Optimal Codes Research Articles

Code and Data Repository for Binary Quantum Control Optimization with Uncertain Hamiltonians

The goal of this software is to implement the gradient-based and rounding algorithms proposed in the paper to solve the binary quantum control optimization problem with uncertain Hamiltonians.

Layer codes

Quantum computers require memories that are capable of storing quantum information reliably for long periods of time. The surface code is a two-dimensional quantum memory with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet optimal code was not previously known. Here we present a family of three dimensional topological codes with optimal scaling code parameters and a polynomial energy barrier. Our codes are based on a construction that takes in a stabilizer code and outputs a three-dimensional topological code with related code parameters. The output codes are topological defect networks formed by layers of surface code joined along one-dimensional junctions, with a maximum stabilizer check weight of six. When the input is a family of good quantum low-density parity-check codes the output codes have optimal scaling. Our results uncover strongly-correlated states of quantum matter that are capable of storing quantum information with the strongest possible protection from errors that is achievable in three dimensions.

Wide-angle low-scattering transmitarray antenna based on transmit-reflect selective metasurface

Abstract A high-gain transmitarray antenna with low radar cross section (RCS) properties is presented in this paper. Compared with conventional high-profile multilayer designs, we introduce a transmit-reflect selective metasurface integrated with high-gain transmission and random scattering functions, achieving a reduced thickness of 0.13 λ 0 (where λ 0 is the wavelength at the center frequency). For the meta-atom design, we combine geometric rotation and dimension optimization to realize 1-bit independent transmit and reflection phase modulation, respectively. Moreover, in metasurface coding strategy, we employ an initial phase optimization method and a simulated annealing algorithm to determine the optimal coding matrices. The experimental results demonstrate high-performance radiation characterized by the peak gain of 23.6 dB, maximum aperture efficiency of 28.5%, and 3 dB gain bandwidth of 18.4%. For x-polarization, measured 10 dB RCS reduction bandwidth under transverse magnetic (TM) 0°-45° and transverse electric (TE) 0°-20° incidence are 9.02–11.36 GHz. For y-polarization, 10 dB RCS reduction bandwidth under TM 0–60° and TE 0–30° incidence is 8.82–10.96 GHz.

FreeTO - Freeform 3D topology optimization using a structured mesh with smooth boundaries in Matlab

Topology optimization has revolutionized the design of structures for various applications, particularly with the advancement of additive manufacturing. However, existing open-source codes for topology optimization have limitations, such as restricted domain initialization and lack of a CAD output after optimization. A novel open-source Matlab code, FreeTO, is presented, and it addresses these limitations by enabling the initialization of 3D arbitrary geometries and providing an STL file post-optimization. FreeTO utilizes a structured mesh and a smooth-edge (boundary) algorithm to generate smooth topological boundaries. The code is demonstrated through six practical design cases, showcasing its effectiveness in compliance minimization, compliant mechanisms, and self-supporting problems. FreeTO offers a user-friendly, all-in-one topology optimization package, making it an invaluable tool for educators, researchers, and practitioners. Future developments will focus on eliminating a few geometrical deviations in the optimized topologies, incorporating speedups, and extending the code to apply to more applications.

SparseAuto: An Auto-scheduler for Sparse Tensor Computations using Recursive Loop Nest Restructuring

Automated code generation and performance enhancements for sparse tensor algebra have become essential in many real-world applications, such as quantum computing, physical simulations, computational chemistry, and machine learning. General sparse tensor algebra compilers are not always versatile enough to generate asymptotically optimal code for sparse tensor contractions. This paper shows how to generate asymptotically better schedules for complex sparse tensor expressions using kernel fission and fusion. We present generalized loop restructuring transformations to reduce asymptotic time complexity and memory footprint. Furthermore, we present an auto-scheduler that uses a partially ordered set (poset)-based cost model that uses both time and auxiliary memory complexities to prune the search space of schedules. In addition, we highlight the use of Satisfiability Module Theory (SMT) solvers in sparse auto-schedulers to approximate the Pareto frontier of better schedules to the smallest number of possible schedules, with user-defined constraints available at compile-time. Finally, we show that our auto-scheduler can select better-performing schedules and generate code for them. Our results show that the auto-scheduler provided schedules achieve orders-of-magnitude speedup compared to the code generated by the Tensor Algebra Compiler (TACO) for several computations on different real-world tensors.

