Constant Weight Codes Research Articles

Regularized Semi-non-negative Matrix Factorization for Hashing

Learning with non-negative matrix factorization (NMF) has significantly benefited large numbers of fields such as information retrieval, computer vision, natural language processing, biomedicine, and neuroscience, etc. However, little research (with NMF) has scratched hashing, which is a sharp sword in approximately nearest neighbors search for economical storage and efficient hardware-level XOR operations. To explore more, we propose a novel hashing model, called Regularized Semi-NMF for Hashing (SeH), which is a minimal optimization between Semi-NMF, semantics preserving, and efficient coding. Tricks such as balance codes, binary-like relaxation, and stochastic learning are employed to yield efficient algorithms which raise the capabilities to deal with a large-scale dataset. SeH is shown to evidently improve retrieval effectiveness over some state-of-the-art baselines on several public datasets (MSRA-CFW, Caltech256, Cifar10, and ImageNet) with different sample scales and feature representations. Furthermore, a case study on Caltech256, that is, three image queries are randomly selected and the corresponding search results are presented, would intuitively exhibit which method is better.

On m-Near-Resolvable Block Designs and q-ary Constant-Weight Codes

We introduce m-near-resolvable block designs. We establish a correspondence between such block designs and a subclass of (optimal equidistant) q-ary constant-weight codes meeting the Johnson bound. We present constructions of m-near-resolvable block designs, in particular based on Steiner systems and super-simple t-designs.

Binary signaling design for visible light communication: a deep learning framework.

This paper develops a deep learning framework for the design of on-off keying (OOK) based binary signaling transceiver in dimmable visible light communication (VLC) systems. The dimming support for the OOK optical signal is achieved by adjusting the number of ones in a binary codeword, which boils down to a combinatorial design problem for the codebook of a constant weight code (CWC) over signal-dependent noise channels. To tackle this challenge, we employ an autoencoder (AE) approach to learn a neural network of the encoder-decoder pair that reconstructs the output identical to an input. In addition, optical channel layers and binarization techniques are introduced to reflect the physical and discrete nature of the OOK-based VLC systems. The VLC transceiver is designed and optimized via the end-to-end training procedure for the AE. Numerical results verify that the proposed transceiver performs better than baseline CWC schemes.

A spectral-efficient dimming control scheme with multi-level incremental constant weight codes in visible light communication systems

As an essential requirement for visible light communication (VLC) system, dimming control has attracted increasing attentions where arbitrary brightness levels can be achieved. Conventional dimming schemes based on binary modulation are spectral inefficient. In this paper, we propose multi-level incremental constant weight codes (ML-ICWC) scheme to achieve dimming control via controlling the number of LEDs on per lighting source simultaneously. Meanwhile, the construction algorithm of the codeword set is developed accordingly to guarantee reliable data transmission. Finally, simulation results show that the proposed scheme achieves significant improvement in terms of spectral efficiency compared with existing dimming schemes under various dimming levels.

On non-full-rank perfect codes over finite fields

The paper deals with perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). We show that the orthogonal code to a q-ary non-full-rank 1-perfect code of length $$n = (q^{m}-1)/(q-1)$$ is a q-ary constant-weight code with Hamming weight equal to $$q^{m - 1}$$ , where m is any natural number not less than two. Necessary and sufficient conditions for q-ary codes to be q-ary non-full-rank 1-perfect codes are obtained. We suggest a generalization of the concatenation construction to the q-ary case and construct a ternary 1-perfect code of length 13 and rank 12.

A novel concept for dynamic adjustment of auditory space

Traditionally, the auditory system is thought to serve reliable sound localization. Stimulus-history driven feedback circuits in the early binaural pathway, however, contradict this canonical concept and raise questions about their functional significance. Here we show that stimulus-history dependent changes in absolute space perception are poorly captured by the traditional labeled-line and hemispheric-difference models of auditory space coding. We therefore developed a new decoding model incorporating recent electrophysiological findings in which sound location is initially computed in both brain hemispheres independently and combined to yield a hemispherically balanced code. This model closely captures the observed absolute localization errors caused by stimulus history, and furthermore predicts a selective dilation and compression of perceptional space. These model predictions are confirmed by improvement and degradation of spatial resolution in human listeners. Thus, dynamic perception of auditory space facilitates focal sound source segregation at the expense of absolute sound localization, questioning existing concepts of spatial hearing.

Data sharing among wireless client devices in cooperative manner with minimum transmissions

A group of nearby wireless end devices such as mobile phones can benefit a fast service to satisfy their required packets by cooperating to exchange their packets after receiving collectively from a common base station. This problem can be formulated as a coding and transmission scheme and solved by the linear network coding. We propose a balanced coding and transmission (BCT) scheme that assigns suitable clients to find and transmit linear combinations of the received packets. The goals of our scheme are to minimize the total number of transmissions, to maintain fairness on the number of transmissions among the participants in the cooperative group and to maintain the limited energy resources until all members satisfy their needs. Moreover, we also introduce transmission scheme with physical layer network coding (BCTS/PNC) for the same problem to further reduce the required transmission time slots and accomplish the data exchange process in short time. We present the performance of the schemes and discussion in terms of the fairness, the number of transmissions and the completion time by testing with various simulation parameters and scenarios.

