Construction Of Codes Research Articles

Australia’s Combustible Cladding Crisis—A Failure in Delegated Legislation?

Australia’s combustible cladding crisis is estimated to cost approximately $6 billion to remediate. No study has been published which determined the causative factors for the magnitude of this issue. Investigators for the Federal Building Ministers’ Forum stated that building practitioners misinterpreted or ignored the requirements of the National Construction Code. However, research by the authors showed that the cause of Australia’s combustible cladding crisis are likely deficiencies in the National Construction Code itself. A comparative analysis of historic National Construction Code requirements and recent National Construction Code changes in response to cladding fires showed that the factors which contributed to Australia’s combustible cladding crisis were present for nearly 20 years. Findings also showed that some of the newly introduced measures incorporated in the National Construction Code to address the combustible cladding crisis do not fully address combustible cladding risks and fail to completely address the historical deficiencies.

On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings

Let Fq be a field of order q, where q is a power of an odd prime p, and α and β are two non-zero elements of Fq. The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]/⟨u12−α2,u22−β2,u1u2−u2u1⟩. We decompose the ring R by using orthogonal idempotents Δ1,Δ2,Δ3, and Δ4 as R=Δ1R⊕Δ2R⊕Δ3R⊕Δ4R, and to construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.

On topology of the moduli space of gapped Hamiltonians for topological phases

The moduli space of gapped Hamiltonians that are in the same topological phase is an intrinsic object that is associated with the topological order. The topology of these moduli spaces has been used recently in the construction of Floquet codes. We propose a systematical program to study the topology of these moduli spaces. In particular, we use effective field theory to study the cohomology classes of these spaces, which includes and generalizes the Berry phase. We discuss several applications for studying phase transitions. We show that a nontrivial family of gapped systems with the same topological order can protect isolated phase transitions in the phase diagram, and we argue that the phase transitions are characterized by screening of topological defects. We argue that the family of gapped systems obeys bulk-boundary correspondence. We show that a family of gapped systems in the bulk with the same topological order can rule out a family of gapped systems on the boundary with the topological order given by the topological boundary condition, constraining phase transitions on the boundary.

A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That Attain It

We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces non-cyclic codes. Furthermore, we prove both necessary conditions and sufficient conditions that specify when the known non-cyclic MR codes may be permuted to become cyclic, thus proving our construction produces cyclic MR codes with new parameters. Furthermore, using our new bound on the field size, we show that the new cyclic MR codes have optimal field size in certain cases. Other known LRCs are also shown to have optimal field size in certain cases.

New Constructions of Optimal Optical Orthogonal Codes Based on Partitionable Sets and Almost Partitionable Sets

Variable-weight optical orthogonal codes (OOCs) were introduced by Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. In this paper, partitionable sets and almost partitionable sets are used to construct variable-weight OOCs. Four new recursive constructions for optimal cyclic packing are presented. Consequently, new infinite classes of optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(v,W,1,Q)$ </tex-math></inline-formula> -OOCs are obtained.

Adjacent-Bits-Swapped Polar Codes: A New Code Construction to Speed up Polarization

The construction of polar codes with code length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n=2^{m}$ </tex-math></inline-formula> involves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the polarization process. More precisely, if the previous bit is more reliable than its next bit under the successive decoder, then switching the decoding order of these two adjacent bits will make the reliable bit even more reliable and the noisy bit even noisier. Based on this observation, we propose a new family of codes called the Adjacent-Bits-Swapped (ABS) polar codes. We add a permutation layer after each polar transform layer in the construction of the ABS polar codes. In order to choose which pairs of adjacent bits to swap in the permutation layers, we rely on a new polar transform that combines two independent channels with 4-ary inputs. This new polar transform allows us to track the evolution of every pair of adjacent bits through different layers of polar transforms, and it also plays an essential role in the successive cancellation list (SCL) decoder for the ABS polar codes. Extensive simulation results show that ABS polar codes consistently outperform standard polar codes by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.15 \mathop {\mathrm {dB}}\nolimits $ </tex-math></inline-formula> — <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.3 \mathop {\mathrm {dB}}\nolimits $ </tex-math></inline-formula> when we use CRC-aided SCL decoder with list size 32 for both codes. The implementations of all the algorithms in this paper are available at <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><uri>https://github.com/PlumJelly/ABS-Polar</uri></monospace>

Watermark-based code construction for finite-state Markov channel with synchronisation errors

