Constant Weight Codes Research Articles

Quantum search algorithm for binary constant weight codes

A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this paper, we propose a quantum search algorithm for binary constant weight codes. Specifically, the search problem is formulated as a polynomial binary optimization problem and Grover adaptive search is used for providing the quadratic speedup. Focusing on the inherent structure of the problem, we derive an upper bound on the minimum of the objective function value and a lower bound on the exact number of solutions. By exploiting these two bounds, we successfully reduced the constant overhead of the algorithm, although the overall query complexity remains exponential due to the NP-complete nature of the problem. In our algebraic analysis, it was found that this proposed algorithm is capable of reducing the number of required qubits, thus enhancing the feasibility. Additionally, our simulations demonstrated that it reduces the average number of classical iterations by 63% as well as the average number of total Grover rotations by 31%. The proposed approach may be useful for other quantum search algorithms and optimization problems.

Toroidal injection angle dependence of EC assisted plasma initiation at DIII-D

Abstract An experimental scan of the electron cyclotron waves (EC) toroidal injection angle in plasma breakdown is performed at the DIII-D tokamak. The second harmonic, extraordinary mode EC is used for the study. The dependence of n e and T e on the EC injection angle cannot be conclusively drawn from this study due to the large error bars in the n e and T e measurements. On the other hand, high T e data points are observed in some discharges which can be explained by nonlinear heating. The D α emission measurement shows a clear relation between the breakdown time and the injection angle. An experimental investigation of the cause of the dependence of breakdown delay on the EC injection angle suggests that when the injection angle is oblique, the EC heating after the reflection at the inboard wall may become ineffective and cause the breakdown delay even when the EC heating before and directly upon injection remains effective. A preliminary run of the heat and transport balance code DYON indicates that the obtained dataset is suitable for a quantitative validation of EC absorption models.

Accurate and rapid reactive flow simulations using dynamic load balancing and sparse analytical Jacobian approach

The present study introduces a rapid and accurate customized solver on the OpenFOAM platform for large-scale industrial computations. Specifically, a sparse analytical Jacobian approach utilizing the SpeedCHEM library was implemented to enhance the efficiency of the ordinary differential equation solver. The dynamic load balancing code was used to distribute computational workloads uniformly across multiple processes. Optimization continued with open multi-processing to improve parallel computing efficiency and the local time stepping scheme to maximize individual cell time steps. The effectiveness and robustness of the customized solver were first validated using Sandia flames D–F as benchmarks. The results showed that the customized solver exhibited better strong scaling characteristics and led to a speed increase of up to 30 times for two-dimensional Sandia flame D calculations. The numerical predictions for temperature and species distribution closely matched the experimental trends, confirming the accuracy of the solver. Subsequently, a three-dimensional numerical study on a 10 kW ammonia co-combustion furnace was conducted, exploring the performance of the solver in large-scale reactive simulations. Results analysis indicated that the acceleration capability was reduced due to increased communication overhead between processors, achieving up to 7.06 times speed-up. However, as the size of the reaction mechanism increases, better acceleration capabilities can be demonstrated. The numerical predictions could closely replicate experimental trends, effectively predicting NO emission trends within the combustion furnace. This study offers one viable solution for rapid and accurate calculations in the OpenFOAM platform, which could be applied in the subsequent ammonia industrial combustion processes.

On optimal constant weight codes derived from $$\omega $$-circulant balanced generalized weighing matrices

On optimal constant weight codes derived from $$\omega $$-circulant balanced generalized weighing matrices

Conscious Experience of Stimulus Presence and Absence Is Actively Encoded by Neurons in the Crow Brain.

