On the decoding of the (24, 12, 8) Golay code

An improved syndrome shift-register decoding algorithm, called the syndrome-weight decoding algorithm, is proposed for decoding three possible errors and detecting four errors in the (24, 12, 8) Golay code. This method can also be extended to decode two other short codes, such as the (15, 5, 7) cyclic code and the (31, 16, 7) quadratic residue (QR) code. The proposed decoding algorithm makes use of the properties of cyclic codes, the weight of syndrome, and the syndrome decoder with a reduced-size lookup table (RSLT) in order to reduce the number of syndromes and their corresponding coset leaders. This approach results in a significant reduction in the memory requirement for the lookup table, thereby yielding a faster decoding algorithm. Simulation results show that the decoding speed of the proposed algorithm is approximately 3.6 times faster than that of the algebraic decoding algorithm.     

High speed decoding of the binary (47, 24, 11) quadratic residue code

An efficient table lookup decoding algorithm (TLDA) is presented to decode up to five possible errors in a binary systematic (47, 24, 11) quadratic residue (QR) code. The main idea of the TLDA is based on the weight of syndrome, the syndrome decoder together with a reduced-size lookup table (RSLT), and the shift-search method given by Reed et al. Thus, the size of the lookup table and computational complexity in a finite field can be significantly reduced. The memory size of the proposed condensed lookup table (CLT) consists of only 36.6 Kbytes and is only about 0.24% of the full lookup table (FLT) and 3.2% of the lookup up table given by Chen et al., respectively. These facts lead to significant reduction of computational time and the decoding complexity. A simulation result shows that the decoding speed of the proposed TLDA is much faster than all existing decoding algorithms. Moreover, it can be extended to decode all QR codes, including the class of the cyclic codes when the code length is moderate. The CLT makes this new decoding algorithm suitable for hardware or firmware implementations.     

An efficient parity detection technique using the two-moduli set {2 − 1, 2 + 1}

Lu and Chiang used both the table lookup and fractional number approaches to discover the parity of an RNS number. To eliminate the need for table space and time for computing fractions, a two-moduli set {2^h − 1, 2^h + 1} is used to speed up the technique proposed by Lu and Chiang. Based on this modified two-moduli set, it is found that the parity of an RNS number X = (x₁, x₂) is if x₁ ? x₂. On the contrary, if x₁ < x₂, the parity of X is .     

Fast, prime factor, discrete Fourier transform algorithms over GF(2) for 8 ? m ? 10

In this paper it is shown that Winograd’s algorithm for computing convolutions and a fast, prime factor, discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2^m − 1 points over GF(2^m), for 8 ? m ? 10. These new transform techniques can be used to decode Reed-Solomon (RS) codes of block length 2^m − 1. The complexity of this new transform algorithm is reduced substantially from more conventional methods. A computer simulation verifies these new results.     

A (4n − 9)/3 diagnosis algorithm on n-dimensional cube network

As a generalization of the precise and pessimistic diagnosis strategies of system-level diagnosis of multicomputers, the t/k diagnosis strategy can significantly improve the self-diagnosing capability of a system at the expense of no more than k fault-free processors (nodes) being mistakenly diagnosed as faulty. In the case k ? 2, to our knowledge, there is no known t/k diagnosis algorithm for general diagnosable system or for any specific system. Hypercube is a popular topology for interconnecting processors of multicomputers. It is known that an n-dimensional cube is (4n − 9)/3-diagnosable. This paper addresses the (4n − 9)/3 diagnosis of n-dimensional cube. By exploring the relationship between a largest connected component of the 0-test subgraph of a faulty hypercube and the distribution of the faulty nodes over the network, the fault diagnosis of an n-dimensional cube can be reduced to those of two constituent (n − 1)-dimensional cubes. On this basis, a diagnosis algorithm is presented. Given that there are no more than 4n − 9 faulty nodes, this algorithm can isolate all faulty nodes to within a set in which at most three nodes are fault-free. The proposed algorithm can operate in O(N log₂ N) time, where N = 2ⁿ is the total number of nodes of the hypercube. The work of this paper provides insight into developing efficient t/k diagnosis algorithms for larger k value and for other types of interconnection networks.     