With advancements in telecommunications, data transmission over increasingly harsher channels that produce synchronisation errors is inevitable. Coding schemes for such channels are available through techniques such as the Davey-MacKay watermark coding; however, this is limited to memoryless channel estimates. Memory must be accounted for to ensure a realistic channel approximation - similar to a Finite State Markov Chain or Fritchman Model. A novel code construction and three decoders are developed to correct synchronisation errors while considering the channel's correlated memory effects by incorporating ideas from the watermark scheme and memory modelling. Simulation results show that using the stationary distribution values as memoryless error probabilities in the proposed code construction and decoder is a viable solution, especially in cases with low memory between errors. Further tests imply that utilising the entire transition matrix in the decoding process may be better suited for cases with more significant memory between errors. The proposed system and decoder may prove helpful in fields such as free-space optics and possibly molecular communication, where harsh channels are used for communication.

Extremal binary self-dual codes from a bordered four circulant construction

In this paper, we present a new bordered construction for self-dual codes which employs λ-circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring of characteristic 2. Moreover, using our bordered construction together with the well-known building-up and neighbour methods, we construct many binary self-dual codes of lengths 56, 62, 78, 92 and 94 with parameters in their weight enumerators that were not known in the literature before.

Constructions of optimal two-dimensional optical orthogonal codes with AM-OPPW restriction for λ = 2

Two-dimensional optical orthogonal codes (2-D OOCs) are of current practical interest as they enable optical communication at a lower chip rate. In this paper, we are concerned about optimal 2-D (u×v,k,2)-OOCs with at most one-pulse per wavelength (AM-OPPW) restriction. An improved upper bound on the size of optimal AM-OPPW 2-D (u×v,k,2)-OOCs is derived, some combinatorial constructions are presented and many new infinite families of optimal AM-OPPW 2-D (u×v,4,2)-OOCs are obtained.

Burst error-correcting quantum stabilizer codes designed from idempotents

Certain classical codes can be viewed isomorphically as ideals of group algebras, while studying their algebraic structures help extracting the code properties. Research has shown that this was remarkably efficient in the case when the code generators are idempotents. In quantum error correction, the theory of stabilizer formalism requires classical self-orthogonal additive codes over the finite field GF(4), which, via the lens of group algebras, are essentially F_2-submodules over GF(4). Therefore, this paper provides a classification on idempotents in commutative group algebra GF(4)G, followed by a criterion that allows idempotents to generate stabilizer subgroups. Later, the construction of quantum stabilizer codes is done in the case when G is a cyclic group C_n, for n=2^m-1 and n=2^m+1. Quantum bounds on their burst error minimum distance are subsequently determined.

Developing a Knowledge Graph for Pharmacokinetic Natural Product-Drug Interactions

BackgroundPharmacokinetic natural product-drug interactions (NPDIs) occur when botanical or other natural products are co-consumed with pharmaceutical drugs. With the growing use of natural products, the risk for potential NPDIs and consequent adverse events has increased. Understanding mechanisms of NPDIs is key to preventing or minimizing adverse events. Although biomedical knowledge graphs (KGs) have been widely used for drug-drug interaction applications, computational investigation of NPDIs is novel. We constructed NP-KG as a first step toward computational discovery of plausible mechanistic explanations for pharmacokinetic NPDIs that can be used to guide scientific research. MethodsWe developed a large-scale, heterogeneous KG with biomedical ontologies, linked data, and full texts of the scientific literature. To construct the KG, biomedical ontologies and drug databases were integrated with the Phenotype Knowledge Translator framework. The semantic relation extraction systems, SemRep and Integrated Network and Dynamic Reasoning Assembler, were used to extract semantic predications (subject-relation-object triples) from full texts of the scientific literature related to the exemplar natural products green tea and kratom. A literature-based graph constructed from the predications was integrated into the ontology-grounded KG to create NP-KG. NP-KG was evaluated with case studies of pharmacokinetic green tea- and kratom-drug interactions through KG path searches and meta-path discovery to determine congruent and contradictory information in NP-KG compared to ground truth data. We also conducted an error analysis to identify knowledge gaps and incorrect predications in the KG. ResultsThe fully integrated NP-KG consisted of 745,512 nodes and 7,249,576 edges. Evaluation of NP-KG resulted in congruent (38.98% for green tea, 50% for kratom), contradictory (15.25% for green tea, 21.43% for kratom), and both congruent and contradictory (15.25% for green tea, 21.43% for kratom) information compared to ground truth data. Potential pharmacokinetic mechanisms for several purported NPDIs, including the green tea-raloxifene, green tea-nadolol, kratom-midazolam, kratom-quetiapine, and kratom-venlafaxine interactions were congruent with the published literature. ConclusionNP-KG is the first KG to integrate biomedical ontologies with full texts of the scientific literature focused on natural products. We demonstrate the application of NP-KG to identify known pharmacokinetic interactions between natural products and pharmaceutical drugs mediated by drug metabolizing enzymes and transporters. Future work will incorporate context, contradiction analysis, and embedding-based methods to enrich NP-KG. NP-KG is publicly available at https://doi.org/10.5281/zenodo.6814507. The code for relation extraction, KG construction, and hypothesis generation is available at https://github.com/sanyabt/np-kg.