New Constant Weight Codes and Packing Numbers

The constant A(n,d,w) is the maximum number of words in an (n,d,w) binary code, that is, a code of minimal distance d, with words of length n and weight w. We improve the best known lower bounds on A(n,d,w) for three sets of parameters by using optimization; in particular, we show that A(29,8,5)≥36, A(30,8,5)≥41, and A(32,8,5)=44 by explicitly giving the respective codes. The (32, 8, 5) code is optimal and leads to eight more new optimal codes. We show this by improving the known result on the problem of finding the packing number P(v,5,2) for v≡12 (mod 20).

Simultaneous Imaging, Sensor Tag Localization, and Backscatter Uplink via Synthetic Aperture Radar

This paper presents an extension of synthetic aperture radar (SAR) techniques to enable simultaneous radar imaging, sensor tag localization, and backscatter-based data uplink from multiple sensor tags in a cluttered environment. A unified system model is presented that leverages coherent processing of backscattered signals gathered over the synthetic aperture for all three of these purposes. The proposed approach, using balanced orthogonal codes for SAR-based localization as well as the backscatter data uplink, is shown to have several favorable properties, including straightforward tag-vs-clutter discrimination, straightforward multiple access among tags, and improved signal-to-noise ratio during localization. A proof-of-principle indoor experiment is presented in the X-band (10–13 GHz) using two custom-designed backscatter tags interrogated by a vector network analyzer functioning as an FMCW radar. The proposed system model is validated by simultaneous imaging of a cluttered scene, tag localization with a maximum range error of 9 mm, and data demodulation from both tags telemetering temperature changes at a rate of 1 bit/s at ranges of 4.4 m and 4.7 m. The resulting point-spread functions of tags demonstrate a range resolution of 4.7 cm and a cross-range resolution of 9.1 cm.

Analysis of the Effect of Multirow and Multipassage Aerodynamic Interaction on the Forced Response Variation in a Compressor Configuration—Part I: Aerodynamic Excitation

The aeroelastic prediction of blade forcing is still a very important topic in turbomachinery design. Usually, the wake from an upstream airfoil and the potential field from a downstream airfoil are considered as the main disturbances. In recent years, it became evident that in addition to those two mechanisms, Tyler–Sofrin modes, also called scattered or spinning modes, may have a significant impact on blade forcing. It was recently shown in literature that in multirow configurations, not only the next but also the next but one blade row is very important as it may create a large circumferential forcing variation, which is fixed in the rotating frame of reference. In the present paper, a study of these effects is performed on the basis of a quasi three-dimensional (3D) multirow and multipassage compressor configuration. For the analysis, a harmonic balancing code, which was developed by DLR Cologne, is used for various setups and the results are compared to full-annulus unsteady calculations. It is shown that the effect of the circumferentially different blade excitation is mainly contributed by the Tyler–Sofrin modes and not to blade-to-blade variation in the steady flow field. The influence of various clocking positions, coupling schemes and number of harmonics onto the forcing is investigated. It is also shown that along a speed-line in the compressor map, the blade-to-blade forcing variation may change significantly. In addition, multirow flutter calculations are performed, showing the influence of the upstream and downstream blade row onto aerodynamic damping. The effect of these forcing variations onto random mistuning effects is investigated in the second part of the paper.

Multiset combinatorial batch codes

Batch codes, first introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai, mimic a distributed storage of a set of n data items on m servers, in such a way that any batch of k data items can be retrieved by reading at most some t symbols from each server. Combinatorial batch codes, are replication-based batch codes in which each server stores a subset of the data items. In this paper, we propose a generalization of combinatorial batch codes, called multiset combinatorial batch codes (MCBC), in which n data items are stored in m servers, such that any multiset request of k items, where any item is requested at most r times, can be retrieved by reading at most t items from each server. The setup of this new family of codes is motivated by recent work on codes which enable high availability and parallel reads in distributed storage systems. The main problem under this paradigm is to minimize the number of items stored in the servers, given the values of n, m, k, r, t, which is denoted by N(n, k, m, t; r). We first give a necessary and sufficient condition for the existence of MCBCs. Then, we present several bounds on N(n, k, m, t; r) and constructions of MCBCs. In particular, we determine the value of N(n, k, m, 1; r) for any $$n\ge \left\lfloor \frac{k-1}{r}\right\rfloor {m\atopwithdelims ()k-1}-(m-k+1)A(m,4,k-2)$$ , where $$A(m,4,k-2)$$ is the maximum size of a binary constant weight code of length m, distance four and weight $$k-2$$ . We also determine the exact value of N(n, k, m, 1; r) when $$r\in \{k,k-1\}$$ or $$k=m$$ .