Comments on “Generalised finite Radon transform for N × N images”

In Kingston and Svalbe [1], a generalized finite Radon transform (FRT) that applied to square arrays of arbitrary size N × N was defined and the Fourier slice theorem was established for the FRT. Kingston and Svalbe asserted that “the original definition by Matúš and Flusser was restricted to apply only to square arrays of prime size,” and “Hsung, Lun and Siu developed an FRT that also applied to dyadic square arrays,” and “Kingston further extended this to define an FRT that applies to prime-adic arrays”. It should be said that the presented generalized FRT together with the above FRT definitions repeated the known concept of tensor representation, or tensor transform of images of size N × N which was published earlier by Artyom Grigoryan in 1984-1991 in the USSR. The above mentioned “Fourier slice theorem” repeated the known tensor transform-based algorithm of 2-D DFT [5-11], which was developed for any order N₁ × N₂ of the transformation, including the cases of N × N, when N = 2^r, (r > 1), and N = L^r, (r ≥ 1), where L is an odd prime. The problem of “over-representation” of the two-dimensional discrete Fourier transform in tensor representation was also solved by means of the paired representation in Grigoryan [6-9].     

Strong (n, t, n) verifiable secret sharing scheme

A (t, n) secret sharing divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret; but fewer than t shares cannot reconstruct the secret. In this paper, we extend the idea of a (t, n) secret sharing scheme and give a formal definition on the (n, t, n) secret sharing scheme based on Pedersen’s (t, n) secret sharing scheme. We will show that the (t, n) verifiable secret sharing (VSS) scheme proposed by Benaloh can only ensure that all shares are t-consistent (i.e. any subset of t shares defines the same secret); but shares may not satisfy the security requirements of a (t, n) secret sharing scheme. Then, we introduce new notions of strong t-consistency and strong VSS. A strong VSS can ensure that (a) all shares are t-consistent, and (b) all shares satisfy the security requirements of a secret sharing scheme. We propose a strong (n, t, n) VSS based on Benaloh’s VSS. We also prove that our proposed (n, t, n) VSS satisfies the definition of a strong VSS.     

In2O3 + xBaO (x = 0.5-5 at.%) - A novel material for trace level detection of NOx in the ambient

Indium oxide (In₂O₃) doped with 0.5-5 at.% of Ba was examined for their response towards trace levels of NO_x in the ambient. Crystallographic phase studies, electrical conductivity and sensor studies for NO_x with cross interference for hydrogen, petroleum gas (PG) and ammonia were carried out. Bulk compositions with x ≤ 1 at.% of Ba exhibited high response towards NO_x with extremely low cross interference for hydrogen, PG and ammonia, offering high selectivity. Thin films of 0.5 at.% Ba doped In₂O₃ were deposited using pulsed laser deposition technique using an excimer laser (KrF) operating at a wavelength of (λ) 248 nm with a fluence of ∼3 J/cm² and pulsed at 10 Hz. Thin film sensors exhibited better response towards 3 ppm NO_x quite reliably and reproducibly and offer the potential to develop NO_x sensors (Threshold limit value of NO₂ and NO is 3 and 25 ppm, respectively).     

Second order (F, α, ρ, d)-convexity and duality in multiobjective programming

A class of second order (F, α, ρ, d)-convex functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for a second order Mond-Weir type multiobjective dual.     

Oriented growth of A2Te3 (A = Sb, Bi) films and their devices with enhanced thermoelectric performance

Oriented thermoelectric (TE) p-Sb₂Te₃ and n-Bi₂Te₃ thin films with special nanostructures have been synthesized by a simple vacuum thermal evaporation technique. The composition and microstructure of the films were studied by X-ray diffraction (XRD) and scanning electron microscopy (SEM), presenting a well preferential crystal growth with dense slender columnar grains grown perpendicular to the substrate, and energy dispersive X-ray spectrum (EDX) indicating the compositions distribution in the films. The electric transport properties, i.e., conductivity and Seebeck coefficient, and the thermal transportation of the oriented films show optimized properties. Prototype devices were built up by p and n elements in series and parallel circuits. The largest output power and cooling could be achieved in Sb₂Te₃ parallel device with P_max = 6.51 μW at ΔT = 106 K, and cooling of 4.1 K at 2 V. The 24-pair p-n couples series device could output maximum voltage of 313 mV at ΔT = 102 K. The power generation and the cooling of the devices show times enhanced TE performances than those consisting of common films. The results proved that introducing nanostructures into films is an effective choice to obtain high-efficient micro TE device.     