Error rates of optically pre-amplified PPM wireless systems with coding and arbitrary optical filter response

We present novel results for the uncoded and coded bit-error probability (BEP) of optically pre-amplified pulse-position modulation (PPM) wireless systems. For uncoded systems, a novel analytic method for the evaluation of the BEP is derived. The method takes into account the non-ideal optical filter response and utilizes a finite Karhunen–Loève series expansion to calculate the BEP. Using the proposed approach, it is possible to accurately evaluate the PPM BEP for arbitrarily shaped filters where the well-established χ2 method only provides approximate results. Considering a Lorentzian filter response, the discrepancy between the two methods amounts to 0.5 dB in a variety of filter bandwidths and PPM modulation orders. The Lorentzian filter response was chosen as an illustrative practical example whose series can be calculated analytically. The proposed method is also valid for any type of optical filter for which the Karhunen–Loève series expansion can be calculated analytically or numerically. Due to the finite number of terms that are required irrespective of the signal energy level, the proposed method can also be applied without loss of accuracy to assess the system performance under the effects of turbulence and adverse weather conditions. For coded systems with Lorentzian filters, Monte-Carlo simulations are utilized to evaluate the BEP performance of the 5G LDPC codes, and it is demonstrated that they impart an energy gain up to 3.3 dB for 4–PPM and 2.3 dB for 16–PPM at a target BEP of 10−5. The optimal code rates are also discussed for several combinations of the optical filter bandwidth and PPM modulation order and it is shown that in almost all of the cases the optimal code rate is 11/13. Moreover, the sum-product and min-sum decoders perform within 0.1 dB from each other for the best code rates, which points towards the utilization of the min-sum decoder in all settings, since its operation does not require knowledge of the filter parameters. Finally, the comparison between the coded systems with Lorentzian and ideal passband filters exhibits the same 0.5 dB discrepancy that was observed for uncoded systems.

Infinite Families of Few Weight Optimal Binary Linear Codes From Multivariable Functions

Infinite Families of Few Weight Optimal Binary Linear Codes From Multivariable Functions

Constructing optimal few weight quaternary linear codes via multivariable functions

Constructing optimal few weight quaternary linear codes via multivariable functions

On the largest minimum distances of [n,6] LCD codes

Linear complementary dual (LCD) codes can be used to resist side-channel attacks and fault noninvasive attacks. Let da(n,6) and dl(n,6) be the minimum weights of all binary optimal linear codes and LCD codes with length n and dimension 6, respectively. In this article, we aim to obtain the values of dl(n,6) for n≥51 by investigating the nonexistence and constructions of LCD codes with given parameters. Suppose that s≥0 and 0≤t≤62 are two integers and n=63s+t. Using the theories of defining vectors, generalized anti-codes, reduced codes and nested codes, we exactly determine dl(n,6) for t∉{21,22,25,26,33,34,37,38,45,46}, while we show that dl(n,6)∈{da(n,6)−1,da(n,6)} for t∈{21,22,26,34,37,38,46} and dl(n,6)∈{da(n,6)−2, da(n,6)−1} for t∈{25,33,45}.

Some Results for Double Cyclic Codes over Fq+vFq+v2Fq.

Let Fq be a finite field with an odd characteristic. In this paper, we present a new result about double cyclic codes over a finite non-chain ring. Specifically, we study the double cyclic code over Fq+vFq+v2Fq with v3=v, which is isomorphic to Fq×Fq×Fq. This study mainly involves generator polynomials and generator matrices. The generating polynomial of the dual code is also obtained. We show the relationship between the generating polynomials of the double cyclic codes and those of their dual codes. Finally, as an application of these results, we construct some optimal codes over F3.

Reinforcement Learning for Jointly Optimal Coding and Control Policies for a Markovian System Controlled over a Communication Channel

This paper develops approximation and optimality results for the optimal control of a networked system. In this system, a Markovian process is managed over a finite-rate, noiseless communication channel. Solving this problem involves determining joint optimal coding and control policies that minimize cost over time. While theoretical results on optimal coding and control structures exist, practical implementation has remained largely infeasible for non-linear systems due to the computational complexities and uncountable state spaces. This research introduces an approach that combines structural results with reinforcement learning (RL) techniques. The method uses regularity properties of the system to approximate the uncountable state space with a countable one, which allows reinforcement learning algorithms to achieve near-optimal solutions. Specifically, we establish that finite model approximations (where infinite state spaces are quantized to finite ones) and sliding finite window approximations (where a finite memory "window" of past control actions is maintained at each time step) can be employed to develop near-optimality. These approximations allow the system to be reformulated as a Markov Decision Problem (MDP) with a finite state space, making RL algorithms implementable. The convergence of the reinforcement learning algorithm to a near-optimal policy (under both the previous approximations) is supported by theoretical analysis and performance simulations. We ensure that the solutions obtained are not only computationally feasible but also nearly optimal with respect to the original problem. The applications of this work extend to many networked control systems, especially those with zero-delay coding and partially observable Markov decision processes (POMDPs). By integrating structural results with learning algorithms, this paper provides a practical framework for implementing optimal control in finite-rate environments.