Constructions for optimal cyclic ternary constant-weight codes of weight four and distance six

A cyclic (n,d,w)q code is a q-ary cyclic code of length n, minimum Hamming distance d and weight w. In this paper, we investigate cyclic (n,6,4)3 codes. A new upper bound on CA3(n,6,4), the largest possible number of codewords in a cyclic (n,6,4)3 code, is given. Two new constructions for optimal cyclic (n,6,4)3 codes based on cyclic (n,4,1) difference packings are presented. As a consequence, the exact value of CA3(n,6,4) is determined for any positive integer n≡0,6,18(mod24). We also obtain some other infinite classes of optimal cyclic (n,6,4)3 codes.

Some sequences of optimal constant weight codes

We introduce some sequences of binary constant weight codes which are constructed from the affine constructions of balanced incomplete block designs. They give the values for the function [Formula: see text] of constant weight codes, and they are optimal since those values reach the Johnson Bound. We focus on the values obtained by this method.

Joint Error-Dimming Control Using Constant Weight Coding in Visible Light Communication Systems

To enhance commercial implementation, visible light communication (VLC) should facilitate dimming control and reliable data transmission simultaneously, where users can adjust the brightness levels arbitrarily. Constant weight code (CWC) based dimming method can achieve higher spectral efficiency, but the codewords need further selection to exponentially map the massage. In this paper, based on CWC, we proposed a method to achieve dimming control as well as improve error performance via optimizing the average Hamming distance of the codeword set. Simulation results show that the optimal codeword set can achieve better error performance.

Организация полностью самопроверяемой схемы встроенного контроля на основе метода логического дополнения до равновесного кода «2 из 4»

The article considers the problem of the synthesis of a self-checking integrated control circuit with optimization of structural redundancy using the Boolean complement method up to 2-out-of-4 constant-weight code. A method for determining the values of control functions is developed, which makes it possible to set their appearance step by step, this ensures the solution of the problem of testing the corresponding elements of addition by modulo two and the tester circuit. In this case, uncertainties are introduced into the values of functions, which makes it possible to minimize the functions themselves, and, accordingly, simplify the circuit of check logic block. The method of constructing the control scheme by the method of logical addition for the 2/4-code is universal, and taking into account the fact that 2/4-TSC has a simple structure, it allows synthesizing embedded control schemes with structural redundancy not exceeding the redundancy of the control scheme when using the duplication method. Such a conclusion can be made on the basis of a large number of experiments on the use of equilibrium codes in the organization of self-verified control schemes

On m-Quasi-resolvable Block Designs and q-ary Constant-Weight Codes

On m-Quasi-resolvable Block Designs and q-ary Constant-Weight Codes

Essential idempotents and codes of constant weight

In this note, we prove that a binary linear code of constant weight is equivalent to a cyclic code which is either generated by an essential idempotent or a repetition code of a code of this kind.

Efficient key generation leveraging channel reciprocity and balanced gray code

Key generation leveraging wireless channel reciprocity can establish secret keys from unauthenticated broadcast channels and thus protect the communication of wireless networks. However, in real environments, the measurements collected by the involved transceivers might have many discrepancies due to the non-simultaneous directional measurements and other factors, such as hardware differences and asymmetric interferences. Meanwhile, if the multi-level quantization in conjunction with source coding is implemented to convert measurements to bits, the resulting high bit mismatch rate makes key agreement inefficient and insecure. In this paper, key generation schemes leveraging channel reciprocity and balanced gray code are proposed. To enhance the efficiency of key generation, an efficient encoding scheme based on balanced gray code is carried out during key generation. The proposed encoding scheme can simultaneously reduce the bit mismatch rate and improve the secret bit rate. In addition, the code book is reusable once it is generated. The proposed key generation schemes can be classified into the uniform and non-uniform schemes according to different quantization processes. Several experiments in real mobile environments are conducted to validate the proposed schemes. The received signal strength measurements are extracted from heterogeneous devices as statistics of channel states in each experiment. The results of these experiments show that (1) the proposed encoding scheme significantly enhances the efficiency of key generation; (2) both the uniform and non-uniform schemes can efficiently generate secret keys between heterogeneous transceivers.

Compact Constant Weight Coding Engines for the Code-Based Cryptography

We present here a more memory efficient method for encoding binary information into words of prescribed length and weight. Existing solutions either require complicated float point arithmetic or additional memory overhead, making it a challenge for resource constrained computing environment. The solution we propose here solves these problems yet obtains better coding efficiency by a memory efficient approximation of the critical intermediate value in constant weight coding. For the time being, the design presented in this brief is the most compact one for any code-based encryption schemes.

Optimal cyclic quaternary constant‐weight codes of weight three

AbstractA cyclic code is a cyclic q‐ary code of length n, constant weight w and minimum distance d. Let denote the largest possible size of a cyclic code. The pure and mixed difference method plays an important role in the determination of upper bound on . By analyzing the distribution of odd mixed and pure differences, an improved upper bound on is obtained for . A new construction based on special sequences is provided and the exact value of is almost completely determined for all d and n except when and . Our constructions reveal intimate connections between cyclic constant weight codes and special sequences, particularly Skolem‐type sequences.