Improvement of jitter transfer characteristics of a 9.95328 Gb/s data recovery DLL using saw filter

This paper presents a design of a high-speed data recovery circuit for non return zero (NRZ) data transmission using delay-locked loop (DLL) with SAW filter. The jitter generation of the circuit is decreased by adjusting the loop gain in DLL whereas surface acoustic wave (SAW) filter with low centered frequency (f_c) improves the jitter transfer function of DLL. It is seen that the circuit using SAW filter of f_c = 1.24416 GHz and Q = 1000 provides the cut off frequency of about 600 kHz which is ∼10 times lower than that of conventional DLL circuit.     

Algebraic decoding of the (41, 21, 9) Quadratic Residue code

In this paper, an algebraic decoding algorithm is proposed to correct all patterns of four or fewer errors in the binary (41, 21, 9) Quadratic Residue (QR) code. The technique needed here to decode the (41, 21, 9) QR code is different from the algorithms developed in [I.S. Reed, T.K. Truong, X. Chen, X. Yin, The algebraic decoding of the (41, 21, 9) Quadratic Residue code, IEEE Transactions on Information Theory 38 (1992 ) 974-986]. This proposed algorithm does not require to solve certain quadratic, cubic, and quartic equations and does not need to use any memory to store the five large tables of the fundamental parameters in GF(2²⁰) to decode this QR code. By the modification of the technique developed in [R. He, I.S. Reed, T.K. Truong, X. Chen, Decoding the (47, 24, 11) Quadratic Residue code, IEEE Transactions on Information Theory 47 (2001) 1181-1186], one can express the unknown syndromes as functions of the known syndromes. With the appearance of known syndromes, one can solve Newton’s identities to obtain the coefficients of the error-locator polynomials. Besides, the conditions for different number of errors of the received words will be derived. Computer simulations show that the proposed decoding algorithm requires about 22% less execution time than the syndrome decoding algorithm. Therefore, this proposed decoding scheme developed here is more efficient to implement and can shorten the decoding time.     

Solving single-product economic lot-sizing problem with non-increasing setup cost,constant capacity and convex inventory cost in O(N log N) time

This paper considers an economic lot sizing model with constant capacity, non-increasing setup cost, and convex inventory cost function. Algorithms with computational time of O(N×TD_N)have been developed for solving the model, where N is the number of planning periods and TD_N is the total demand. This study partially characterizes the optimal planning structure of the model. A new efficient algorithm with computational time of O(N log N) has also been developed based on the partial optimal structure. Moreover, computational study demonstrates that the new algorithm is efficient.     

Evaluation of a 3 year intervention to increase adoption of safer nursery crop production practices

Background

We conducted a 3 year intervention to increase awareness and adoption of eight more profitable nursery crop production practices that reduced certain traumatic and musculoskeletal injury hazards.

Methods

We disseminated information to nursery managers across seven states using information channels they were known to rely on (e.g. trade publications, public events, university Extension, other managers). We evaluated rolling, independent, probability samples (n = 1200) with mail questionnaires before the intervention and after each of 3 intervention years. We also evaluated samples (n = 250) from a comparison group of New Zealand nursery managers.

Results

The intervention was associated with increased awareness of four of the eight practices among US managers after year 3 compared to their baseline: zippers (20 vs. 32%, p ≤ 0.000), stools (11 vs. 22%, p ≤ 0.001), pruners (29 vs. 40%, p ≤ 0.014), and tarps (24 vs. 33%, p ≤ 0.009). There were no changes in adoption. New Zealand manager awareness was increased for hoes after year 2 compared to their baseline (35 vs. 52%, p ≤ 0.010).

Conclusions

A modest, regionwide information dissemination intervention was associated with increased awareness, but not adoption.     

