Reversible Codes Research Articles

Optimized area efficient quantum dot cellular automata based reversible code converter circuits: design and energy performance estimation

Quantum-dot cellular automata (QCA) based circuit designs are creating a surge in transistorless computational technologies. Due to its quasi-adiabatic switching resulting in extremely low leakage power dissipation as there is no continuous path. These circuits also enjoy extremely high packaging density of the order of 10 $$^{12}$$ devices/ $$\hbox {cm}^2$$ because of its extremely scaled area of 18 nm x 18 nm along with very high 100 GHz frequency of operation. Further the loss of bit information could be abolished by reversible logic computing. This thereby realizes an energy efficient logic operations owing to bijective relation between inputs and outputs in reversible logic. This work investigates the code converter circuits which converts 4-bit binary code to excess-3 code and vice versa based on reversible QCA logic gates for the first time. Moreover an area efficient design for 4-bit binary to gray and vice-versa code converters also designed here. All these four code converter circuits are designed using reversible logic gate Feynman and Peres gates by deploying the QCA Designer and Designer-E tool v2.0.3. Finally the in depth performance estimation of the proposed circuits in terms of circuit complexity, quantum cost and energy dissipation are also presented here. Moreover, these QCA based circuits provide a strong evidence that reversible logic based QCA circuits can be efficiently deployed for these code converter circuits.

Design and Development of 4-Bit Gray Code Counter Circuit Using Reversible Logic Gate

Aim: This paper proposed the design and development of 4-Bit Gray Code Counter Circuit Using Reversible Logic Gate. Methods: The 4-Bit Gray Code Counter Circuit can be design using SAM gate, Feynman gate (FG), double Feynman gate (DFG) and NOT gate. The proposed circuit is the combined application of 4-bit binary asynchronous counter and 4-bit binary to gray code converter circuit. Results: The proposed gray code counter is designed using four no. of SAM gate, three no. of DFG, one FG and seven reversible NOT gate. The QC, GO and CI of proposed circuit are correspondingly 30, 4 and 7. Conclusion: The novel reversible gray code counter have been designed using existing reversible logic gate. The proposed gray code counter is designed using four no. of SAM gate, three no. of DFG, one FG and seven reversible NOT gate. The QC, GO and CI of proposed circuit are correspondingly 30, 4 and 7.

Construction of reversible cyclic codes over ℤ p k

For a prime p and integer k > 1, we find the unique set of generators for cyclic codes over . Besides, the necessary and sufficient conditions for cyclic codes to be reversible are obtained. Finally, as an application, some computational examples are given in support of our results.

Reversible DNA codes from skew cyclic codes over a ring of order 256

We introduce skew cyclic codes over the finite ring $\R$, where $u^{2}=0,v^{2}=v,w^{2}=w,uv=vu,uw=wu,vw=wv$ and use them to construct reversible DNA codes. The 4-mers are matched with the elements of this ring. The reversibility problem for DNA 4-bases is solved and some examples are provided.

A Journey in Lanthanide Coordination Chemistry: From Evaporable Dimers to Magnetic Materials and Luminescent Devices.

