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

TL;DR

This paper introduces a randomized lattice decoding method using Klein's sampling technique, enhancing performance over traditional algorithms and achieving near-ML performance in moderate dimensions with efficient implementation.

Contribution

It presents a novel randomized decoding algorithm based on Klein's sampling, with optimized decoding radius and efficient implementation, improving performance and computational efficiency.

Findings

Achieves near-ML performance with moderate samples in dimensions up to 32.

Provides a fixed gain in decoding radius over Babai's decoding at polynomial complexity.

Demonstrates effectiveness in moderate dimensions where sphere decoding is costly.

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.