RNS-To-Binary Converter for a New Three-Moduli Set {2n+1−1,2n,2n−1}

In this brief, the design of residue number system (RNS) to binary converters for a new powers-of-two related three-moduli set {2ⁿ⁺¹ - 1, 2ⁿ, 2ⁿ - 1} is considered. This moduli set uses moduli of uniform word length (n to n + 1 bits). It is derived from a previously investigated four-moduli set {2ⁿ - 1, 2ⁿ, 2ⁿ + 1, 2^{n +1} - 1}. Three RNS-to-binary converters are proposed for this moduli set: one using mixed radix conversion and the other two using Chinese remainder theorem. Detailed architectures of the three converters as well as comparison with some earlier proposed converters for three-moduli sets with uniform word length and the four-moduli set {2ⁿ - 1, 2ⁿ, 2ⁿ + 1, 2ⁿ⁺¹ - 1} are presented.     

A Residue-to-Binary Converter for a New Five-Moduli Set

The efficiency of the residue number system (RNS) depends not only on the residue-to-binary converters but also the operand sizes and the modulus in each residue channel. Due to their special number theoretic properties, RNS with a moduli set consisting of moduli in the form of 2 ⁿplusmn1 is more attractive than those with other forms of moduli. In this paper, a new five-moduli set RNS {2ⁿ-1,2ⁿ,2ⁿ+1,2ⁿ+1-1,2 ^n-1-1} for even n is proposed. The new moduli set has a dynamic range of (5n-1) bits. It incorporates two additional moduli to the celebrated three-moduli set, {2ⁿ-1,2ⁿ,2ⁿ +1} with VLSI efficient implementations for both the binary-to-residue conversion and the residue arithmetic units. This extension increases the parallelism and reduces the size of each residue channel for a given dynamic range. The proposed residue-to-binary converter relies on the properties of an efficient residue-to-binary conversion algorithm for {2ⁿ-1,2ⁿ,2ⁿ+1,2ⁿ+1-1} and the mixed-radix conversion (MRC) technique for the two-moduli set RNS. The hardware implementation of the proposed residue-to-binary converter employs adders as the primitive operators. Besides, it can be easily pipelined to attain a high throughput rate     

Adder based residue to binary number converters for(2n-1, 2n, 2n+1)

Based on an algorithm derived from the new Chinese remainder theorem I, we present three new residue-to-binary converters for the residue number system (2ⁿ-1, 2ⁿ, 2ⁿ+1) designed using 2n-bit or n-bit adders with improvements on speed, area, or dynamic range compared with various previous converters. The 2n-bit adder based converter is faster and requires about half the hardware required by previous methods. For n-bit adder-based implementations, one new converter is twice as fast as the previous method using a similar amount of hardware, whereas another new converter achieves improvement in either speed, area, or dynamic range compared with previous converters     

2n modified prime codes for use in fibre optic CDMAnetworks

2ⁿ modified prime codes are designed for all-optical code-division multiple access (CDMA) networks using very simple encoders and decoders. The proposed code is obtained from an original 2ⁿ prime code of prime number P. By padding P-1 zeros in each `subsequence' of codewords in the corresponding 2ⁿ prime code. The cross-correlation constraint of the resulting 2ⁿ modified prime code is equal to one, as opposed to two for a 2ⁿ prime code. For a given bit error rate (BER), the proposed code can thus be used to support a larger number of active users in the fibre optic CDMA network than a 2ⁿ prime code. Moreover, using the former can also reduce code length and weight compared with employing the latter to achieve the same BER     

Generalized Kasami Sequences: The Large Set

In this correspondence, new binary sequence families F^k of period 2ⁿ-1 are constructed for even n and any k with gcd(k,n)=2 if n/2 is odd or gcd(k,n)=1 if n/2 is even. The distribution of their correlation values is completely determined. These families have maximum correlation 2^n/2+1 and family size 2^3n/2 + 2^n/2 for odd n/2 or 2^3n/2+2^n/2-1 for even n/2. The proposed families include the large set of Kasami sequences, where the k is taken as k=n/2+1.     

