591 research outputs found
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
A Non-commutative Cryptosystem Based on Quaternion Algebras
We propose BQTRU, a non-commutative NTRU-like cryptosystem over quaternion
algebras. This cryptosystem uses bivariate polynomials as the underling ring.
The multiplication operation in our cryptosystem can be performed with high
speed using quaternions algebras over finite rings. As a consequence, the key
generation and encryption process of our cryptosystem is faster than NTRU in
comparable parameters. Typically using Strassen's method, the key generation
and encryption process is approximately times faster than NTRU for an
equivalent parameter set. Moreover, the BQTRU lattice has a hybrid structure
that makes inefficient standard lattice attacks on the private key. This
entails a higher computational complexity for attackers providing the
opportunity of having smaller key sizes. Consequently, in this sense, BQTRU is
more resistant than NTRU against known attacks at an equivalent parameter set.
Moreover, message protection is feasible through larger polynomials and this
allows us to obtain the same security level as other NTRU-like cryptosystems
but using lower dimensions.Comment: Submitted for possible publicatio
Sigma Partitioning: Complexity and Random Graphs
A of a graph is a partition of the vertices
into sets such that for every two adjacent vertices and
there is an index such that and have different numbers of
neighbors in . The of a graph , denoted by
, is the minimum number such that has a sigma partitioning
. Also, a of a graph is a
function , such that for every two adjacent
vertices and of , ( means that and are adjacent). The of , denoted by , is the minimum number such
that has a lucky labeling . It was
conjectured in [Inform. Process. Lett., 112(4):109--112, 2012] that it is -complete to decide whether for a given 3-regular
graph . In this work, we prove this conjecture. Among other results, we give
an upper bound of five for the sigma number of a uniformly random graph
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