# Decoding by Sampling: A Randomized Lattice Algorithm for Bounded Distance Decoding

(formerly "Randomized Lattice Decoding")
### Shuiyin Liu, Cong Ling and Damien Stehlé

Abstract: Despite its reduced complexity, lattice reduction-aided
decoding exhibits a widening gap to maximum-likelihood (ML)
performance as the dimension increases. To improve its performance,
this paper presents randomized lattice decoding based on Klein's
sampling technique, which is a randomized version of Babai's nearest
plane algorithm (i.e., successive interference cancelation (SIC)). To
find the closest lattice point, Klein's algorithm is used to sample
some lattice points and the closest among those samples is
chosen. Lattice reduction increases the probability of finding the
closest lattice point, and only needs to be run once during
pre-processing. Further, the sampling can operate very efficiently in
parallel. The technical contribution of this paper is two-fold: we
analyze and optimize the decoding radius of sampling decoding
resulting in better error performance than Klein's original algorithm,
and propose a very efficient implementation of random rounding. Of
particular interest is that a fixed gain in the decoding radius
compared to Babai's decoding can be achieved at polynomial
complexity. The proposed decoder is useful for moderate dimensions
where sphere decoding becomes computationally intensive, while lattice
reduction-aided decoding starts to suffer considerable
loss. Simulation results demonstrate near-ML performance is achieved
by a moderate number of samples, even if the dimension is as high as
32.
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