Evaluation on Nonirradiated Thermo-mechanical Response of WCCB TBM Following RCC-MRx

Since the submodules as the most important structural component in Water-Cooled Ceramic Breeder (WCCB) Test Blanket Module (TBM) contributes to tritium breeding and extracting, structural integrity assessment is necessary to keep normal operation and function of WCCB TBM-set. Recently, the nonirradiated material properties of F82H which is considered as the structural material of submodule has been summarized following the requirement of RCC-MRx, combined with EU directive, French order, and pressure vessel construction code (RCC-MRx), structural integrity assessment is investigated under the ITER relevant thermo-mechanical load in this study. Meanwhile, cooling water conditions of WCCB TBM-set with its operation scenario, relationship, and detailed values (temperature and pressure) are constituted. Based on the determined structural integrity assessment procedure from RCC-MRx and numerical analysis results, structural integrity of current design of submodule in WCCB TBM-set could be validated. According to the current achievements and established structural integrity assessment procedure, further evaluation on structural integrity combined with electromagnetic load shall be investigated.

Application research of polar coded OFDM underwater acoustic communications

To further accelerate the practical process of polar codes in underwater acoustic communication (UWC) and improve the reliability and efficiency of underwater data transmission, we first propose a polar code construction method suitable for the underwater acoustic channel, which drastically reduces the complexity and meets the need for practical UWC. Then, we establish a practical polar coded UWC scheme by devising a two-step procedure based on the Orthogonal Frequency Division Multiplexing technique. Moreover, through simulation, the scheme's performances with the unimproved and the proposed polar code construction method are analyzed. Moreover, its performances with four different polar decoders are also given. The performance comparison with the LDPC coded UWC system is studied as well. Furthermore, lake-trial results under two different channel conditions demonstrate that the proposed construction method and the scheme effectively guarantee the reliability of data transmission, achieving error-free transmission at a transmission distance of 1718 m with the signal-to-noise-ratio (SNR) of 21 dB, and a transmission distance of 749 m with the SNR of 16.5 dB, better than the LDPC coded system with same conditions. The semi-experimental results show that the proposed polar coded system under the Cyclic Redundancy Check-Aided Successive Cancellation List decoder outperforms the LDPC coded system by approximately 2.1–3.7 dB.

Lower Bounds for Quasi-Cyclic Codes and New Binary Quantum Codes

This paper considers three kinds of quasi-cyclic codes of index two with one generator or two generators and their applications in quantum code construction. In accordance with the algebraic structure of linear codes, we determine the lower bounds of the symplectic weights of these quasi-cyclic codes. Quasi-cyclic codes with the dual-containing property enable the construction of quantum codes. Defining the coefficient symmetric polynomials of the generator polynomials gives a concise condition for the dual-containing of the quasi-cyclic codes. The lower bound results can significantly reduce the scope of the search for a larger minimum distance of quasi-cyclic codes. With these algebraic results and computer supports, we obtain classical quasi-cyclic codes with better parameters and some new quantum codes under the symplectic construction. In particular, two examples of the new quantum codes [[63,42,6]]2,[[51,35,5]]2 improve the corresponding codes in Grassl’s code table.

Identify the Dynamic Position of Moving Vessels using Big Data and Deep Learning Approaches

Recently, various purposes such as computer vision, self-driving vehicles, self-directed shipping, and so on. Therefore, machine learning and deep learning algorithms have demonstrated strong routine. Using machine learning applications, we can implement sophisticated functionality without relying on complex code constructions. An alternative is to train a learning system on a collected training dataset and ensure that it performs as expected. Two main benefits of a deep-learning-based system over a hard-coded one exist. A Reinforcement Learning, and deep learning-based system does not require such complex hard-coded algorithms, which makes it less prone to error and easier to implement. In this study we proposed a deep learning-driven systems are able to adapt to different situations by retraining their algorithms on collected data. Proposed method influenced varying obtain leaning to another example of changing conditions. Systems can adapt even when input distributions change over time.