ConspectusLanthanide ions are prime ingredients for the design of compounds, materials, and devices with unique magnetic and optical properties. Accordingly, coordination chemistry is one of the best tools for building molecular edifices from these ions because it allows careful control of the ions' environment and of the dimensionality of the final compound.In this Account, we review our results on lanthanide-based dimers. We show how a pure fundamental study on lanthanide coordination chemistry allows the investigation of a full continuum of results from the compound to materials and then to devices. The conversion of molecules into materials is a tricky task because it requires strong molecular robustness toward the surface deposition processes as well as the preservation and detectability of the molecular properties in the material. Additionally, the passage of a material toward a device implies a material with a given function, for example, a tailored response to an external stimulus.To do so, we targeted neutral and isolated molecules whose transfer on surfaces by chemi- or physisorption is much easier than that of charged molecules or extended coordination networks. Then, we focused on molecules with very strong evaporability to avoid wet chemistry deposition processes that are more likely to damage the molecules and/or distort their geometries.We thus designed lanthanide dimers based on fluorinated β-diketonates and pyridine-N-oxide ligands. As expected, they show remarkable evaporability but also strong luminescence and interesting magnetic behavior because they behave as single-molecule magnets (SMMs). Ligand substitutions and stoichiometric modifications allow the optimization of the geometric organization of the dimers in the crystal packing as well as their evaporability, SMM behavior, luminescent properties, or their ability to be anchored on surfaces. Most of all, this family of molecules shows a strong ability to form thick films on various substrates. This allows converting these molecules to magnetic materials and luminescent devices.Magnetic materials can be designed by creating thick films of the dimers deposited on gold. These films have been designed and investigated with the most advanced techniques of on-surface imaging (atomic force microscopy, AFM), on-surface physicochemical characterization (X-ray photoelectron spectroscopy (XPS), time of flight-secondary ion mass spectroscopy (Tof-SIMS)), and on-surface magnetic investigation (low-energy muon spin relaxation (LE-μSR)). Contrary to what was previously observed on other SMM films, no depth dependence of the SMM behavior was observed. This means that the dimers do not suffer from the vacuum or substrate interface and behave similarly, whatever their localization. This exceptional magnetic robustness is a key ingredient in the creation of materials for molecular magnetic data storage.Luminescent devices can be obtained by layering molecular films of the dimers with a copper-rich solid-state electrolyte between ITO/Pt electrodes. The electromigration of Cu2+ ions into films of Eu3+, Tb3+, and Dy3+ dimers quenches their luminescence. This luminescence tuning by electromigration is reversible, and this setup can be considered to be a proof of concept of full solid-state luminescent device where reversible coding can be tailored by an electric field. It is envisioned for optical data storage purposes. In the future, it could also benefit from the SMM properties of the molecules to pave the way toward multifunctional molecular data storage devices.

Reversible cyclic codes over a class of chain rings and their application to DNA codes

Reversible cyclic codes over a class of chain rings and their application to DNA codes

Multi-Wavelength Magnetic Coding of Helical Luminescence in Ferromagnetic 2D Layered CrI <sub>3</sub>

Two-dimensional (2D) van der Waals (vdW) ferromagnets have opened new avenues for manipulating spin at the limits of single or few atomic layers, and for creating unique magneto-exciton devices through the coupling of long-range ferromagnetic (FM) orders and excitons. However, 2D vdW ferromagnets explored so far have rarely possessed exciton behaviors; to date, FM CrI3 have been recently revealed to show ligand-field photoluminescence correlated with FM ordering, but typically with a broad emission peak. Alternatively, many-body excitons have been observed in antiferromagnetic (AFM) NiPS3, but the coupling of excitons with AFM orders is exponentially more difficult, owing to extremely high coercivity. Here, we report a straightforward approach to realize strong coupling of narrow helical emission and FM orders at a low magnetic field in CrI3 through a relatively simple microsphere cavity. We show that the resonant whispering-gallery-modes (WGM) of SiO2 microspheres give rising to a series of strong oscillation helical emissions with a full width at half-maximum (FWHM) of ~5 nm under continuous wave excitation. Reversible magnetic control and coding of helical luminescence with multiwavelength is realized in the range of 950-1100 nm. This work enables plenty of opportunities for creating magnetic encoding lasing for photonic integrated chips.

Design and Analysis of LT Codes With a Reverse Coding Framework

In this paper, an improved LT code with a reverse coding framework is designed to reduce the error floor caused by low-degree information nodes. For the proposed coding scheme, a well-designed threshold is used to mark the information nodes whose degrees are less than the threshold, and these nodes will be coded reversely to connect to enough candidate check nodes. To design the optimal threshold, firstly, the information degree distribution and the check degree distribution of the improved LT code are deduced. Then, the parameter extrinsic information gain-loss-ratio (GLR) is designed to evaluate the convergence behavior of the improved LT code. Finally, the ‘slow increase region’ of the GLR is set, and the boundary value of this region is used to deduce the optimal threshold which matches with the channel state information (CSI) and decoding overhead. To make the proposed LT code not limited to a fixed code rate, we further modify the proposed scheme. The segment coding method is used to generate a redundant generator matrix, and the check nodes corresponding to this matrix can be transmitted independently and are not limited to a fixed number. Furthermore, the connection relationship between information nodes and check nodes can be easily recorded, which improves the decoding efficiency. The advantages of the improved LT code are that the degree distributions can be formulated, the convergence behavior can be predicted, and the lowest information degree can be adjusted. Simulation results show that the improved LT code can reduce the error floor by up to 4 orders of magnitude. Besides, the designed LT code outperforms the existing LT codes in literature in terms of bit error rate (BER) performance.

