44 research outputs found
Decoding by Embedding: Correct Decoding Radius and DMT Optimality
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP)
are the core algorithmic problems on Euclidean lattices. They are central to
the applications of lattices in many problems of communications and
cryptography. Kannan's \emph{embedding technique} is a powerful technique for
solving the approximate CVP, yet its remarkable practical performance is not
well understood. In this paper, the embedding technique is analyzed from a
\emph{bounded distance decoding} (BDD) viewpoint. We present two complementary
analyses of the embedding technique: We establish a reduction from BDD to
Hermite SVP (via unique SVP), which can be used along with any Hermite SVP
solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL)
algorithm), and show that, in the special case of LLL, it performs at least as
well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis
helps to explain the folklore practical observation that unique SVP is easier
than standard approximate SVP. It is proven that when the LLL algorithm is
employed, the embedding technique can solve the CVP provided that the noise
norm is smaller than a decoding radius , where
is the minimum distance of the lattice, and . This
substantially improves the previously best known correct decoding bound . Focusing on the applications of BDD to decoding of
multiple-input multiple-output (MIMO) systems, we also prove that BDD of the
regularized lattice is optimal in terms of the diversity-multiplexing gain
tradeoff (DMT), and propose practical variants of embedding decoding which
require no knowledge of the minimum distance of the lattice and/or further
improve the error performance.Comment: To appear in IEEE Transactions on Information Theor
Integer-Forcing MIMO Linear Receivers Based on Lattice Reduction
A new architecture called integer-forcing (IF) linear receiver has been
recently proposed for multiple-input multiple-output (MIMO) fading channels,
wherein an appropriate integer linear combination of the received symbols has
to be computed as a part of the decoding process. In this paper, we propose a
method based on Hermite-Korkine-Zolotareff (HKZ) and Minkowski lattice basis
reduction algorithms to obtain the integer coefficients for the IF receiver. We
show that the proposed method provides a lower bound on the ergodic rate, and
achieves the full receive diversity. Suitability of complex
Lenstra-Lenstra-Lovasz (LLL) lattice reduction algorithm (CLLL) to solve the
problem is also investigated. Furthermore, we establish the connection between
the proposed IF linear receivers and lattice reduction-aided MIMO detectors
(with equivalent complexity), and point out the advantages of the former class
of receivers over the latter. For the and MIMO
channels, we compare the coded-block error rate and bit error rate of the
proposed approach with that of other linear receivers. Simulation results show
that the proposed approach outperforms the zero-forcing (ZF) receiver, minimum
mean square error (MMSE) receiver, and the lattice reduction-aided MIMO
detectors.Comment: 9 figures and 11 pages. Modified the title, abstract and some parts
of the paper. Major change from v1: Added new results on applicability of the
CLLL reductio
Wyner-Ziv reconciliation for key exchange based on Ring-LWE
We consider a key encapsulation mechanism (KEM) based on ring-LWE where reconciliation is performed on an N-dimensional lattice using Wyner-Ziv coding. More precisely, we consider Barnes-Wall lattices and use Micciancio and Nicolosi's bounded distance decoder with polynomial complexity O(N log(N)^2). We show that in the asymptotic regime for large N, the achievable key rate is Θ(log N) bits per dimension, while the error probability P_e ≈ O(e −Nε). Unlike previous works, our scheme does not require a dither