Output Permutation Research Articles

Design of a modern fast Fourier transform and cache effective bit-reversal algorithm

ABSTRACT This article deals with efficient vectorization of the fast Fourier transform algorithm while focusing on Cooley–Tukey versions with power-of-two radixes. Aside from examples of optimizations for 256 and 512-bit vectors, this work also discusses relations between individual radix-based versions, vectorization and OpenMP threading. Ideas are progressing into a timeless design of the FFT algorithm, which can work with any vector size and radix version through conversion into radix-2 output permutation. Furthermore, the implementation of the Cache Optimized Bit-Reversal algorithm, which doubles the performance of its predecessor, is introduced.

Table Substitution Box Method for Increasing Security in Interval Splitting Arithmetic Coding

Amalgamation of compression and security is indispensable in the field of multimedia applications. A novel approach to enhance security with compression is discussed in this  research paper. In secure arithmetic coder (SAC), security is provided by input and output permutation methods and compression is done by interval splitting arithmetic coding. Permutation in SAC is susceptible to attacks. Encryption issues associated with SAC is dealt in this research method. The aim of this proposed method is to encrypt the data first by Table Substitution Box (T-box) and then to compress by Interval Splitting Arithmetic Coder (ISAC). This method incorporates dynamic T-box in order to provide better security. T-box is a method, constituting elements based on the random output of Pseudo Random Generator (PRNG), which gets the input from Secure Hash Algorithm-256 (SHA-256) message digest. The current scheme is created, based on the key, which is known to the encoder and decoder. Further, T-boxes are created by using the previous message digest as a key.  Existing interval splitting arithmetic coding of SAC is applied for compression of text data. Interval splitting finds a relative position to split the intervals and this in turn brings out compression. The result divulges that permutation replaced by T-box method provides enhanced security than SAC. Data is not revealed when permutation is replaced by T-box method. Security exploration reveals that the data remains secure to cipher text attacks, known plain text attacks and chosen plain text attacks. This approach results in increased security to Interval ISAC. Additionally the compression ratio is compared by transferring the outcome of T-box to traditional arithmetic coding. The comparison proved that there is a minor reduction in compression ratio in ISAC than arithmetic coding. However the security provided by ISAC overcomes the issues of compression ratio in arithmetic coding.Â

Relative Localization in Wireless Sensor Networks for Measurement of Electric Fields under HVDC Transmission Lines

In the wireless sensor networks (WSNs) for electric field measurement system under the High-Voltage Direct Current (HVDC) transmission lines, it is necessary to obtain the electric field distribution with multiple sensors. The location information of each sensor is essential to the correct analysis of measurement results. Compared with the existing approach which gathers the location information by manually labelling sensors during deployment, the automatic localization can reduce the workload and improve the measurement efficiency. A novel and practical range-free localization algorithm for the localization of one-dimensional linear topology wireless networks in the electric field measurement system is presented. The algorithm utilizes unknown nodes' neighbor lists based on the Received Signal Strength Indicator (RSSI) values to determine the relative locations of nodes. The algorithm is able to handle the exceptional situation of the output permutation which can effectively improve the accuracy of localization. The performance of this algorithm under real circumstances has been evaluated through several experiments with different numbers of nodes and different node deployments in the China State Grid HVDC test base. Results show that the proposed algorithm achieves an accuracy of over 96% under different conditions.

On the Security of the Secure Arithmetic Code

In 2007, Kim et al. proposed a secure compression code called the secure arithmetic code (SAC). The code was claimed to be secure against chosen plaintext attacks. However, we find that the SAC is not as secure as the authors have claimed. In this paper, we show the code is prone to two attacks. The first attack completely breaks the code using an adaptive chosen plaintext attack with a polynomial number of queries. The second attack is a ciphertext-only attack, which removes a part of the output permutation.

A method to obtain the semi-canonical Morse's form of a linear multivariable system

A method is presented in this paper to obtain an element of a transformation group, which takes a state space representation of a linear multivariable system to its semi-canonical Morse's form. The system under consideration is supposed to be right invertible, controllable and with no invariant zeros. The element of the transformation group involves state feedback, permutation of outputs and change of basis in states and inputs.

Feature Selection for MLP Neural Network: The Use of Random Permutation of Probabilistic Outputs

This paper presents a new wrapper-based feature selection method for multilayer perceptron (MLP) neural networks. It uses a feature ranking criterion to measure the importance of a feature by computing the aggregate difference, over the feature space, of the probabilistic outputs of the MLP with and without the feature. Thus, a score of importance with respect to every feature can be provided using this criterion. Based on the numerical experiments on several artificial and real-world data sets, the proposed method performs, in general, better than several selected feature selection methods for MLP, particularly when the data set is sparse or has many redundant features. In addition, as a wrapper-based approach, the computational cost for the proposed method is modest.

Priority Queue Sorting and Labeled Trees

We construct a bijection between labeled trees and allowable pairs of permutations sorted by a priority queue. These are also the pairs of permutations that avoid the pattern pairs (12, 21) and (321, 132). Our bijection has the additional property that it maps leaves in the tree to descents in the output permutation in the allowable pair and, more generally, preserves the edge-deletion distribution of the tree.

A neural network approach to PLA folding problems

A near-optimum parallel algorithm for solving PLA folding problems is presented in this paper where the problem is NP-complete and one of the most fundamental problems in VLSI design. The proposed system is composed of n/spl times/n neurons based on an artificial two-dimensional maximum neural network where n is the number of inputs and outputs or the number of product lines of PLA. The two-dimensional maximum neurons generate the permutation of inputs and outputs or product lines. Our algorithm can solve not only a simple folding problem but also multiple, bipartite, and constrained folding problems. We have discovered improved solutions in four benchmark problems over the best existing algorithms using the proposed algorithm.

Priority Queues and Permutations

A priority queue transforms an input permutation $\sigma $ of some set of size n into an output permutation $\tau $ The set $R_n $ of such related pairs $(\sigma ,\tau )$ is studied. Efficient algorithms for determining $s(\tau ) = |\sigma :(\sigma ,\tau ) \in R_n |$, and $t(\sigma ) = |\tau :(\sigma ,\tau ) \in R_n |$ are given, a new proof that $|R_n | = (n + 1)^{n - 1} $ is given, and the transitive closure of $R_n $ is found.