On the {m-QAM}2 modulation

The aim of this letter is to analyze a modulation technique called {m-QAM}² in terms of bit error rate (BER). The performance of the {m-QAM}² is compared to the traditional M-QAM modulation scheme, taking into account the same spectral efficiency, where m and M are related by M=2ⁱ and i=√m, …, 2√m-1. Performance curves obtained by the theoretical model and by computer simulation are shown     

Efficient Reverse Converters for 4-Moduli Sets {2^{2n-1}-1, 2^{n}, 2^{n}+1, 2^{n}-1} and {2^{2n-1}, 2^{2n-1}-1, 2^{n}+1, 2^{n}-1} Based on CRTs Algorithm

Speed and complexity of a reverse converter are two important factors that affect the performance of a residue number system. In this paper, two efficient reverse converters are proposed for the 4-moduli sets {2 \(^{2n-1}-1\) , 2 \(^{n}\) , 2 \(^{n}+1\) , 2 \(^{n}-1\) } and {2 \(^{2n-1}\) , 2 \(^{2n-1}-1\) , 2 \(^{n}+1\) , 2 \(^{n}-1\) } with 5 \(n\) -bit and 6 \(n\) -bit dynamic range, respectively. The proposed reverse converter for moduli set {2 \(^{2n-1}-1\) , 2 \(^{n}\) , 2 \(^{n}+1\) , 2 \(^{n}-1\) } has been designed based on CRT and New CRT-I algorithms and in two-level structure. Also, an efficient reverse converter for moduli set {2 \(^{2n-1}\) , 2 \(^{2n-1}-1\) , 2 \(^{n}+1\) , 2 \(^{n}-1\) } has been designed by applying New CRT-I algorithm. The proposed reverse converters are based on adders and hence can be simply implemented by VLSI circuit technology. The proposed reverse converters offer less delay and hardware cost when compared with the recently introduced reverse converters for the moduli sets {2 \(^{n}+1\) , 2 \(^{n}-1\) ,2 \(^{n}\) , 2 \(^{2n+1}-1\) } and {2 \(^{n}+1\) , 2 \(^{n}-1\) , 2 \(^{2n}\) , 2 \(^{2n+1}-1\) }.     

On the binary quadratic residue system with noncoprime moduli

The residue number system (RNS) appropriate for implementing fast digital signal processors since it can support parallel, carry-free, high-speed arithmetic. A development in residue arithmetic is the quadratic residue number system (QRNS), which can perform complex multiplications with only two integer multiplications instead of four. An RNS/QRNS is defined by a set of relatively prime integers, called the moduli set, where the choice of this set is one of the most important design considerations for RNS/QRNS systems. In order to maintain simple QRNS arithmetic, moduli sets with numbers of forms 2ⁿ+1 (n is even) have been considered. An efficient such set is the three-moduli set (2^2k-2+1.2^2k+1.2^2k+2+1) for odd k. However, if large dynamic ranges are desirable, QRNS systems with more than three relatively prime moduli must be considered. It is shown that if a QRNS set consists of more than four relatively prime moduli of forms 2ⁿ+1, the moduli selection process becomes inflexible and the arithmetic gets very unbalanced. The above problem can be solved if nonrelatively prime moduli are used. New multimoduli QRNS systems are presented that are based on nonrelatively prime moduli of forms 2ⁿ +1 (n even). The new systems allow flexible moduli selection process, very balanced arithmetic, and are appropriate for large dynamic ranges. For a given dynamic range, these new systems exhibit better speed performance than that of the three-moduli QRNS system     