Metalens Topology Optimization

Photonic metasurfaces are thin optical elements comprised of structures arranged strategically upon a surface to manipulate electromagnetic waves. To produce metasurfaces at a large scale, it is beneficial to obtain not just an optimal design, but also an understanding of which areas of the metasurface are most influential on the overall performance of the device and require greater manufacturing accuracy. My work consisted of implementing and testing a new physics-based method for identifying the relative importance of different regions of a proposed metasurface design. This method built on an existing topology optimization code, where the designable region of the metasurface was discretized, and the material density of each point in the design was optimized such that incoming light was maximally focussed to a target location. The existing optimization algorithm was then coupled to a molecular dynamics model called a Nosé-Hoover thermostat, by modelling the discrete locations on the design region as particles and their corresponding material densities as their positions. By numerically integrating the equations of motion of the thermostat model, I was able to generate metasurface designs at different thermostat temperatures, and observe how the designs changed with increasing temperature. To determine the most important areas of the metasurface design, I calculated the entropy of each of the "particles" for all temperature samples, and looked for design regions that had low entropy even at high temperatures, indicating strong convergence on an optimal material density value amidst high thermal noise. Once I implemented this design analysis framework, I tested it on both a metalens and a reflector design at multiple wavelengths of incoming light. My results demonstrated that this physics-based method provides easily interpretable information about the relative importance of different elements of a metasurface design.

Optimization framework of clean heat and CO2 supply for agricultural greenhouses exploiting industrial symbiosis

The rising demand for greenhouse cultivation poses a challenge in providing environmentally friendly energy to maintain favorable greenhouse indoor conditions. This research presents an optimization model to identify cost-optimal symbiotic pathways to replace the import of three key greenhouse crops (tomato, cucumber, lettuce) with local greenhouse production. The proposed solutions involve greenhouses that can meet these crops' heat and CO2 demands via industrial symbiosis. Switzerland is investigated as the case study, and the (waste) heat suppliers are municipal solid waste incinerators, cement production plants and biogas plants. Upgrading biomethane production plants are also considered potential CO2 suppliers. The objective is to minimize the discounted cost when replacing 25%–100 % of vegetable imports with local agricultural greenhouses, considering availability of suitable land as well as waste heat and CO2 suppliers. Optimization results suggest prioritizing northeast and west Switzerland for greenhouse development, due to the availability of suitable land and proximity of waste heat and CO2 suppliers. Waste incinerators could provide 50%–70 % of the necessary heat, while Organic Rankine cycle in cement plants could generate 63 % of the electricity of supplementary lighting demand of greenhouses. While tailored for Switzerland, the optimization framework's general formulation can be adapted also to other regions to optimize greenhouses' heat and CO2 demands. The optimization code is provided open source for associated applications.

Design of an Anti-interference long-range acoustic Communication System Based on optimal length segment coding

Abstract With the increased demand for unmanned vehicles in marine development, the development of underwater acoustic communication technology has received much attention. One of the key technologies in the research of long-range underwater acoustic communication technology is the use of underwater acoustic channels for efficient and stable data transmission. The harsh environment of the underwater acoustic channel has a significant impact on the rate and quality of underwater acoustic communication, making it a challenging research direction to achieve high-speed and reliable telecommunication systems underwater. In this paper, a high-speed remote command-based communication system is investigated, and a long-range acoustic communication system with good adaptability to sudden and continuous interference is designed based on a remote unmanned platform. A method for encoding the communication message in segments of optimal length is proposed in this paper. This coding method can enhance the anti-sudden interference capability of the communication system which has a certain degree of communication confidentiality, and the performance of this anti-interference communication system is verified by laboratory tests and field tests. The verification results show that the proposed telecommunication system based on optimal length segment coding has better performance in anti-sudden interference and continuous interference, which can make the communication system performance more stable and increase the success rate of command-based communication significantly.

