18,476 research outputs found
On Pseudocodewords and Improved Union Bound of Linear Programming Decoding of HDPC Codes
In this paper, we present an improved union bound on the Linear Programming
(LP) decoding performance of the binary linear codes transmitted over an
additive white Gaussian noise channels. The bounding technique is based on the
second-order of Bonferroni-type inequality in probability theory, and it is
minimized by Prim's minimum spanning tree algorithm. The bound calculation
needs the fundamental cone generators of a given parity-check matrix rather
than only their weight spectrum, but involves relatively low computational
complexity. It is targeted to high-density parity-check codes, where the number
of their generators is extremely large and these generators are spread densely
in the Euclidean space. We explore the generator density and make a comparison
between different parity-check matrix representations. That density effects on
the improvement of the proposed bound over the conventional LP union bound. The
paper also presents a complete pseudo-weight distribution of the fundamental
cone generators for the BCH[31,21,5] code
Improving random number generators by chaotic iterations. Application in data hiding
In this paper, a new pseudo-random number generator (PRNG) based on chaotic
iterations is proposed. This method also combines the digits of two XORshifts
PRNGs. The statistical properties of this new generator are improved: the
generated sequences can pass all the DieHARD statistical test suite. In
addition, this generator behaves chaotically, as defined by Devaney. This makes
our generator suitable for cryptographic applications. An illustration in the
field of data hiding is presented and the robustness of the obtained data
hiding algorithm against attacks is evaluated.Comment: 6 pages, 8 figures, In ICCASM 2010, Int. Conf. on Computer
Application and System Modeling, Taiyuan, China, pages ***--***, October 201
Improving chaos-based pseudo-random generators in finite-precision arithmetic
One of the widely-used ways in chaos-based cryptography to generate pseudo-random
sequences is to use the least significant bits or digits of finite-precision numbers defined by the chaotic
orbits. In this study, we show that the results obtained
using such an approach are very prone to rounding
errors and discretization effects. Thus, it appears that
the generated sequences are close to random even when parameters correspond to non-chaotic oscillations. In
this study, we confirm that the actual source of pseudo-random properties of bits in a binary representation
of numbers can not be chaos, but computer simulation. We propose a technique for determining the maximum number of bits that can be used as the output of
a pseudo-random sequence generator including chaos-based algorithms. The considered approach involves
evaluating the difference of the binary representation of
two points obtained by different numerical methods of
the same order of accuracy. Experimental results show
that such estimation can significantly increase the performance of the existing chaos-based generators. The
obtained results can be used to reconsider and improve
chaos-based cryptographic algorithms
Driving Markov chain Monte Carlo with a dependent random stream
Markov chain Monte Carlo is a widely-used technique for generating a
dependent sequence of samples from complex distributions. Conventionally, these
methods require a source of independent random variates. Most implementations
use pseudo-random numbers instead because generating true independent variates
with a physical system is not straightforward. In this paper we show how to
modify some commonly used Markov chains to use a dependent stream of random
numbers in place of independent uniform variates. The resulting Markov chains
have the correct invariant distribution without requiring detailed knowledge of
the stream's dependencies or even its marginal distribution. As a side-effect,
sometimes far fewer random numbers are required to obtain accurate results.Comment: 16 pages, 4 figure
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