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This paper investigates quantization of channel state information (CSI) and bit allocation across wireless links in a multi-source, single-relay cooperative cellular network. Our goal is to minimize the loss in performance, measured as the achievable sum rate, due to limited-rate quantization of CSI. We develop both a channel quantization scheme and allocation of limited feedback bits to the various wireless links. We assume that the quantized CSI is reported to a central node responsible for optimal resource allocation. We first derive tight lower and upper bounds on the difference in rates between the perfect CSI and quantized CSI scenarios. These bounds are then used to derive an effective quantizer for arbitrary channel distributions. Next, we use these bounds to optimize the allocation of bits across the links subject to a budget on total available quantization bits. In particular, we show that the optimal bit allocation algorithm allocates more bits to those links in the network that contribute the most to the sum-rate. Finally, the paper investigates the choice of the central node; we show that this choice plays a significant role in CSI bits required to achieve a target performance level.