The emergence of consciousness from brain activity constitutes one of the great riddles in biology. It is commonly assumed that only the conscious perception of the presence of a stimulus elicits neuronal activation to signify a "neural correlate of consciousness," whereas the subjective experience of the absence of a stimulus is associated with a neuronal resting state. Here, we demonstrate that the two subjective states "stimulus present" and "stimulus absent" are represented by two specialized neuron populations in crows, corvid birds. We recorded single-neuron activity from the nidopallium caudolaterale of crows trained to report the presence or absence of images presented near the visual threshold. Because of the task design, neuronal activity tracking the conscious "present" versus "absent" percept was dissociated from that involved in planning a motor response. Distinct neuron populations signaled the subjective percepts of "present" and "absent" by increases in activation. The response selectivity of these two neuron populations was similar in strength and time course. This suggests a balanced code for subjective "presence" versus "absence" experiences, which might be beneficial when both conscious states need to be maintained active in the service of goal-directed behavior.

Optical Multi-Path Interference Mitigation for PAM4-IMDD Systems Using Balanced Coding

Optical Multi-Path Interference Mitigation for PAM4-IMDD Systems Using Balanced Coding

Alpha heating and avalanche effect simulations for low density proton-boron fusion plasma

The initial interest in p-11B fusion, which produces three (3) alpha particles with total energy of 8.7 MeV, was regained the last few years, due to the important experimental measurements on alpha particle production and theoretical and numerical investigations. The re-evaluation of proton-boron fusion, as an important vector for “aneutronic” energy production, is based on the consideration of the “chain reactions alpha heating effect and the related avalanche effect”, as the important process, for the increase of the fusion species (p, 11B) temperatures, to temperatures corresponding to the optimump-11B fusion cross sections. Investigation of ignition and self-sustained conditions for low density (∼ 1020 m-3) proton-boron fusion plasmas is an interesting study topic for application in magnetic confinement. We use a multi-fluid, global particle and energy balance code, describing the temporal evolution of the physical parameters of the fusion medium, as a function of the initial conditions of density and temperature of the fusion species (p, 11B). For the establishment of the distinct contribution role of the avalanche effect in proton-boron fusion, we explore cases of low (<100 keV) and high (>100 keV) initial p-11B medium temperatures. For these temperature cases, density ratios np /nB > 1between the fusion species (p, 11B) are considered, for the optimization of Bremsstrahlung radiation losses. Simulations using the multi-fluid code in a low density p-11B medium with np /nB > 1, enable the evaluation of the initial temperatures range, which is necessary for the temporal increase of the alpha density, the rapid improvement in the p-11B fusion reaction rate (RR), the temperature rise of the fusion species (p, 11B) and the achievement of higher than 1 Q (Pf /P Brems) values, due to the manifestation of the avalanche effect.In the case of high initial fusion medium temperatures in the range: 150 keV ≤ T in ≤ 350 keV, the chain reactions alpha heating effect and the related avalanche effect contribute to the maintenance and the rise of the fusion species (p, 11B) temperature to high values, for ignition and self-sustained fusion (Q > 1).

New Construction of Balanced Codes Based on Weights of Data for DNA Storage

New Construction of Balanced Codes Based on Weights of Data for DNA Storage

Cyclic Partial Geometries and Their Associated LDPC and Constant-Weight Codes

Cyclic Partial Geometries and Their Associated LDPC and Constant-Weight Codes

A family of diameter perfect constant-weight codes from Steiner systems

If S is a transitive metric space, then |C|⋅|A|≤|S| for any distance-d code C and a set A, “anticode”, of diameter less than d. For every Steiner S(t,k,n) system S, we show the existence of a q-ary constant-weight code C of length n, weight k (or n−k), and distance d=2k−t+1 (respectively, d=n−t+1) and an anticode A of diameter d−1 such that the pair (C,A) attains the code–anticode bound and the supports of the codewords of C are the blocks of S (respectively, the complements of the blocks of S). We study the problem of estimating the minimum value of q for which such a code exists, and find that minimum for small values of t.

White Box Watermarking for Convolution Layers in Fine-Tuning Model Using the Constant Weight Code.

Deep neural network (DNN) watermarking is a potential approach for protecting the intellectual property rights of DNN models. Similar to classical watermarking techniques for multimedia content, the requirements for DNN watermarking include capacity, robustness, transparency, and other factors. Studies have focused on robustness against retraining and fine-tuning. However, less important neurons in the DNN model may be pruned. Moreover, although the encoding approach renders DNN watermarking robust against pruning attacks, the watermark is assumed to be embedded only into the fully connected layer in the fine-tuning model. In this study, we extended the method such that the model can be applied to any convolution layer of the DNN model and designed a watermark detector based on a statistical analysis of the extracted weight parameters to evaluate whether the model is watermarked. Using a nonfungible token mitigates the overwriting of the watermark and enables checking when the DNN model with the watermark was created.