Constructions of near MDS codes which are optimal locally recoverable codes

A linear code with length n, dimension k and minimum distance n−k is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as a near maximum distance separable (NMDS for short) code. NMDS codes have nice applications in finite geometry, combinatorics, cryptography and data storage. In this paper, we first present several constructions of NMDS codes and determine their weight enumerators. In particular, some constructions produce NMDS codes with the same parameters but different weight enumerators. Then we determine the locality of the NMDS codes and obtain many families of distance-optimal and dimension-optimal locally recoverable codes.

GHW for (x,x+y)-construction of codes

Suppose that A1 and A2 are two linear codes over Fm with parameters [n,k] and [n,k′], respectively. For the code A={(x,x+y):x∈A1,y∈A2}, we asked about dr(A) in terms of dr(A1) and dr(A2), so we obtained an upper bound for dr(A) in terms of them. In addition, we obtained d2(A) in which A1 and A2 are codes over F2. Additionally, we obtained d2(A) in non-binary case, where it is different of what we have for binary case. Suppose that M is a linear code over a finite field. The minimum of the support sizes among r-dimensional sub-codes of M is called the r-th generalized Hamming weight of M that we will denote it by dr(M).

Short Blocklength Wiretap Channel Codes via Deep Learning: Design and Performance Evaluation

We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint with hash functions. For blocklengths smaller than or equal to 128, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper for our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper’s channel observations, and is empirically measured via a neural network-based mutual information estimator. Our simulation results provide examples of codes with positive secrecy rates that outperform the best known achievable secrecy rates obtained non-constructively for the Gaussian wiretap channel. Additionally, we show that our code design is suitable for the compound and arbitrarily varying Gaussian wiretap channels, for which the channel statistics are not perfectly known but only known to belong to a pre-specified uncertainty set. These models not only capture uncertainty related to channel statistics estimation, but also scenarios where the eavesdropper jams the legitimate transmission or influences its own channel statistics by changing its location.

Construction of DNA Codes From Composite Matrices and a Bio-Inspired Optimization Algorithm

In this work, we present a new construction method for reversible codes. We employ composite matrices derived from group rings and show how to construct these matrices so that they are also reversible. Also in this work, we give an algorithm for calculating conflict free DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement, the GC-content constraints with each DNA codeword being free from reverse complement sub-strings. By employing our construction method for reversible codes and our algorithm, we construct a number of DNA codes that satisfy the above constraints. Many of the codes we obtain have better parameters than some known DNA codes and many have parameters that are new to the literature.

A Direct Construction of Golay Complementary Pairs and Binary Complete Complementary Codes of Length Non-Power of Two

Golay complementary pairs (GCPs) and complete complementary codes (CCCs) have found a wide range of practical applications in coding, signal processing and wireless communication due to their ideal correlation properties. The binary CCCs have special advantages in spread spectrum communication for their simple modulo-2 arithmetic operation, modulation, and correlation simplicity; however, they are limited in length. In this paper, we present a direct construction of GCPs, mutually orthogonal Golay complementary sets (MOGCSs) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -ary, including binary CCCs of non-power of two lengths to widen their application in the recent communication field. First, a generalised Boolean function (GBF) based truncation technique is used to construct GCPs of non-power of two lengths which has never been reported before. Then Golay complementary sets (GCSs) and MOGCSs of lengths of the form <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{m-1}+2^{m-3}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m \geq 5$ </tex-math></inline-formula> ) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{m-1}+2^{m-2}+2^{m-4}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m \geq 6$ </tex-math></inline-formula> ) are generated by higher order GBFs. The later length of MOGCSs with direct construction is not available in the literature. Finally, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -ary sequences including binary CCCs with non-power of two lengths are constructed using the union of MOGCSs. There is no such direct construction of binary CCC of non-power of two lengths available in the literature. The column sequence peak to mean envelope power ratio (PMEPR) have been investigated for GCSs and CCCs respectively, and compared with existing works. The column sequence PMEPR of resultant CCCs is effectively upper bounded by 2, which is much lower than that of paraunitary based CCC construction. The proposed construction is also compared with existing works.