63 research outputs found
Full Diversity Unitary Precoded Integer-Forcing
We consider a point-to-point flat-fading MIMO channel with channel state
information known both at transmitter and receiver. At the transmitter side, a
lattice coding scheme is employed at each antenna to map information symbols to
independent lattice codewords drawn from the same codebook. Each lattice
codeword is then multiplied by a unitary precoding matrix and sent
through the channel. At the receiver side, an integer-forcing (IF) linear
receiver is employed. We denote this scheme as unitary precoded integer-forcing
(UPIF). We show that UPIF can achieve full-diversity under a constraint based
on the shortest vector of a lattice generated by the precoding matrix . This constraint and a simpler version of that provide design criteria for
two types of full-diversity UPIF. Type I uses a unitary precoder that adapts at
each channel realization. Type II uses a unitary precoder, which remains fixed
for all channel realizations. We then verify our results by computer
simulations in , and MIMO using different QAM
constellations. We finally show that the proposed Type II UPIF outperform the
MIMO precoding X-codes at high data rates.Comment: 12 pages, 8 figures, to appear in IEEE-TW
On Massive MIMO Physical Layer Cryptosystem
In this paper, we present a zero-forcing (ZF) attack on the physical layer
cryptography scheme based on massive multiple-input multiple-output (MIMO). The
scheme uses singular value decomposition (SVD) precoder. We show that the
eavesdropper can decrypt/decode the information data under the same condition
as the legitimate receiver. We then study the advantage for decoding by the
legitimate user over the eavesdropper in a generalized scheme using an
arbitrary precoder at the transmitter. On the negative side, we show that if
the eavesdropper uses a number of receive antennas much larger than the number
of legitimate user antennas, then there is no advantage, independent of the
precoding scheme employed at the transmitter. On the positive side, for the
case where the adversary is limited to have the same number of antennas as
legitimate users, we give an upper bound on the
advantage and show that this bound can be approached using an inverse precoder.Comment: To be presented at ITW 2015, Jeju Island, South Korea. 6 Pages, 1
Figur
On the performance of 1-level LDPC lattices
The low-density parity-check (LDPC) lattices perform very well in high
dimensions under generalized min-sum iterative decoding algorithm. In this work
we focus on 1-level LDPC lattices. We show that these lattices are the same as
lattices constructed based on Construction A and low-density lattice-code
(LDLC) lattices. In spite of having slightly lower coding gain, 1-level regular
LDPC lattices have remarkable performances. The lower complexity nature of the
decoding algorithm for these type of lattices allows us to run it for higher
dimensions easily. Our simulation results show that a 1-level LDPC lattice of
size 10000 can work as close as 1.1 dB at normalized error probability (NEP) of
.This can also be reported as 0.6 dB at symbol error rate (SER) of
with sum-product algorithm.Comment: 1 figure, submitted to IWCIT 201
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
Lattice Codes for CRYSTALS-Kyber
This paper describes a constant-time lattice encoder for the National
Institute of Standards and Technology (NIST) recommended post-quantum
encryption algorithm: Kyber. The first main contribution of this paper is to
refine the analysis of Kyber decoding noise and prove that Kyber decoding noise
can be bounded by a sphere. This result shows that the Kyber encoding problem
is essentially a sphere packing in a hypercube. The original Kyber encoder uses
the integer lattice for sphere packing purposes, which is far from optimal. Our
second main contribution is to construct optimal lattice codes to ensure denser
packing and a lower decryption failure rate (DFR). Given the same ciphertext
size as the original Kyber, the proposed lattice encoder enjoys a larger
decoding radius, and is able to encode much more information bits. This way we
achieve a decrease of the communication cost by up to 32.6%, and a reduction of
the DFR by a factor of up to 2^{85}. Given the same plaintext size as the
original Kyber, e.g., 256 bits, we propose a bit-interleaved coded modulation
(BICM) approach, which combines a BCH code and the proposed lattice encoder.
The proposed BICM scheme significantly reduces the DFR of Kyber, thus enabling
further compression of the ciphertext. Compared with the original Kyber
encoder, the communication cost is reduced by 24.49%, while the DFR is
decreased by a factor of 2^{39}. The proposed encoding scheme is a
constant-time algorithm, thus resistant against the timing side-channel
attacks.Comment: 22 pages,3 figure
Phase Precoded Compute-and-Forward with Partial Feedback
In this work, we propose phase precoding for the compute-and-forward (CoF)
protocol. We derive the phase precoded computation rate and show that it is
greater than the original computation rate of CoF protocol without precoder. To
maximize the phase precoded computation rate, we need to 'jointly' find the
optimum phase precoding matrix and the corresponding network equation
coefficients. This is a mixed integer programming problem where the optimum
precoders should be obtained at the transmitters and the network equation
coefficients have to be computed at the relays. To solve this problem, we
introduce phase precoded CoF with partial feedback. It is a quantized precoding
system where the relay jointly computes both a quasi-optimal precoder from a
finite codebook and the corresponding network equations. The index of the
obtained phase precoder within the codebook will then be fedback to the
transmitters. A "deep hole phase precoder" is presented as an example of such a
scheme. We further simulate our scheme with a lattice code carved out of the
Gosset lattice and show that significant coding gains can be obtained in terms
of equation error performance.Comment: 5 Pages, 4 figures, submitted to ISIT 201
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