100 research outputs found
Profitable Double-Spending Attacks
Our aim in this paper is to investigate the profitability of double-spending
(DS) attacks that manipulate a priori mined transaction in a blockchain. Up to
date, it was understood that the requirement for successful DS attacks is to
occupy a higher proportion of computing power than a target network's
proportion; i.e., to occupy more than 51% proportion of computing power. On the
contrary, we show that DS attacks using less than 50% proportion of computing
power can also be vulnerable. Namely, DS attacks using any proportion of
computing power can occur as long as the chance to making a good profit is
there; i.e., revenue of an attack is greater than the cost of launching it. We
have novel probability theory based derivations for calculating time finite
attack probability. This can be used to size up the resource needed to
calculate the revenue and the cost. The results enable us to derive sufficient
and necessary conditions on the value of a target transaction which make DS
attacks for any proportion of computing power profitable. They can also be used
to assess the risk of one's transaction by checking whether or not the
transaction value satisfies the conditions for profitable DS attacks. Two
examples are provided in which we evaluate the attack resources and the
conditions for profitable DS attacks given 35% proportion of computing power
against Syscoin and BitcoinCash networks, and quantitatively shown how
vulnerable they are.Comment: 13 pages, 1 figure. Submitted to IEEE Transactions on Information
Forensics and Security. Table 1 Has been correcte
Concise Probability Distributions of Eigenvalues of Real-Valued Wishart Matrices
In this paper, we consider the problem of deriving new eigenvalue
distributions of real-valued Wishart matrices that arises in many scientific
and engineering applications. The distributions are derived using the tools
from the theory of skew symmetric matrices. In particular, we relate the
multiple integrals of a determinant, which arises while finding the eigenvalue
distributions, in terms of the Pfaffian of skew-symmetric matrices. Pfaffians
being the square root of skew symmetric matrices are easy to compute than the
conventional distributions that involve Zonal polynomials or beta integrals. We
show that the plots of the derived distributions are exactly coinciding with
the numerically simulated plots.Comment: Submitted to Math Journal, 7 page
On the Compressed Measurements over Finite Fields: Sparse or Dense Sampling
We consider compressed sampling over finite fields and investigate the number
of compressed measurements needed for successful L0 recovery. Our results are
obtained while the sparseness of the sensing matrices as well as the size of
the finite fields are varied. One of interesting conclusions includes that
unless the signal is "ultra" sparse, the sensing matrices do not have to be
dense.Comment: 10 pages, 2 figures, other essential inf
Detection-Directed Sparse Estimation using Bayesian Hypothesis Test and Belief Propagation
In this paper, we propose a sparse recovery algorithm called
detection-directed (DD) sparse estimation using Bayesian hypothesis test (BHT)
and belief propagation (BP). In this framework, we consider the use of
sparse-binary sensing matrices which has the tree-like property and the
sampled-message approach for the implementation of BP.
The key idea behind the proposed algorithm is that the recovery takes
DD-estimation structure consisting of two parts: support detection and signal
value estimation. BP and BHT perform the support detection, and an MMSE
estimator finds the signal values using the detected support set. The proposed
algorithm provides noise-robustness against measurement noise beyond the
conventional MAP approach, as well as a solution to remove quantization effect
by the sampled-message based BP independently of memory size for the message
sampling.
We explain how the proposed algorithm can have the aforementioned
characteristics via exemplary discussion. In addition, our experiments validate
such superiority of the proposed algorithm, compared to recent algorithms under
noisy setup. Interestingly the experimental results show that performance of
the proposed algorithm approaches that of the oracle estimator as SNR becomes
higher
On Detection-Directed Estimation Approach for Noisy Compressive Sensing
In this paper, we investigate a Bayesian sparse reconstruction algorithm
called compressive sensing via Bayesian support detection (CS-BSD). This
algorithm is quite robust against measurement noise and achieves the
performance of a minimum mean square error (MMSE) estimator that has support
knowledge beyond a certain SNR threshold. The key idea behind CS-BSD is that
reconstruction takes a detection-directed estimation structure consisting of
two parts: support detection and signal value estimation. Belief propagation
(BP) and a Bayesian hypothesis test perform support detection, and an MMSE
estimator finds the signal values belonging to the support set. CS-BSD
converges faster than other BP-based algorithms, and it can be converted to a
parallel architecture to become much faster. Numerical results are provided to
verify the superiority of CS-BSD compared to recent algorithms.Comment: 22 pages, 7 figures, 1 table, 1 algorithm tabl
Restricted Isometry Random Variables: Probability Distributions, RIC Prediction and Phase Transition Analysis for Gaussian Encoders
In this paper, we aim to generalize the notion of restricted isometry
constant (RIC) in compressive sensing (CS) to restricted isometry random
variable (RIV). Associated with a deterministic encoder there are two RICs,
namely, the left and the right RIC. We show that these RICs can be generalized
to a left RIV and a right RIV for an ensemble of random encoders. We derive the
probability and the cumulative distribution functions of these RIVs for the
most widely used i.i.d. Gaussian encoders. We also derive the asymptotic
distributions of the RIVs and show that the distribution of the left RIV