Constant Weight Codes With Gabor Dictionaries and Bayesian Decoding for Massive Random Access

This paper considers a general framework for massive random access based on sparse superposition coding. We provide guidelines for the code design and propose the use of constant-weight codes in combination with a dictionary design based on Gabor frames. The decoder applies an extension of approximate message passing (AMP) by iteratively exchanging soft information between an AMP module that accounts for the dictionary structure, and a second inference module that utilizes the structure of the involved constant-weight code. We apply the encoding structure to (i) the unsourced random access setting, where all users employ a common dictionary, and (ii) to the “sourced” random access setting with user-specific dictionaries. When applied to a fading scenario, the communication scheme essentially operates non-coherently, as channel state information is required neither at the transmitter nor at the receiver. We observe that in regimes of practical interest, the proposed scheme compares favorably with state-of-the art schemes, in terms of the (per-user) energy-per-bit requirement, as well as the number of active users that can be simultaneously accommodated in the system. Importantly, this is achieved with a considerably smaller size of the transmitted codewords, potentially yielding lower latency and bandwidth occupancy, as well as lower implementation complexity.

Exponential Decay of Intersection Volume With Applications on List-Decodability and Gilbert-Varshamov Type Bound

We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) wellspread, and (iii) a certain random variable on the boundary of a ball has a small tail. As applications, we show that the volume of intersection of balls in Hamming, Johnson spaces and symmetric groups decay exponentially as their centers drift apart. To verify condition (iii), we prove some large deviation inequalities ‘on a slice’ for functions with Lipschitz conditions. We then use these estimates on intersection volumes to ∙ obtain a sharp lower bound on list-decodability of random <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -ary codes, confirming a conjecture of Li and Wootters; and ∙ improve the classical bound of Levenshtein from 1971 on constant weight codes by a factor linear in dimension, resolving a problem raised by Jiang and Vardy. Our probabilistic point of view also offers a unified framework to obtain improvements on other Gilbert-Varshamov type bounds, giving conceptually simple and calculation-free proofs for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -ary codes, permutation codes, and spherical codes. Another consequence is a counting result on the number of codes, showing ampleness of large codes.

On Hierarchies of Balanced Sequences

Balanced sequences and balanced codes have attracted a lot of research in the last seventy years due to their diverse applications in information theory as well as other areas of computer science and engineering. There have been some methods to classify balanced sequences. This work suggests two new different hierarchies to classify these sequences. The first one is based on the largest <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell $ </tex-math></inline-formula> for which each <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell $ </tex-math></inline-formula> -tuple is contained the same amount of times in the sequence. This property is a generalization for the property required for de Bruijn sequences. The second hierarchy is based on the number of balanced derivatives of the sequence. Enumeration for each such family of sequences and efficient encoding and decoding algorithms are provided in this paper.

A new construction for q-ary constant weight codes

For a given prime power q, a new method for constructing q-ary constant weight codes is presented, and then several classes of q-ary constant weight codes are given by using the trace map over finite fields. Especially, for q=2, some of these codes are optimal, and then the maximal possible sizes of two classes of binary constant weight codes are determined.

