Constant Weight Codes Research Articles

This paper gives some theory and efficient design of $q$-ary block codes capable of controlling the single peak-shifts of one direction (left or right shift) of size $l$. This problem of controlling $l_{L}(l_{R})$-peak-shift is shown to be equivalent to the efficient design of some $L_{1}$ metric asymmetric error control codes over the natural alphabet, $\inat$. From the relations with the $L_{1}$ distance error control codes and constant weight codes, new improved upper and lower bounds on the size of the optimal single $l_{L}(l_{R})$-peak-shifts error correcting codes are given. Furthermore, some non-systematic code designs are also given. Decoding can be efficiently performed by algebraic means with the Extended Euclidean Algorithm.

In the big data era, data are created in huge volume. This leads to the development of storage devices. Many technologies are proposed for the next generation of storage fields. However, among them, holographic data storage (HDS) has attracted much attention and has been introduced as the promising candidate to meet the increasing demand for capacity and speed. For signal processing, HDS faces two major challenges: inter-page interference (IPI) and two-dimensional (2D) interference. To access the IPI problem, we can use balanced coding, which converts user data into an intensity level with uniformly distributed values for each page. For 2D interference, we can use the equalizer and detection to mitigate the 2D interference. However, the often-used equalizer and detection are methods in wireless communication and only handle the one-dimensional (1D) signal. Thus, we can combine the equalizer, detection, and estimator to reduce 2D interference into 1D interference. In this paper, we proposed a combined model using serial maximum a posteriori (MAP) detection and estimator to improve the detection of HDS systems. In our proposed model, instead of using an estimator with the Viterbi algorithm to predict the upper–lower interference (UPI) or left–right interference (LRI) and converting the received signal into 1D ISI, we used the estimator to predict the extrinsic information for serial MAP detection. This preserves the 2D information in the received signal in serial MAP detection and improves the detection of serial MAP detection by extrinsic information. The simulation results demonstrate that our proposed model significantly improves the bit-error rate (BER) performance compared to previous studies.

New Results on Optimal (υ, 4, 1) Binary Cyclically Permutable Constant-Weight Codes

Aneutronic p-11B nuclear fusion is promising for clean energy production, as it produces three (3) alpha particles with 8.7 MeV total energy. However, the main difficulty for p-11B fusion ignition (Q = Pfus/PBrems≥ 1) concerns the nuclear cross section and thus, reactivity efficiency at higher than 200 keV medium temperatures. To overcome this difficulty, the present work emphasizes on the numerical investigation of medium schemes (configurations) with enhanced reactivity. The configurations refer to the addition of energetic protons in a low-density 11boron or proton–11boron medium (n = 1020 m−3), with (np/nB) > 1 for Bremsstrahlung losses optimization and initial temperature in the range of 1 keV ≤ Tin≤ 400 keV. A self-consistent multi-fluid global particle and energy balance code, including collisions between all medium species (p, 11B, e, α), is used for the description of the temporal evolution of all fusion medium physical parameters and the evaluation of the optimum initial conditions for the obtainment of Q ≥ 1. The numerical simulation results show that the coupling between the 200 keV < Ep,0≤ 750 keV energetic protons and the 1 keV ≤ Tin≤ 400 keV initial fusion medium leads to ignition, 1 ≤ Q < 1.4, below Tin= 100 keV. In all the presented initial medium temperature cases, and especially, the lower (<) than 100 keV, the ignition condition (Pfus/PBrems) > 1 arises, as a consequence of the chain reactions and the related avalanche alpha heating effect.

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.

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.

Abstract A design is said to be super‐simple if the intersection of any two blocks has at most two elements. A design with index is said to be completely reducible, if its blocks can be partitioned into nonempty collections , such that each together with the point set forms a design with index unity. In this paper, it is proved that there exists a completely reducible super‐simple (CRSS) balanced incomplete block design (‐BIBD for short) if and only if and or . A ‐ary constant weight code (CWC) of length with weight and distance is denoted as a code. The maximum size of a code is denoted as , and the codes achieving this size are called optimal. CRSS designs with index are closely related to ‐ary CWCs. By using the results of CRSS ‐BIBDs, s are determined for all .

Approximate generalized Steiner systems and near-optimal constant weight codes

An Update on Optimal $(v,4,1)$ Binary Cyclically Permutable Constant Weight Codes and Cyclic $2$-$(v,4,1)$ Designs with Small $v$

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

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

In paper of Staddon and Wei [4] ; there were open problems (1) “ Do there exist w- IPP codes with the property w < q < [(w + 2)2 / 4] ? ” (2) “Can we construct interesting w-TA(w-traceable) codes with n < q and q < w2 ? ” Here in this paper we give that answer and suggest some Combinatorial Designs which meet the above conditions and prove them to be 2-TA and 3-TA Codes. In this paper our spotlight is mainly on Equireplicate Codes and Lexicographic Codes where each element occurs equally often. A few of these codes discussed in (Sinha et. al.2008) are also experimental to be excellent Equidistant Constant Weight Codes

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

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

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

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.

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.