Optimal Codes Research Articles

Two Classes of Optimal Ternary Cyclic Codes with Minimum Distance Four

Two Classes of Optimal Ternary Cyclic Codes with Minimum Distance Four

Optimal Binary Few-Weight Codes Using a Mixed Alphabet Ring and Simplicial Complexes

Optimal Binary Few-Weight Codes Using a Mixed Alphabet Ring and Simplicial Complexes

Near-Optimal Performance of Quantum Error Correction Codes.

The Knill-Laflamme conditions distinguish exact quantum error correction codes, and they have played a critical role in the discovery of state-of-the-art codes. However, the family of exact codes is a very restrictive one and does not necessarily contain the best-performing codes. Therefore, it is desirable to develop a generalized and quantitative performance metric. In this Letter, we derive the near-optimal channel fidelity, a concise and optimization-free metric for arbitrary codes and noise. The metric provides a narrow two-sided bound to the optimal code performance, and it can be evaluated with exactly the same input required by the Knill-Laflamme conditions. We demonstrate the numerical advantage of the near-optimal channel fidelity through multiple qubit code and oscillator code examples. Compared to conventional optimization-based approaches, the reduced computational cost enables us to simulate systems with previously inaccessible sizes, such as oscillators encoding hundreds of average excitations. Moreover, we analytically derive the near-optimal performance for the thermodynamic code and the Gottesman-Kitaev-Preskill code. In particular, the Gottesman-Kitaev-Preskill code's performance under excitation loss improves monotonically with its energy and converges to an asymptotic limit at infinite energy, which is distinct from other oscillator codes.

DMMC: A Polar Code Construction Method for Improving Performance in TLC NAND Flash

3D TLC NAND flash memory significantly increases the storage capacity but makes data more prone to errors. To address the reliability problem, Polar Code is one coding method that can reach the channel capacity1. However, the 3D NAND flash memory channel is uncertain due to the variation of retention time and program/erase(P/E) cycle. So it is difficult to construct Polar Code in NAND flash memory. This paper proposes a new Polar Code construction method called Dynamic Merge Monte Carlo(DMMC). DMMC uses the Monte Carlo method to obtain the optimal Polar Code construction and then reduces the space overhead by combining similar construction so that it can be used in flash memory systems. Compared with the conventional method, the uncorrectable bit error rate(UBER) of the proposed method can reduce by up to 90.5%, and the read latency can reduce by more than 50%.

Some new constructions of optimal linear codes and alphabet-optimal $$(r,\delta )$$-locally repairable codes

Some new constructions of optimal linear codes and alphabet-optimal $$(r,\delta )$$-locally repairable codes

Topology optimization for magnetic circuits with continuous adjoint method in 3D

PurposeThe purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.Design/methodology/approachTo provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.FindingsIn this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.Originality/valueIn this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

Topological optimization in 3D-magnetostatics: development of adjoint methods using the equations of magnetic moments

PurposeThe purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.Design/methodology/approachFirst, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.FindingsIn this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.Research limitations/implicationsThis research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.Originality/valueThe problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

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

Data-driven modeling and fast adjustment for digital coded metasurfaces database: Application in adaptive electromagnetic energy harvesting

Metasurfaces (MSs) show great promise in efficient electromagnetic energy harvesting (EMEH) due to their compactness, high efficiency, and long-distance transmission capabilities. Nonetheless, the conventional iterative and time-consuming solving process of MSs significantly escalates computational demands. Furthermore, once processed, the MS shape remains fixed and cannot be adapted to changing requirements. Accordingly, a critical challenge is the development of a new efficient solver for MS real-time tuning. Here, we introduce a class of digital coded MS databases including multiple pre-defined resonant frequency MS. The combination of multiple MS base functions from the database enables swift resonance frequency adjustments to adapt to changing environmental conditions. A topology optimization method based on data-driven modeling is employed to rapidly acquire the optimal digital coding for the corresponding MS at various operating frequencies, facilitating the construction of a database. This approach integrates a convolutional neural network and genetic algorithm (CNNGA). It not only enables more accurate and expedited forward prediction of MSs' electromagnetic (EM) response but also facilitates inverse design based on specified requirements. We employ this method to design a MS that achieves perfect energy harvesting (EH) over a broad range of incident angles and polarization directions. In addition, a data-driven modeling is used to establish an EH efficiency predictive model corresponding to MS combination. This model serves as a guide for real-time MS adjustments as per changing requirements. Compared to previously designed MSs, this model achieves rapid design and adaptive adjustment capabilities. Through the incorporation of various functional MS base functions into the database, this method can be universally applied to MS combinations tailored to specific functions, including EM cloaking, ultra-thin flat lenses, and computational MSs.

Towards Hybrid-Optimization Video Coding

Video coding that pursues the highest compression efficiency is the art of computing for rate-distortion optimization. The optimization has been approached in different ways, exemplified by two typical frameworks: block-based hybrid video coding and end-to-end learned video coding. The block-based hybrid framework encompasses more and more coding modes that are available at the decoder side; an encoder tries to search for the optimal coding mode for each block to be coded. This is an online, discrete, search-based optimization strategy. The end-to-end learned framework embraces more and more sophisticated neural networks; the network parameters are learned from a collection of videos, typically using gradient descent-based methods. This is an offline, continuous, numerical optimization strategy. Having analyzed these two strategies, both conceptually and with concrete schemes, this paper suggests investigating hybrid -optimization video coding, that is to combine online and offline, discrete and continuous, search-based and numerical optimization. For instance, we propose a hybrid-optimization video coding scheme, where the decoder consists of trained neural networks and supports several coding modes, and the encoder adopts both numerical and search-based algorithms for the online optimization. Our scheme achieves promising compression efficiency on par with H.265/HM for the random-access configuration.