A non-Shannon-type conditional inequality of information quantities

Given n discrete random variables Ω={X₁,…,X_n}, associated with any subset α of {1,2,…,n}, there is a joint entropy H(X_α) where X_α={X_i: i∈α}. This can be viewed as a function defined on 2^{1,2,…,n} taking values in [0, +∞). We call this function the entropy function of Ω. The nonnegativity of the joint entropies implies that this function is nonnegative; the nonnegativity of the conditional joint entropies implies that this function is nondecreasing; and the nonnegativity of the conditional mutual information implies that this function is two-alternative. These properties are the so-called basic information inequalities of Shannon's information measures. An entropy function can be viewed as a 2ⁿ -1-dimensional vector where the coordinates are indexed by the subsets of the ground set {1,2,…,n}. As introduced by Yeng (see ibid., vol.43, no.6, p.1923-34, 1997) Γ_n stands for the cone in IR(2ⁿ-1) consisting of all vectors which have all these properties. Let Γ_n* be the set of all 2ⁿ -1-dimensional vectors which correspond to the entropy functions of some sets of n discrete random variables. A fundamental information-theoretic problem is whether or not Γ¯_n*=Γ_n. Here Γ¯_n * stands for the closure of the set Γ_n*. We show that Γ¯_n* is a convex cone, Γ₂*=Γ₂, Γ₃*≠Γ₃, but Γ¯₃ *=Γ₃. For four random variables, we have discovered a conditional inequality which is not implied by the basic information inequalities of the same set of random variables. This lends an evidence to the plausible conjecture that Γ¯_n*≠Γ_n for n>3     

Fast Bit Parallel-Shifted Polynomial Basis Multipliers in GF(2n)

A new nonpipelined bit-parallel-shifted polynomial basis multiplier for GF(2ⁿ) is presented. For some irreducible trinomials, the space complexity of the multiplier matches the best results available in the literature, and its gate delay is equal to T _A+lceillog₂nrceilT_X, where T_A and T_X are the delay of one two-input and and xor gates, respectively. To the best of our knowledge, this is the first time that the gate delay bound T_A+lceillog₂nrceilT_X is reached. For some irreducible pentanomials, its gate delay is equal to T_A +(1+lceillog₂nrceil)T_X. NIST has recommended five binary fields for the elliptic curve digital signature algorithm applications: GF(2¹⁶³), GF(2²³³), GF(2 ²⁸³), GF(2⁴⁰⁹), and GF(2⁵⁷¹), but no irreducible trinomials exist for three degrees, viz., 163, 283 and 571. For the three corresponding binary fields, we show that the gate delay of the proposed multiplier is T_A+(1+lceillog₂nrceil)T_X. This result outperforms the previously known results     

Kinetic model of photolytic O2(1Δ) generation

Kinetic analysis of photolysis of O3:O2:He mixtures by UV light has been studied. Dependence of O2(¹Δ) yield on partial pressures, flashlamp intensity, and duration was investigated. Results indicate sufficient O2(¹Δ) yield for operation of a high-power atomic iodine laser on the I*(²P_{1/2})underrightarrow{1.31 mu}m I(²p_{3/2}) transition.     

The influence of the optical stark shift on the two-photon excitation of the molecular hydrogen E, F1Σ+gstate

The first demonstration of the use of the optical Stark effect to secure resonance for a two-quantum process in the ultraviolet is reported. Following excitation of molecular hydrogen by 193 nm radiation, intense stimulated emission on both the Lyman and Werner bands is observed. The Werner (2-5)Q(1)transition at 117.5 nm exhibits a conversion efficiency of ∼0.2 percent. It is found that electron collisions with excited molecules provide the most probable mechanism for excitation of theC^{1}Pi_{u}levels with a rate constant estimated to bek_{e} sim 7 times 10^{-6}cm³/s.     

An efficient solution of the congruencex^2 + ky^2 = mpmod{n}

The equation of the title arose in the proposed signature scheme of Ong-Schnorr-Shamir. The large integersn, kandmare given and we are asked to find any solutionx, y. It was believed that this task was of similar difficulty to that of factoring the modulusn;we show that, on the contrary, a solution can easily be found ifkandmare relatively prime ton. Under the assumption of the generalized Riemann hypothesis, a solution can be found by a probabilistic algorithm inO(log n)^{2}|loglog|k||)arithmetical steps onO(log n)-bit integers. The algorithm can be extended to solve the equationX^{2} + KY^{2} = M pmod{n}for quadratic integersK, M in {bf Z}[sqrt{d}]and to solve in integers the equationx^{3} + ky_{3} + k^{2}z^{3} - 3kxyz = m pmod{n}.     

