We present a universal MSE algorithm for lattice decoding in dimensions up to 1024 for both Gaussian and Rayleigh fading channels. This algorithm can be applied to decode high diversity multidimensional rotations. The decoding is performed by a decision feedback equalizer and provides soft output which allows a concatenation of the lattice codes with other type of error-correcting codes. The problem of selecting a good rotation is also considered, and we show that a high dimensional random rotation exhibits very good performance on a Rayleigh fading channel.
