925 research outputs found
Tensor-based trapdoors for CVP and their application to public key cryptography
We propose two trapdoors for the Closest-Vector-Problem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a lattice-based cryptosystem which resembles to the McEliece scheme
Construction of Capacity-Achieving Lattice Codes: Polar Lattices
In this paper, we propose a new class of lattices constructed from polar
codes, namely polar lattices, to achieve the capacity \frac{1}{2}\log(1+\SNR)
of the additive white Gaussian-noise (AWGN) channel. Our construction follows
the multilevel approach of Forney \textit{et al.}, where we construct a
capacity-achieving polar code on each level. The component polar codes are
shown to be naturally nested, thereby fulfilling the requirement of the
multilevel lattice construction. We prove that polar lattices are
\emph{AWGN-good}. Furthermore, using the technique of source polarization, we
propose discrete Gaussian shaping over the polar lattice to satisfy the power
constraint. Both the construction and shaping are explicit, and the overall
complexity of encoding and decoding is for any fixed target error
probability.Comment: full version of the paper to appear in IEEE Trans. Communication
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
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