converges (in distribution) to the Weibull distribution, whereas that of the
right RIV converges to the Gumbel distribution. By adopting the RIV framework,
we bring to forefront that the current practice of using eigenvalues for RIC
prediction can be improved. We show on the one hand that the eigenvalue-based
approaches tend to overestimate the RICs. On the other hand, the RIV-based
analysis yields precise estimates of the RICs. We also demonstrate that this
precise estimation aids to improve the previous RIC-based phase transition
analysis in CS.Comment: 15 pages; In revisio
Bernoulli-Gaussian Approximate Message-Passing Algorithm for Compressed Sensing with 1D-Finite-Difference Sparsity
This paper proposes a fast approximate message-passing (AMP) algorithm for
solving compressed sensing (CS) recovery problems with 1D-finite-difference
sparsity in term of MMSE estimation. The proposed algorithm, named ssAMP-BGFD,
is low-computational with its fast convergence and cheap per-iteration cost,
providing phase transition nearly approaching to the state-of-the-art. The
proposed algorithm is originated from a sum-product message-passing rule,
applying a Bernoulli-Gaussian (BG) prior, seeking an MMSE solution. The
algorithm construction includes not only the conventional AMP technique for the
measurement fidelity, but also suggests a simplified message-passing method to
promote the signal sparsity in finite-difference. Furthermore, we provide an
EM-tuning methodology to learn the BG prior parameters, suggesting how to use
some practical measurement matrices satisfying the RIP requirement under the
ssAMP-BGFD recovery. Extensive empirical results confirms performance of the
proposed algorithm, in phase transition, convergence speed, and CPU runtime,
compared to the recent algorithms.Comment: 17 pages, 13 figures, submitted to the IEEE Transactions on Signal
Processin
Holistic random encoding for imaging through multimode fibers
The input numerical aperture (NA) of multimode fiber (MMF) can be effectively
increased by placing turbid media at the input end of the MMF. This provides
the potential for high-resolution imaging through the MMF. While the input NA
is increased, the number of propagation modes in the MMF and hence the output
NA remains the same. This makes the image reconstruction process
underdetermined and may limit the quality of the image reconstruction. In this
paper, we aim to improve the signal to noise ratio (SNR) of the image
reconstruction in imaging through MMF. We notice that turbid media placed in
the input of the MMF transforms the incoming waves into a better format for
information transmission and information extraction. We call this
transformation as holistic random (HR) encoding of turbid media. By exploiting
the HR encoding, we make a considerable improvement on the SNR of the image
reconstruction. For efficient utilization of the HR encoding, we employ sparse
representation (SR), a relatively new signal reconstruction framework when it
is provided with a HR encoded signal. This study shows for the first time to
our knowledge the benefit of utilizing the HR encoding of turbid media for
recovery in the optically underdetermined systems where the output NA of it is
smaller than the input NA for imaging through MMF.Comment: under review for possible publication in Optics expres
Intentional Aliasing Method to Improve Sub-Nyquist Sampling System
A modulated wideband converter (MWC) has been introduced as a sub-Nyquist
sampler that exploits a set of fast alternating pseudo random (PR) signals.
Through parallel sampling branches, an MWC compresses a multiband spectrum by
mixing it with PR signals in the time domain, and acquires its sub-Nyquist
samples. Previously, the ratio of compression was fully dependent on the
specifications of PR signals. That is, to further reduce the sampling rate
without information loss, faster and longer-period PR signals were needed.
However, the implementation of such PR signal generators results in high power
consumption and large fabrication area. In this paper, we propose a novel
aliased modulated wideband converter (AMWC), which can further reduce the
sampling rate of MWC with fixed PR signals. The main idea is to induce
intentional signal aliasing at the analog-to-digital converter (ADC). In
addition to the first spectral compression by the signal mixer, the intentional
aliasing compresses the mixed spectrum once again. We demonstrate that AMWC
reduces the number of sampling branches and the rate of ADC for lossless
sub-Nyquist sampling without needing to upgrade the speed or period of PR
signals. Conversely, for a given fixed number of sampling branches and sampling
rate, AMWC improves the performance of signal reconstruction.Comment: 13 pages with 6 figures, published in IEEE Trans. signal Proces
Time-Variant Proof-of-Work Using Error-Correction Codes
The protocol for cryptocurrencies can be divided into three parts, namely
consensus, wallet, and networking overlay. The aim of the consensus part is to
bring trustless rational peer-to-peer nodes to an agreement to the current
status of the blockchain. The status must be updated through valid
transactions. A proof-of-work (PoW) based consensus mechanism has been proven
to be secure and robust owing to its simple rule and has served as a firm
foundation for cryptocurrencies such as Bitcoin and Ethereum. Specialized
mining devices have emerged, as rational miners aim to maximize profit, and
caused two problems: i) the re-centralization of a mining market and ii) the
huge energy spending in mining. In this paper, we aim to propose a new PoW
called Error-Correction Codes PoW (ECCPoW) where the error-correction codes and
their decoder can be utilized for PoW. In ECCPoW, puzzles can be intentionally
generated to vary from block to block, leading to a time-variant puzzle
generation mechanism. This mechanism is useful in repressing the emergence of
the specialized mining devices. It can serve as a solution to the two problems
of recentralization and energy spending.Comment: 13page
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