Obtaining new classes of optimal linear codes by puncturing and shortening optimal cyclic codes

AbstractIn this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new classes of optimal linear codes achieving the Griesmer bound. The weight distributions for these codes are settled. We also investigate their dual codes and show that they are either optimal or almost optimal with respect to the sphere-packing bound. Moreover, these duals contain classes of almost maximum distance separable codes which are shown to be proper for error detection. Further, some of the obtained optimal linear codes are suitable for constructing secret sharing schemes with nice access structures.

Optimization of nonlinear turbulence in stellarators

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles.

A new look at the fluorescent protein-based approach for identifying optimal coding sequence for recombinant protein expression in E. coli.

Due to the degeneracy of the genetic code, most amino acids are encoded by several codons. The choice among synonymous codons at the N-terminus of genes has a profound effect on protein expression in Escherichia coli. This is often explained by the different contributions of synonymous codons to mRNA secondary structure formation. Strong secondary structures at the 5'-end of mRNA interfere with ribosome binding and affect the process of translation initiation. In silico optimization of the gene 5'-end can significantly increase the level of protein expression; however, this method is not always effective due to the uncertainty of the exact mechanism by which synonymous substitutions affect expression; thus, it may produce nonoptimal variants as well as miss some of the best producers. In this paper, an alternative approach is proposed based on screening a partially randomized library of expression constructs comprising hundreds of selected synonymous variants. The effect of such substitutions was evaluated using the gene of interest fused to the reporter gene of the fluorescent protein with subsequent screening for the most promising candidates according to the reporter's signal intensity. The power of the approach is demonstrated by a significant increase in the prokaryotic expression of three proteins: canine cystatin C, human BCL2-associated athanogene 3 and human cardiac troponin I. This simple approach was suggested which may provide an efficient, easy, and inexpensive optimization method for poorly expressed proteins in bacteria.

On construction of ternary optimal self-orthogonal codes

On construction of ternary optimal self-orthogonal codes

Entropic Bounds on the Average Length of Codes with a Space.

We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that their average length differs from the minimum possible by at most one. We obtain our results by uncovering a relation between our class of codes and the class of one-to-one codes. Additionally, we derive upper and lower bounds to the average length of optimal prefix-free codes with a space in terms of the source entropy.

B-ITO: A MATLAB toolbox for isogeometric topology optimization with Bézier extraction of NURBS

The Bézier extraction can decompose the NURBS-based isogeometric analysis (IGA) elements into a series of Bézier elements with C0 continuity, which is considered into developing a higher efficient isogeometric topology optimization (ITO) method. The main focus of the current work is to develop a MATLAB toolbox for isogeometric topology optimization (ITO) with the Bézier extraction of NURBS, termed by the B-ITO. An isogeometric Bézier element data structure is constructed using the extraction operator, which keeps an analogous structure of classic finite element methods (FEM). It can effectively ensure the IGA to be easily integrated into the existing FEM codes with a little modification, which can also promote the development of the ITO in several problems using existing FEMs and topology optimization codes. The B-ITO toolbox mainly consists of the following modules: MODEL, PREIGA, BOUND, EXTRABEZIER2D, SHAPE2D, STIFFBEZ2D, SHEPHARD, ASSEMBLE2D, SOLVE, PLOT and OC. It allows engineers and researchers to easily perform optimization problems in the toolbox with direct modifications of the related modules for design objectives. Moreover, a much higher efficient version of the B-ITO with a module STIFFBER2D is proposed for the rectangular design domains with the help of the local persevering property of the Bernstein basis function space, which can to a great extent reduce the computational cost. Finally, several numerical examples are discussed using the B-ITO to demonstrate its effectiveness and efficiency.

E2F-Net: Eyes-to-face inpainting via StyleGAN latent space

Face inpainting, the technique of restoring missing or damaged regions in facial images, is pivotal for applications like face recognition in occluded scenarios and image analysis with poor-quality captures. This process not only needs to produce realistic visuals but also preserve individual identity characteristics. The aim of this paper is to inpaint a face given periocular region (eyes-to-face) through a proposed new Generative Adversarial Network (GAN)-based model called Eyes-to-Face Network (E2F-Net). The proposed approach extracts identity and non-identity features from the periocular region using two dedicated encoders have been used. The extracted features are then mapped to the latent space of a pre-trained StyleGAN generator to benefit from its state-of-the-art performance and its rich, diverse and expressive latent space without any additional training. We further improve the StyleGAN's output to find the optimal code in the latent space using a new optimization for GAN inversion technique. Our E2F-Net requires a minimum training process reducing the computational complexity as a secondary benefit. Through extensive experiments, we show that our method successfully reconstructs the whole face with high quality, surpassing current techniques, despite significantly less training and supervision efforts. We have generated seven eyes-to-face datasets based on well-known public face datasets for training and verifying our proposed methods. The code and datasets are publicly available.11https://github.com/fatemejamalii/E2F-Net

Optimal Construction for Decoding 2D Convolutional Codes over an Erasure Channel

In general, the problem of building optimal convolutional codes under a certain criteria is hard, especially when size field restrictions are applied. In this paper, we confront the challenge of constructing an optimal 2D convolutional code when communicating over an erasure channel. We propose a general construction method for these codes. Specifically, we provide an optimal construction where the decoding method presented in the bibliography is considered.

Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function

There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin–Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin–Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.

New Constructions of Optimal Linear Codes From Simplicial Complexes

New Constructions of Optimal Linear Codes From Simplicial Complexes