Size Of Submatrices Research Articles

Recovering the Parameters of an LDPC Code From Noisy Intercepted Sequences

Blind identification of channel codes is a key technology in non-cooperative communication as well as intelligent communication. In this letter, we are interested in recovering the parameters of low-density parity-check (LDPC) codes without any a priori information. We propose to find dual codewords from noisy intercepted sequences and prove that the problem is NP-complete. Afterward, we propose an improved collision-based algorithm that can avoid most of the invalid searches and thus allowing a significant reduction in complexity. The algorithm produces almost no errors when the noise is small. While in the case of non-negligible noise, we propose to use soft information to detect the outputs of the algorithm, and errors in which can therefore be extensively eliminated. After a sufficient number of dual codewords have been found, one can easily recover the code lengths and code rates of LDPC codes, as well as the sizes of sub-matrices for Quasi-Cyclic LDPC codes. Experimental results show that the proposed method has an improved noise tolerance and can be more efficient than existing methods.

Building matrices with prescribed size and number of invertible submatrices

Given an ordered triple of positive integers (n,r,b), where 1≤b≤nr, does there exist a matrix of size r×n with exactly b invertible submatrices of size r×r? Such a matrix is called an (n,r,b)-matrix. This question is a stronger version of an open problem in matroid theory raised by Dominic Welsh. In this paper, we prove that an (n,r,b)-matrix exists when the corank satisfies n−r≤3, unless (n,r,b)=(6,3,11). Furthermore, we show that an (n,r,b)-matrix exists when the rank r is large relative to the corank n−r.

Remote-3DD: un nuevo método para la detección de homólogos remotos que usa propiedades fisicoquímicas

En este artículo se presenta un nuevo método para la detección de homólogos remotos, llamado remote-3DD, que combina mapas de contacto predichos y una distribución de los valores en las matrices de interacción. Los mapas de contacto predichos son una aproximación de la forma 3D de proteína que se puede obtener a partir de su estructura primaria. Por su parte, una matriz de interacción permite representar una proteína a partir de las propiedades fisicoquímicas de los aminoácidos que la conforman. Remote-3DD se propone como una estrategia para mejorar la exactitud del método remote-C3D en el cual se utilizan solamente mapas de contacto. La hipótesis que se plantea en este artículo es que se puede mejorar la exactitud del método remote-C3D al incorporar las distribuciones de la matriz de interacción. Los resultados de las pruebas muestran que el método remote-3DD alcanza una exactitud mayor que los métodos basados en composición y en algunos casos una exactitud comparable con los métodos basados en perfiles. Además, las pruebas permiten demostrar que el método remote-3DD, en general, presenta exactitudes mayores que el método remote-C3D cuando se utiliza la misma cantidad de modelos y tamaños de submatrices.

A Comparison Study of an Algorithm for Non Conflict Schedule with Diagonal Activation of Joint Sub Matrices in a Large Scale Switching Matrix

Abstract The aim of this study is to determine the influence of the size of submatrices in a lagre scale connections matrix on the performance of an algorithm for non conflict scheduling with diagonal activation of joint submatrices (ADAJS). We have used a software model (SMADAJS) of the algorithm developed in MATLAB programming environment. A comparison is made with similar algorithms with diagonal activation of the connections matrix with respect to performance time and memory required.

On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix

We investigate the maximal size of distinguished submatrices of a Gaussian random matrix. Of interest are submatrices whose entries have an average greater than or equal to a positive constant, and submatrices whose entries are well fit by a two-way ANOVA model. We identify size thresholds and associated (asymptotic) probability bounds for both large-average and ANOVA-fit submatrices. Probability bounds are obtained when the matrix and submatrices of interest are square and, in rectangular cases, when the matrix and submatrices of interest have fixed aspect ratios. Our principal result is an almost sure interval concentration result for the size of large average submatrices in the square case.

On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix

On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix

Low-Complexity Switch Network for Reconfigurable LDPC Decoders

In this paper, we propose an efficient low-complexity switch network design for reconfigurable low-density parity-check (LDPC) decoders. The proposed architecture leads to significant reductions in hardware complexity. Since the structured quasi-cyclic (QC) LDPC codes for most modern wireless communication systems include multiple code rates, various block lengths, and different sizes of submatrices, a reconfigurable LDPC decoder is desirable and the barrel shifter needs to be programmable. The Benes network cannot be optimized as the barrel shifter for a reconfigurable LDPC decoder when the input size of barrel shifter is not a power of 2. Also, it is not trivial to generate all the control signals on-the-fly for numerous 2 × 2 switches in the switch network. In this paper, a novel low-complexity switch network design is proposed, which can be used efficiently when the input size of barrel shifters is not a power of 2. Furthermore, we propose a novel algorithm to generate all the control signals, which can be implemented with a small size of lookup table (LUT) or a simple combination logic on-the-fly, using the properties that both the full-size switch network can be broken into two half-size switch networks and the barrel shifters for the structured QC LDPC decoders require only cyclic shifts. Compared with conventional Benes networks using a dedicated LUT or a complicated signal generating algorithm, the proposed architectures achieve significant hardware reductions in implementing the barrel shifters for reconfigurable LDPC decoders. In synthesis result using the TSMC 0.18-¿m standard cell CMOS technology, the proposed switch network for a reconfigurable LDPC decoder of IEEE 802.16e and IEEE 802.11n can be implemented with an area of 0.772 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , which leads to a significant area reduction.

Permutation Network for Reconfigurable LDPC Decoder Based on Banyan Network

Since the structured quasi-cyclic low-density parity-check (QC-LDPC) codes for most modern wireless communication systems include multiple code rates, various block lengths, and the corresponding different sizes of submatrices in parity check matrix (PCM), the reconfigurable LDPC decoder is desirable and the permutation network is needed to accommodate any input number (IN) and shift number (SN) for cyclic shift. In this paper, we propose a novel permutation network architecture for the reconfigurable QC-LDPC decoders based on Banyan network. We prove that Banyan network has the nonblocking property for cyclic shift when the IN is power of 2, and give the control signal generating algorithm. Through introducing the bypass network, we put forward the nonblocking scheme for any IN and SN. In addition, we present the hardware design of the control signal generator, which can greatly reduce the hardware complexity and latency. The synthesis results using the TSMC 0.18 μm library demonstrate that the proposed permutation network can be implemented with the area of 0.546 mm 2 and the frequency of 292 MHz.

On the Size and Recovery of Submatrices of Ones in a Random Binary Matrix

Binary matrices, and their associated submatrices of 1s, play a central role in the study of random bipartite graphs and in core data mining problems such as frequent itemset mining (FIM). Motivated by these connections, this paper addresses several statistical questions regarding submatrices of 1s in a random binary matrix with independent Bernoulli entries. We establish a three-point concentration result, and a related probability bound, for the size of the largest square submatrix of 1s in a square Bernoulli matrix, and extend these results to non-square matrices and submatrices with fixed aspect ratios. We then consider the noise sensitivity of frequent itemset mining under a simple binary additive noise model, and show that, even at small noise levels, large blocks of 1s leave behind fragments of only logarithmic size. As a result, standard FIM algorithms, which search only for submatrices of 1s, cannot directly recover such blocks when noise is present. On the positive side, we show that an error-tolerant frequent itemset criterion can recover a submatrix of 1s against a background of 0s plus noise, even when the size of the submatrix of 1s is very small.