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This letter describes a belief-propagation decoder for low-density lattice codes of finite dimension, in which the messages are represented as single Gaussian functions. Compared to previously-proposed decoders, memory is reduced because each message consists of only two values, the mean and variance. Complexity is also reduced because the check node operations are on single Gaussians, avoiding approximations needed previously, and because the variable node performs approximations on a smaller number of Gaussians. For lattice dimension n = 1000 and 10,000, this decoder looses no more than 0.1 dB in SNR, compared to the decoders which use much more memory.