Bounded Distance Decoding for Random Lattices
Computational Complexity
2025-06-23 v1
Abstract
The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for these ensembles the BDD problem is NP-hard in the worst case. Then, we introduce a polynomial-time algorithm based on singular value decomposition (SVD) and establish, both theoretically and through extensive experiments, that, for a random selected lattice from the same ensemble, the algorithm solves the BDD problem with high probability. To the best of our knowledge, this work provides the first example of a lattice problem that is NP-hard in the worst case yet admits a polynomial time algorithm on the average case.
Cite
@article{arxiv.2506.16662,
title = {Bounded Distance Decoding for Random Lattices},
author = {Shuhong Gao},
journal= {arXiv preprint arXiv:2506.16662},
year = {2025}
}