Impact of sea ice on the retrieval of water-leaving reflectance, chlorophyll a concentration and inherent optical properties from satellite ocean color data

Two physical phenomena by which satellite remotely sensed ocean color data are contaminated by sea ice at high latitudes are described through simulations and observations: (1) the adjacency effect that occurs along sea ice margins and (2) the sub-pixel contamination by a small amount of sea ice within an ocean pixel. The signal at the top of the atmosphere (TOA) was simulated using the 6S radiative transfer code that allows modeling of the adjacency effect for various types of sea ice surrounding an open water area. In situ sea ice reflectance spectra used in the simulations were measured prior to and during the melt period as part of the 2004 Canadian Arctic Shelf Exchange Study (CASES). For sub-pixel contamination, the TOA signal was simulated for various surface reflectances obtained by linear mixture of both sea ice and water-leaving reflectances (ρ_w). The standard atmospheric correction algorithm was then applied to the simulated TOA spectra to retrieve ρ_w spectra from which chlorophyll a concentrations (CHL) and inherent optical properties (IOPs) were derived. The adjacency effect was associated with large errors (> 0.002) in the retrieval of ρ_w as far as 24 km from an ice edge in the blue part of the spectrum (443 nm). Therefore, for moderate to high CHL (> 0.5 mg m^− 3), any pixel located within a distance of ∼ 10-20 km from the ice edge were unreliable. It was also found necessary to consider the adjacency effect when the total absorption coefficient (a_t) was to be retrieved using a semi-analytical algorithm. a_t(443) was underestimated by more than 35% at a distance of 20 km from an ice edge for CHL > 0.5 mg m^− 3. The effect on the retrieval of the particle backscattering coefficient (b_bp) was important only for clear waters (CHL ∼ 0.05 mg m^− 3). In contrast, sub-pixel contamination by a small amount of sea ice produced systematic underestimation of ρ_w in the blue because of incorrect interpretation of enhanced reflectance in the near infrared that is attributed to higher concentrations of atmospheric aerosols. In general, sub-pixel contamination was found to result in overestimations of CHL and a_t, and underestimations of b_bp. A simple method was proposed to flag pixels contaminated by adjacency effect.     

Garden of eden configurations for 2-D cellular automata with rule 2460 N

An important problem in cellular automata theory is the reversibility of a cellular automaton which is related to the existence of Garden of Eden configurations in cellular automata. In this paper, we study new local rules for two-dimensional cellular automata over the ternary field Z₃ (the set of integers modulo three) with some of their important characteristics. We obtain necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional ternary cellular automata. Also by making use of the matrix representation of two-dimensional cellular automata, we provide an algorithm to obtain the number of Garden of Eden configurations for two-dimensional cellular automata defined by rule 2460 N. We present an application of the reversible two-dimensional ternary cellular automata to cryptography.     

A four-band semi-analytical model for estimating chlorophyll a in highly turbid lakes: The case of Taihu Lake, China

Accurate estimation of phytoplankton chlorophyll a (Chla) concentration from remotely sensed data is particularly challenging in turbid, productive waters. The objectives of this study are to validate the applicability of a semi-analytical three-band algorithm in estimating Chla concentration in the highly turbid, widely variable waters of Taihu Lake, China, and to improve the algorithm using a proposed four-band algorithm. The improved algorithm is expressed as [Rrs(λ₁)^− 1 − Rrs(λ₂)^− 1][Rrs(λ₄)^− 1 − Rrs(λ₃)^− 1]^− 1. The two semi-analytical algorithms are calibrated and evaluated against two independent datasets collected from 2007 and 2005 in Taihu Lake. Strong linear relationships were established between measured Chla concentration and that derived from the three-band algorithm of [Rrs^− 1(660) − Rrs^− 1(692)]Rrs(740) and the four-band algorithm of [Rrs^− 1(662) − Rrs^− 1(693)][Rrs^− 1(740) − Rrs^− 1(705)]^− 1. The first algorithm accounts for 87% and 80% variation in Chla concentration in the 2007 and 2005 datasets, respectively. The second algorithm accounts for 97% of variability in Chla concentration for the 2007 dataset and 87% of variation in the 2005 dataset. The three-band algorithm has a mean relative error (MRE) of 43.9% and 34.7% for the 2007 and 2005 datasets. The corresponding figures for the four-band algorithm are 26.7% and 28.4%. This study demonstrates the potential of the four-band model in estimating Chla even in highly turbid case 2 waters.     

