help of a DF relay. To study the limited feedback channel, two cases are proposed: Perfect channel distribution information (CDI)-quantized channel state information (CSI) and quantized CDI-quantized CSI. While in the former, the space of channel gains is quantized into a finite number of regions, in the latter case, the space of CDI parameters is also quantized. We formulate the proposed resource allocation into an optimization problem whose objective is to maximize the average achievable rate under an average transmission power constraint. To solve the proposed optimization problems, we adopt the block coordinated descent algorithm, which is based on the space of variables partitioning into finite sets, and particle swarm optimization (PSO), which is an evolutionary computation technique. To solve the optimization problem for quantized CDI-quantized CSI case, we consider an approach based on the Lloyd algorithm. We also model and study the error in the feedback channel. Finally, the impact of different system parameters on the performance of the proposed scheme is investigated through simulations.