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A new precoder that reduces the feedback overhead in an orthogonal frequency-division multiplexing (OFDM)-based relay network is proposed. A joint singular value decomposition (SVD) and QR decomposition is employed on the source-destination link and the source-relay-destination link. Using the proposed precoder, only one precoding matrix needs to be fed back, independent of the total number of subcarriers. Kernel density estimation is applied to determine approximate forms of unknown distributions of the end-to-end effective channel powers obtained by this precoder. Using approximated probability density functions (pdfs) for these effective channel powers, closed-form expressions for the link achievable average sum-rate and the outage probability can be derived and then their accuracies verified via Monte Carlo simulations. The achievable sum-rates are also compared with that of SVD-based precoders and for varying codebook size.