Optimal RS Codes and GRS Codes Against Adversarial Insertions and Deletions and Optimal Constructions

Optimal RS Codes and GRS Codes Against Adversarial Insertions and Deletions and Optimal Constructions

Construction of Optimal Two-Dimensional Optical Orthogonal Codes with at Most One Pulse per Wavelength.

Two-dimensional optical orthogonal codes have important applications in optical code division multiple access networks. In this paper, a generic construction of two-dimensional optical orthogonal codes with at most one pulse per wavelength (AM-OPPW 2D OOCs) is proposed. As a result, some optimal AM-OPPW 2D OOCs with new parameters can be yielded. The new AM-OPPW 2D OOC may support more subscribers and heavier asynchronous traffic compared with known constructions.

Roof stability analysis for a shallow-buried cylindrical tunnel in Hoek-Brown rock strata

Roof stability of shallow-buried cylindrical tunnels in rock strata following the generalized Hoek-Brown criterion (GHB) is analyzed in this work. Based on the limit analysis method, a three-dimensional (3D) shallow-buried collapse mechanism for tunnel roofs is developed to derive various stability measures. Optimization codes are programmed to capture the optimal stability measure solutions. The effects of the 3D geometric characteristics, the rock mass strength parameters, and the buried depth on tunnel roof stability are investigated by a parametric analysis. The critical buried depth ratios corresponding to the transition between the shallow-buried and deep-buried tunnel roof collapse mechanisms are also presented. Thereafter a series of stability charts of the required supporting pressure and the factor of safety (FoS) is proposed for design purposes. This study provides a theoretical basis for design and engineering of tunnels with limited buried depth.

Optimal Local Identifying and Local Locating-dominating Codes

We introduce two new classes of covering codes in graphs for every positive integer r. These new codes are called local r-identifying and local r-locating-dominating codes and they are derived from r-identifying and r-locating-dominating codes, respectively. We study the sizes of optimal local 1-identifying codes in binary hypercubes. We obtain lower and upper bounds that are asymptotically tight. Together the bounds show that the cost of changing covering codes into local 1-identifying codes is negligible. For some small n optimal constructions are obtained. Moreover, the upper bound is obtained by a linear code construction. Also, we study the densities of optimal local 1-identifying codes and local 1-locating-dominating codes in the infinite square grid, the hexagonal grid, the triangular grid and the king grid. We prove that seven out of eight of our constructions have optimal densities.

Characterization and classification of optimal ternary linear one-dimensional hull codes

Characterization and classification of optimal ternary linear one-dimensional hull codes

Solubility of 2,5-Furandicarboxylic Acid in Pure and Mixed Organic Solvent Systems at 293 K Predicted Using Hansen Solubility Parameters.

Central to the production of polyethylene furanoate (PEF), a bioplastic that could potentially replace petroleum-derived plastics, is 2,5-furandicarboxylic acid (FDCA). FDCA is a chemical derived from biomass that has low solubility in traditionally used solvents such as water. Thus, identifying solvents that can solubilize significant amounts of FDCA could allow for lower PEF production costs. In this study, FDCA solubility was investigated in nine pure solvents including H2O, acetonitrile (ACN), γ-valerolactone (GVL), γ-butyrolactone (GBL), ethanol (EtOH), methanol (MeOH), dimethyl sulfoxide (DMSO), sulfolane (SULF), and tetrahydrofuran (THF), eight binary, and three ternary solvent blends at 293 K. For all binary systems excluding DMSO and MeOH, the solubility of FDCA increased 1.5-65 times compared to the pure organic solvent, and the FDCA solubility was at least 10 times higher when compared to pure water. Specifically, the 20/80 w/w H2O/DMSO system solubilized 23.1 wt % FDCA, the highest of any binary blend studied, and 190 times more solubility than in pure water. In 20/80 w/w H2O/THF, the FDCA solubility was 60 times higher than pure water. In ternary blends that included DMSO, H2O, and either GVL, THF, or SULF, solubility increased by at least 6.6 times relative to the pure secondary organic component and 54 times relative to pure water. Using Hansen solubility parameters (HSPs), the radius of interaction (R i,j ) was found to be more strongly correlated to FDCA solubility than individual HSPs or the total solubility parameter. A MATLAB-based optimization code was developed and successful in minimizing the R i,j of a solvent blend to maximize FDCA solubility in binary and ternary aqueous solvents.