Correction: A new binary (17,4,5) constant weight code

Correction: A new binary (17,4,5) constant weight code

Identification Codes: A Topical Review With Design Guidelines for Practical Systems

A wide range of information technology applications require the identification of a particular message or label that represents the identity of an object at a distance, e.g., over a wireless channel. Conventionally, the underlying information that represents the identity is transmitted over the channel, following the information-theoretic concept of message transmission. If the purpose of the interaction over the channel is only to verify (match) an identity, then the concept of identification over channels—utilizing the identification codes that have been developed by the information theory community—can provide an exponential efficiency gain over message transmission. This topical review article conducts for the first time a comprehensive detailed evaluation of the existing identification codes for the practically relevant regime of finite parameters. We examine essentially all published identification codes, including codes based on inner constant weight codes that are concatenated with outer linear block codes, such as Reed-Solomon and Reed-Muller codes. Specifically, we conduct a holistic identification code comparison based on the logarithm of the number of representable identities (in shannon), the size (in bit) of the transmitted cue that represents an identity, and the corresponding type II error probability bound for essentially all existing identification codes. Based on the resulting insights, we formulate guidelines for the design of practical (finite-parameter) identification codes. For instance, we find that a linear block code (without concatenation with a sophisticated inner constant-weight code) is sufficient for most practical identification code usages.

Minimally Modified Balanced Codes

We present and analyze a new construction of bipolar balanced codes where each codeword contains equally many −1’s and +1’s. The new code is minimally modified as the number of symbol changes made to the source word for translating it into a balanced codeword is as small as possible. The balanced codes feature low redundancy and time complexity. Large look-up tables are avoided.

МЕТОД СИНТЕЗА САМОПРОВЕРЯЕМЫХ УСТРОЙСТВ С КОНТРОЛЕМ ВЫЧИСЛЕНИЙ ПО ДВУМ ДИАГНОСТИЧЕСКИМ ПАРАМЕТРАМ С ПРЕДВАРИТЕЛЬНЫМ СЖАТИЕМ СИГНАЛОВ ОТ ОБЪЕКТА ДИАГНОСТИРОВАНИЯ

The structure of self-checking digital devices with calculation control by two diagnostic parameters has been proposed. The belonging of being formed in in-built control circuit codeword to constant-weight code “2-out-of-4” is used as a first parameter. A second parameter is the belonging of each being calculated function to the class of self-dual Boolean functions. The specificity of being described in the article the organization structure of self-checking digital devices is the presence of the circuit of preliminary compression of signals from diagnosis object. Its usage allows to cut structural redundancy of end device down essentially. Besides, nevertheless, errors can be masked at the inputs of compression elements. The article underlines the features of the choice of being compressed outputs of diagnosis object and the algorithm is proposed allowing to minimize the risk of undetectable error occurrence at compression scheme output. The algorithm of built-in control scheme synthesis by two diagnosis parameters has been presented which takes into account conditions for the formation of full set of test combinations for testers and elements of transformation in signal correction block. The example of realization of synthesis algorithm for fully self-checking device Logisim is considered. Key features of built-in control scheme are denoted; the scheme is embodied according to the proposed structure. The way of organizing calculation control by two diagnostic parameters is of interest at the synthesis of fully self-checking digital calculation devices and systems.

Label Guided Discrete Hashing for Cross-Modal Retrieval

Due to their low storage capacity and fast retrieval speed, hashing techniques have received much attention in cross-modal retrieval. However, there are some issues that need to be further explored. First, some existing hashing methods use the labels to construct the semantic similarity matrix between pairwise data, ignoring the potential manifold structure between heterogeneous data. Second, some existing methods underestimate the importance of multi-label and the gaps between different class labels, making the learned hash codes less discriminative. Third, few of them embed both manifold and balanced structures within the same model, and the relaxation of discrete constraints will lead to an increasing quantization error. To mitigate these problems, this paper proposes a novel supervised hashing method, termed Label Guided Discrete Hashing (LGDH), which simultaneously preserves the comprehensive manifold structure and discriminative balanced codes that are both constructed by label information into Hamming space. We develop a local category distribution of the nearest neighbors, to excavate the underlying manifold structure of heterogeneous data. To maximize the gaps of different categories, a balanced matrix is constructed by labels to generate hash codes with balanced bits. For multi-label data, we also design a novel multi-label manifold and balanced structure matrix to adapt the real-world scenarios. An effective discrete optimization method is used to optimize our proposed objective function instead of the relaxation one. Extensive experiments on three benchmark datasets verify the effectiveness of LGDH. The comparison results demonstrat that LGDH achieves about 2% and 3% improved to different cross-modal tasks on average.