We propose a lattice coding scheme that achieves the capacity of the compound block-fading channel. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. A by-product of our results is a refined analysis of the probability of error of the lattice Gaussian distribution in the AWGN channel.
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