A continuous variable quantum key distribution protocol based on multi-dimensiondata reconciliation with Polar code

The continuous variable quantum key distribution protocol (CV-QKD) has the advantages of easy generation of quantum signals, convenient measurement and high communication capacity. However, the multi-dimensional data reconciliation is mainly implemented by binary LDPC code as quantum error correction code, which is greatly affected by complex environments and the bit error rate is high. In order to solve this problem, acontinuous variable quantum key distribution protocol based onmulti-dimension data reconciliation with Polar code, that can be applied to long-distance transmission in power systems, is proposed. First, we prepare an EPR quantum state, and perform heterodyne detection on one of the quantum states, and obtain the values of two orthogonal components at the same time which is the coherent state of the information carrier. Then the continuous variable quantum key distribution is realized by six steps (i.e., quantum state preparation, gaussian random detection, data filtering, calculation of bit error rate, data reconciliation, privacy amplification).In data reconciliation, we use Polar code as the error correction code and use reverse coding technology to achieve key error correction, which can effectively improve the negotiation efficiency. Numerical simulation verifies the feasibility of the protocol, and the protocol is more efficient than the multi-dimensiondata reconciliation protocol based on LDPC code under the same conditions.

Control of network representation efficiency in neurogenesis

The article discusses a method to increase the efficiency of evolutionary genetic search in coding of modular network structures. A method for unfolding a genotype to form a phenotype using production rules generated by applying formal apparatus of L-systems and repair mechanisms is proposed. Forward and reverse coding techniques are considered. The method provides a combination of compactness of genetic code representation and advanced capabilities to increase dimension of resulting networks.

Constacyclic and Linear Complementary Dual Codes Over Fq + uFq

This article discusses linear complementary dual (LCD) codes over ℜ = Fq+uFq(u2=1) where q is a power of an odd prime p. Authors come up with a new Gray map from ℜn to F2nq and define a new class of codes obtained as the gray image of constacyclic codes over .ℜ Further, we extend the study over Euclidean and Hermitian LCD codes and establish a relation between reversible cyclic codes and Euclidean LCD cyclic codes over ℜ. Finally, an application of LCD codes in multisecret sharing scheme is given.

Designing DNA codes from reversible self-dual codes over [formula omitted

We present an explicit method for designing DNA codes from reversible self-dual codes over the finite field GF(4) of order 4. We use Euclidean reversible self-dual codes (Euclidean RSD codes for short) since they have some advantages in designing DNA codes; hence, in this work RSD codes mean Euclidean RSD codes. We first work on a construction method for reversible self-dual codes over GF(4), and we study their properties in the aspect of their connection to DNA codes. We then obtain an efficient and feasible algorithm for designing DNA codes from RSD codes over GF(4). We point out that our algorithm takes advantage of reversibility and self-duality of RSD codes over GF(4). Finally, we produce DNA codes up to length 42 using our method and discuss the GC-weight distributions of DNA codes. We obtain many new DNA codes with better parameters when compared to the previously known results, and we also improve the lower bounds on the maximum size of DNA codes of a fixed code length and dimension.

Tersinirlik Problemi Hakkında

By defining a non-trivial automorphism over R=Z_4+uZ_4+vZ,_4+uvZ_4 where u^2=u, v^2=v, uv=vu and Z_4={0,1,2,3} , the skew cyclic codes over the finite ring R are introduced. By using the skew cyclic codes over R , it is solved the reversibility problem for DNA 4-bases. Thanks to this, the reversible DNA codes are obtained.