Porous GaN on Si(1 1 1) and its application to hydrogen gas sensor

The growth of heterostructure of n-type GaN/AlN/Si(1 1 1) is carried out using the molecular beam epitaxy (MBE) Veeco model Gen II system. The surface morphology of the as-grown GaN sample showed pits on the GaN surface in a ratio small than those found by other research groups. Porous GaN samples were synthesized by an electrochemical etching technique combined with increasing the current density to 75 mA/cm². The formation of pore structures are of different sizes, the etched surface became hexagonal, and pore structures are confined to a smaller size. The PL results showed greater blue shift luminescence in comparison to results found by other research groups. The reduction in crystallite size is confirmed by an increase in the broadening of XRD spectra. Raman spectra also displayed a strong band at 522 cm⁻¹ from the Si(1 1 1) substrate, and a small band at 301 cm⁻¹. These are due to the acoustic phonons of Si. Two Raman active optical phonons are assigned to h-GaN at 139 cm⁻¹ and 568 cm⁻¹, due to E2 (low) and E2 (high) respectively. The sensitivity of the gas sensor is increased as a function of the hydrogen flow rate and they became much higher compared to the as-grown sample.     

Load-sharing system model and its application to the real data set

This study deals with the classical and Bayesian estimation of the parameters of a k-components load-sharing parallel system model in which each component's lifetime follows Lindley distribution. Initially, the failure rate of each of the k components in the system is h(t,θ₁) until the first component failure. However, upon the first failure within the system, the failure rates of the remaining (k − 1) surviving components change to h(t,θ₂) and remain the same until next failure. After second failure, the failure rates of (k − 2) surviving components change to h(t,θ₃) and finally when the (k − 1)th component fails, the failure rate of the last surviving component becomes h(t,θ_k). In classical set up, the maximum likelihood estimates of the load share parameters, system reliability and hazard rate functions along with their standard errors are computed. 100 × (1 − γ)% confidence intervals and two bootstrap confidence intervals for the parameters have also been constructed. Further, by assuming Jeffrey's invariant and gamma priors of the unknown parameters, Bayes estimates along with their posterior standard errors and highest posterior density credible intervals of the parameters are obtained. Markov Chain Monte Carlo technique such as Metropolis–Hastings algorithm has been utilized to generate draws from the posterior densities of the parameters.     

Retrieval of high-resolution sea surface temperature data for Sendai Bay, Japan, using the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER)

We studied sea surface temperature (SST) retrieval algorithms for Sendai Bay, using output from the thermal-infrared channels of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) on board Terra. While the highest resolutions of other satellite SST products are about 1 km, the ASTER thermal-infrared channels provide 90-m spatial resolution. To develop the ASTER algorithm, we employed statistical methods in which SSTs retrieved from the thermal-infrared measurements were tuned against the Moderate Resolution Imaging Spectroradiometer (MODIS) SST product with a 1-km spatial resolution. Terra also carries a MODIS sensor, which observed the same area as the ASTER sensor at the same time. The MODIS SST was validated around Sendai Bay, revealing a bias of −0.15 °C and root mean-square difference (RMSD) of 0.67 °C against in situ SSTs. Taking into account the spatial-resolution difference between ASTER and MODIS, match-up was generated only if the variability of ASTER brightness temperatures (T₁₃) was small in a pixel of MODIS SST (MP). The T₁₃ within one MP was about 121 pixels. The standard deviation (σ₁₃) of T₁₃ was calculated for each cloud-free MP, and the threshold of σ₁₃ for choosing match-up MPs was decided by analyzing the σ₁₃ histogram of one ASTER image. The 15 synchronous pairs of ASTER/MODIS images are separated into two groups of 8 pairs called set (A) and 7 pairs called set (B). Using the common procedure, the match-ups are generated for set (A) and set (B). The former is used for developing the ASTER Multi-Channel SST (MCSST) algorithm, and the latter for validation of the developed ASTER SST. Analysis of the whole 15 pairs indicated that ASTER SST does not depend on the satellite zenith angle. We concluded that, using Akaike's information criterion with set (A) match-ups, the multiple regression formula with all five thermal-infrared channels was adequate for the ASTER SST retrieval. Validation of ASTER SST using match-up set (B) indicated a bias of 0.101 °C and RMSD of 0.455 °C.