An exhaustive search based lattice decoder for finite dimensional lattice codes is considered. The decoder is genie-aided and can exhaustively search through all possible scaling factors α∈R. We show that this decoder can achieve lower word error rate (WER) than the one-shot decoder using only α_(MMSE) as a scaling factor. A lower bound on the WER for the decoder is found by considering the covering sphere of the lattice Voronoi region. The proposed decoder and the bound are valid for both power-constrained lattice codes and lattices. A method for estimating the WER of the decoder is provided by considering the effective sphere of the lattice Voronoi region, which shows an accurate estimate for lattice codes with sphere-like Voronoi region.
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