Efficient and Explicit Balanced Primer Codes

To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands with specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit constructions of error-correcting codes that are suitable as primer addresses and equip these constructions with efficient encoding algorithms. Specifically, our constructions take cyclic or linear codes as inputs and produce sets of primers with similar error-correcting capabilities. Using certain classes of BCH codes, we obtain infinite families of primer sets of length $n$ , minimum distance $d$ with $(d+1) \log _{4}\,\,n +O(1)$ redundant symbols. Our techniques involve reversible cyclic codes (1964), an encoding method of Tavares et al. (1971) and Knuth’s balancing technique (1986). In our investigation, we also construct efficient and explicit binary balanced error-correcting codes and codes for DNA computing.

Abstract P166: Sex And Age Differences In Ambulatory Blood Pressure Monitoring Tolerability

Background: Recent guidelines endorse the use of ambulatory blood pressure monitoring (ABPM) for out-of-office BP measurement and HTN management. Past literature has described patient perceptions of ABPM tolerability but differences between sex and age have not previously been determined. The objective of this study was to evaluate sex and age differences in such patient perceptions. Methods: This was a prospective, single-arm trial (NCT03920956) of a community pharmacy-driven ABPM service that enrolled 52 patients at least 18 years of age who were suspected of having white coat, masked, or sustained HTN, have symptoms of hypotension, or require confirmation of an initial diagnosis of HTN. We evaluated the tolerability of the ABPM device (Oscar 2; SunTech Medical, Morrisville, NC) as a secondary outcome with a previously published 8-question survey using a 0-10 scale (0=not at all, 5=somewhat, 10=extremely). The responses were dichotomized as either favorable (0-4) or unfavorable (5-10) with reverse coding for positively-worded questions. Descriptive statistics and Chi-square analyses were used to describe sex and age differences. Results: A total of 50 surveys (96%) were completed and returned. Respondents were 50% female (n=25) with a mean (SD) age of 57.5 (15.8), and 58% (n=29) were at least 55 years of age. Female respondents were more likely to find the monitor cumbersome to wear at times other than at home, work, or driving (16/21, 76.2% vs. 10/25, 40%, p = 0.014). Although nonsignificant, male respondents were more likely to find the monitor embarrassing to wear (7/25, 28.0% vs. 2/24, 8.3%, p = 0.076). In comparisons of tolerability by age, subjects less than 55 years of age were more likely to report being disturbed by the pump during driving (8/21, 38.1% vs. 1/24, 4.2%, p = 0.005), at other times (7/20, 35.0% vs. 2/24, 8.3%, p = 0.029), and found the monitor embarrassing to wear (7/21, 33.3% vs. 2/28, 7.1%, p = 0.019). Conclusions: Previous studies suggest that ABPM is generally well-tolerated by patients but may cause some discomfort or disturbed sleep. Differences in tolerability appear to become more evident across age groups and sex. These data suggest select patients may require additional counseling and education to ensure adherence to ABPM.

Construction of reversible self-dual codes

We study a construction method of binary reversible self-dual codes in this paper. Reversible codes have good properties in applications, and it is interesting to note that a class of reversible codes is closely connected to BCH codes and LCD codes. We first characterize binary reversible self-dual codes. Using these characteristics of reversible self-dual codes, we find an explicit method for constructing all the binary reversible self-dual codes up to equivalence. Furthermore, using this construction, we obtain nine optimal reversible self-dual codes of length 70 which are all inequivalent, and these codes are all new with respect to binary self-dual codes; they all have the same parameter [70,35,12] and their automorphism groups have the same order two.

Об одном алгоритмическом решении задачи восстановления остатка числа в системе остаточных классов

