Lattice reduction does not change the solution vector for many algorithms in vector perturbation precoding due to a unique lattice structure, and LLL-aided nearest plane methods do not beat conventional THP under mutual information.
Effects of the LLL Reduction on the Success Probability of the Babai Point and on the Complexity of Sphere Decoding,
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Is Lattice Reduction Necessary for Vector Perturbation Precoding?
Lattice reduction does not change the solution vector for many algorithms in vector perturbation precoding due to a unique lattice structure, and LLL-aided nearest plane methods do not beat conventional THP under mutual information.