Photoexcitation and photodissociation lasers--Part I: Nitric oxide laser emissions resulting from C(2π) → A(2Σ+) and D(2Σ+) → A(2Σ+) transitions

-1-μm laser emission was detected when NO or NO2was flash-photolyzed, with or without dilution, in the vacuum UV above 165 nm. The emission was identified as theC(²π)rightarrow A(²Sigma+)     

Vibration-vibration energy transfer in the v3mode of CO2

The vibration-vibration energy transfer of CO2gas initially excited to the first asymmetric stretch level (00⁰1) has been observed. Collisional pumping to the (01¹1) combination level is measured by monitoring the fluorescence due to the (01¹1) → (01¹0) band. The rate constant for the process: CO2(01¹1) + CO2(00⁰0) → CO2(00⁰1) + CO2(01¹0) is found to be(5.3 pm 1) times 10^{6}s^-1torr^-1.     

Junction depth versus sheet resistivity in BF2+-implanted rapid-thermal-annealed silicon

Conditions to achieve shallow p+-junctions with low sheet resistance by using ion implantation and rapid thermal annealing (RTA), are presented. This work shows that (junction depth) × (sheet resistivity)rho_{s}X_{j}has a smaller value with increasing implant dose and anneal temperature (boron solubility), and decreasing implant energy. However, the value is saturated for higher doses than 10¹⁶Xjcm², where Xjis junction depth in micrometers, and anneal temperature should be lower than 1100°C, because of considerable boron diffusion even in 10-s RTA.rho_{s}X_{j} = 18Ω.µm is achieved by BF2+ implantation with 5 × 10¹⁵-cm^-2dose at 30 keV and 1000°C RTA. The possibility of further improvement inrho_{s}X_{j}value is discussed.     

Sensitivity of Pr+3: LaCl3infrared quantum counter

The NEPλand response time of the Pr³⁺:LaCl3Infra-red Quantum Counter have been measured for the wavelengths 1.48 μ, 1.58 μ, 2.03 μ and 2.33 μ at the nominal temperatures of 300°K, 77°K, and 4.2°K. The experimental arrangement is described and suggestions for improvement are made. The best results obtained are anNEP_{2.03_mu} = 2 times 10^{-5}watts(c/s)^{-1/2}and a temperature independent response time of 20-30 ms.     

Production of electronically excited iodine atoms, I(2P1/2), following injection of HI into a flow of discharge oxygen

The emission from the transition I*(5²P_{1/2}) rightarrowI(5²P_{3/2}) at 1.315 μm following injection of HI into a microwave-discharged He/O2flow has been studied. Relative I*(5²P_{1/2}) emission intensities have been recorded as a function of HI and O²flow rates and as a function of time after injection. Pulsed gain measurements using an iodine photodissociation laser as a source show that the ratio,N_{I}*/ (N_{I} +N_{I}*,) approx 0.15-0.25, is less than that required for population inversion. This observation will be discussed in terms of known chemical processes involving O(³P), HI, O2(¹Δg), and iodine atoms.     

Gain measurement and upconversion analysis in Tm3+, Ho3+ co-doped alumino-zirco-fluoride glass

The small signal gain coefficients were measured in Tm³⁺,Ho³⁺ co-doped alumino-zirco-fluoride glass. A gain of 15%/cm at 2.05 μm was obtained for pump power density of 42 kW/cm². The temperature increase of the glass was found to be more than 150 K with this pump power, which was estimated from a comparison between fluorescence intensities of Tm^{3+ 3} F₄-³H₆ and Ho^{3+ 5} I₇-⁵I₈. An upconversion rate constant of 12.5×10^-17 cm³ sec^-1 from a coupled (Tm^{3+ 3}F₄, Ho^{3+ 5}I₇) level to a coupled (Tm^{3+ 3}H₅, Ho^{3+ 5}I₆) level was determined by fitting the experimentally obtained gain coefficients to the calculated one which takes into consideration any temperature increase     

Tr（...）的二阶非线性度下界

作为影响系统安全的重要因素,对称密码中的密码函数应具有较高的r阶非线性度。对于r>1,目前对r阶非线性度的研究主要根据布尔函数微商的非线性度与其二阶非线性度之间的关系来进行。对于正整数n≡2（mod 4）,确定了一类布尔函数Tr(x^{2n/2+2n/2-1+1})的二阶非线性度下界。与相同变元数的两类已知布尔函数相比,研究的函数具有更紧的二阶非线性度下界。