При выполнении операций расширения диапазона представления чисел, деления, определения переполнения, масштабирования, контроля ошибок вычислений возникает задача восстановления остатка числа по данному модулю на основании остатков этого числа по остальным модулям системы. Табличное выполнение операции восстановления остатка числа реализуется с помощью базового алгоритма. Метод решения основан на определении остатка по данному модулю на основании полученных остатков по остальным модулям системы. Такое определение выполняется последовательным вычитанием констант из полученных остатков и суммированием этих констант к результататам, которые формируются по данному модулю. При этом константы на каждой итерации выбираются в зависимости от значения остатка в анализируемом разряде. При несомненном достоинстве метода сохраняются требования к быстродействию выполнения операции восстановления остатка числа. Целью исследования является аналитическое рассмотрение подхода к ускоренной реализации базовой операции восстановления остатка числа по данному модулю на основании остатков этого числа по остальным модулям системы. Одна из реализаций алгоритма состоит в одновременном его выполнении по базовому варианту для искомого числа и числа, обратного искомому. При этом искомый остаток определяется по значению остатка того из чисел, для которого первым получается результат поиска. Приведены варианты реализации алгоритма с переходами от представления числа в прямом коде к представлению этого числа в обратном коде и от представления числа в обратном коде к его представлению в прямом коде. Рассмотренный алгоритм реализации в системе остаточних классов базовой немодульной операции восстановления значения остатка числа по данному модулю на основании значений остатков этого числа по остальным модулям системы обеспечивает получение искомого результата. На основе предложенных подходов достигается ускоренная реализация базовой операции восстановления остатка числа по данному модулю. Представляется целесообразным применить предложенные подходы в качестве перспективных направлений исследований этой операции в системе остаточных классов.

A large-scale study on the adoption of anti-debugging and anti-tampering protections in android apps

Android apps are subject to malicious reverse engineering and code tampering for many reasons, like premium features unlocking and malware piggybacking. Scientific literature and practitioners proposed several Anti-Debugging and Anti-Tampering protections, readily implementable by app developers, to empower Android apps to react against malicious reverse engineering actively. However, the extent to which Android app developers deploy these protections is not known.In this paper, we describe a large-scale study on Android apps to quantify the practical adoption of Anti-Debugging and Anti-Tampering protections. We analyzed 14,173 apps from 2015 and 23,610 apps from 2019 from the Google Play Store. Our analysis shows that 59% of these apps implement neither Anti-Debugging nor Anti-Tampering protections. Moreover, half of the remaining apps deploy only one protection, not exploiting the variety of available protections. We also observe that app developers prefer Java to Native protections by a ratio of 99 to 1. Finally, we note that apps in 2019 employ more protections against reverse engineering than apps in 2015.

Reversible complement cyclic codes over Galois rings with application to DNA codes

Let R be a Galois ring of characteristic pa and cardinality pam, where p is a prime and a,m are natural numbers. For a unit u and an element k∈R such that u2=1 and uk=k, a generalized notion of a complement of an element e in R with respect to u and k has been given in this paper. Using this notion of complement, reversible complement cyclic codes with respect to u and k have been defined. Further, a necessary and sufficient condition for a reversible cyclic code of arbitrary length over R to be a reversible complement cyclic code with respect to u and k has been obtained. This generalization is significant in view of the fact that a reversible cyclic code of length n over R may be reversible complement with respect to one choice of u and k but may not be reversible complement with respect to some other choice of u and k. Further, reversible complement cyclic codes with respect to u and k (for different values of u and k) over a special Galois ring, Z4, have been used to construct some DNA codes. It has been observed that codes over Z4 in some cases give better DNA codes than DNA codes over fields and some rings of equal cardinality. A tradeoff between the two DNA properties namely avoiding secondary structure formation and constant GC−content has also been observed.

Con(dif)fused voice to convey secret: a dual-domain approach

Owing to the rapid development and advancements in the field of networks and communication, sharing of multimedia contents over insecure networks has become vital. The confidentiality of audio signals is predominantly needed in military and intelligence bureau applications. The proposed algorithm addresses this issue by encrypting audio signal using chaotic maps in spatial and transform domain. Discrete Fourier transform (DFT), discrete cosine transform (DCT) and integer wavelet transform (IWT) approaches are considered for the experiment. The algorithm involves three-layer security of confusion and diffusion in the spatial domain, and confusion in the transform domain. The confusion in the transform domain is equivalent to diffusion in the spatial domain. Different sizes of audio samples are considered to validate the effectiveness of the proposed scheme. Experimental results prove that the DFT-assisted encryption scheme is more efficient than the DCT- and IWT-based methods because the DFT scheme employs effective diffusion through reversible phase coding. Effectiveness of the proposed method is substantiated using various metrics. Correlation coefficients arrive significantly closer to zero; number of samples changes rate (NSCR) value is at 100% and scrambling degree close to 1. Besides, the proposed scheme has a larger keyspace higher than 2128. Thus, the proposed algorithm has the potency to withstand the statistical, differential and brute force attacks.