Random Binary Matrices Research Articles

Blind Interleaver Parameter Estimation From Scant Data

A method for blind estimation of interleaver parameter was recently reported which made additional data from a limited amount of received data. However, the process of making additional data creates undesirable linearity which degrades estimation performance. Promise for improved estimation therefore lies in enhancing blind estimation of interleaver parameter without making additional data. In this paper, we propose an improved method to blindly estimate interleaver parameter under the condition of scant data. We first generate a matrix by using the received data. From this matrix we then make square submatrices and obtain their rank deficiency distribution. Finally, we estimate the interleaver parameter by comparing the rank deficiency distribution of the square submatrices and that of random binary matrices. Through computer simulations, we validate the proposed method in terms of detection probability and the number of false alarms. Simulation results show that the proposed method works better than the conventional method given scarce received data.

On-Chip Neural Data Compression Based On Compressed Sensing With Sparse Sensing Matrices.

On-chip neural data compression is an enabling technique for wireless neural interfaces that suffer from insufficient bandwidth and power budgets to transmit the raw data. The data compression algorithm and its implementation should be power and area efficient and functionally reliable over different datasets. Compressed sensing is an emerging technique that has been applied to compress various neurophysiological data. However, the state-of-the-art compressed sensing (CS) encoders leverage random but dense binary measurement matrices, which incur substantial implementation costs on both power and area that could offset the benefits from the reduced wireless data rate. In this paper, we propose two CS encoder designs based on sparse measurement matrices that could lead to efficient hardware implementation. Specifically, two different approaches for the construction of sparse measurement matrices, i.e., the deterministic quasi-cyclic array code (QCAC) matrix and -sparse random binary matrix [-SRBM] are exploited. We demonstrate that the proposed CS encoders lead to comparable recovery performance. And efficient VLSI architecture designs are proposed for QCAC-CS and -SRBM encoders with reduced area and total power consumption.

Binary Matrices for Compressed Sensing

For an $m\times n$ binary matrix with $d$ nonzero elements per column, it is interesting to identify the minimal column degree $d$ that corresponds to the best recovery performance. Consider this problem is hard to be addressed with currently known performance parameters, we propose a new performance parameter, the average of nonzero correlations between normalized columns. The parameter is proved to perform better than the known coherence parameter, namely the maximum correlation between normalized columns, when used to estimate the performance of binary matrices with high compression ratios $n/m$ and low column degrees $d$ . By optimizing the proposed parameter, we derive an ideal column degree $d=\lceil \sqrt{m}\rceil$ , around which the best recovery performance is expected to be obtained. This is verified by simulations. Given the ideal number $d$ of nonzero elements in each column, we further determine their specific distribution by minimizing the coherence with a greedy method. The resulting binary matrices achieve comparable or even better recovery performance than random binary matrices.

Statistical Simulation for the Invertibility Test of Binary Random Matrices

One specific mathematical problem is discussed by combining the knowledge of statistical simulation and linear algebra. Aiming to solve this easy-to-understand yet hard-to-answer problem, this paper tries in two ways to test the invertibility of large random binary matrices. By generating random entries of the matrices, and using sparse sampling strategies to get matrices, we also consider programming techniques in order to break the bottleneck of computing power. The proportion of singular matrices changes with the increase of matrix order and the trend is presented. The advantages and disadvantages of the methods are also analyzed from the aspects of result accuracy, time efficiency and applicability. This paper is an example of computer-aided teaching to assist students in enhancing their understanding and practical ability.

An ECG Compressed Sensing Method of Low Power Body Area Network

Aimed at low power problem in body area network, an ECG compressed sensing method of low power body area network based on the compressed sensing theory was proposed. Random binary matrices were used as the sensing matrix to measure ECG signals on the sensor nodes. After measured value is transmitted to remote monitoring center, ECG signal sparse representation under the discrete cosine transform and block sparse Bayesian learning reconstruction algorithm is used to reconstruct the ECG signals. The simulation results show that the 30% of overall signal can get reconstruction signal which’s SNR is more than 60dB, each numbers in each rank of sensing matrix can be controlled below 5, which reduces the power of sensor node sampling, calculation and transmission. The method has the advantages of low power, high accuracy of signal reconstruction and easy to hardware implementation. DOI : http://dx.doi.org/10.11591/telkomnika.v12i1.3995

The Rank of Random Binary Matrices and Distributed Storage Applications

Random binary matrices appear in a variety of signal processing and encoding problems. They play an important role in rateless codes and in distributed storage applications. This paper focuses on block angular matrices, a class of random rectangular binary matrices that are particularly suited to distributed storage applications. We address one of the key issues regarding binary random matrices in general, and block angular matrices in particular: the probability of obtaining a full rank matrix, when drawing uniformly at random from the set of binary matrices with compatible structure. This paper gives a closed-form expression for this probability, as well as some bounds and approximations.

Random binary matrices in biogeographical ecology—Instituting a good neighbor policy

Binary matrices originating from presence/absence data on species (rows) distributed over sites (columns) have been a subject of much controversy in ecological biogeography. Under the null hypothesis that every matrix is equally likely, the distributions of some test statistics measuring co-occurrences between species are sought, conditional on the row and column totals being fixed at the values observed for some particular matrix. Many ad hoc methods have been proposed in the literature, but at least some of them do not provide uniform random samples of matrices. In particular, some “swap” algorithms have not accounted for the number of neighbors each matrix has in the universe of matrices with a set of fixed row and column sums. We provide a Monte-Carlo method using random walks on graphs that gives correct estimates for the distributions of statistics. We exemplify its use with one statistic.

Higher-dimensional Hadamard matrices

The concept of a Hadamard matrix as a binary orthogonal matrix is extended to higher dimensions. An n -dimensional Hadamard matrix [h_{ijk \cdots n}] is defined as one in which all parallel (n - 1) -dimensional layers, in any axis-normal orientation, are uncorrelated. This is equivalent to the requirements that h_{ijk \cdots n} = \pm1 and that \sum_{p} \sum_{q} \sum_{r} \cdots \sum_{y} h_{pqr \cdots yb}= m^{(n-1)} \delta_{ab} where (pqr \cdots yz) represents all permutations of (ijk \cdots n) . A n -dimensional Hadamard matrix is defined as a special case of the above in which all two-dimensional layers, in all axis-normal orientations, are Hadamard matrices, as a consequence of which all intermediate-dimensional layers are also Hadamard matrices. Procedures are described for deriving three- and four-dimensional Hadamard matrices of varying propriety from two-dimensional Hadamard matrices. A formula is given for a fully proper n -dimensional matrix of order two, which can be expanded by direct multiplication to yield proper (2^{t})^{n} Hadamard matrices. It is suggested that proper higher dimensional Hadamard matrices may find application in error-correcting cedes, where their hierarchy of orthogonalitias permit a variety of checking procedures. Other types of Hadamard matrices may be of use in security codes on the basis of their resemblance to random binary matrices.