Optimal probability-of-error thresholds and performance for twoversions of the sign detector

Expressions are obtained for specifying the optimal error probability (minimum P_e) thresholds λ₀₁ and λ₀₂ for the traditional and modified sign detectors, respectively. These thresholds are shown to depend on the parameters p, P₁, and M where: M is the number of observations z_i used in the test statistic; P₁=P(H₁ ) is the prior probability for hypothesis H₁ that signal s₁ is present and 1-P₁ =P(H₀) corresponds to the hypothesis H₀ that signal s₀ is present; and p=Pr{z_i⩾0|H₁} with s₀=0 for the traditional sign detector and p=Pr{z_i⩾λ|H₁ }=Pr{z_i<λ|H₀} with λ =(s₀+s₁)/2 for the modified sign detector. The expressions for λ₀₁ and λ₀₂, are given explicitly, and shown to be independent of P₁ for sufficiently large M. Optimal P_e versus M performance curves, corresponding to both versions of the sign detector, are obtained for a representative range of values for p and P₁     

An efficient numerical approach, for determining the dispersioncharacteristics of dual-mode elliptical-core optical fibers

Based on vectorial formulations which combine the surface integral equation method and the finite-element method, a novel numerical approach is proposed for calculating the dispersion coefficients of dual-mode elliptical-core fibers with arbitrary refractive index profiles. By differentiating the original formulations involving the propagation constant β and the guided mode fields H_x and H_y once and twice with respect to the normalized frequency V, the new formulations for {dβ/dV, dH_x/dV, dH_y/dV} and for {d²β/dV², d² H_x/dV², d²H_y/dV² } are obtained respectively. Once {β, H_x, H_y } is solved through the eigenvalue procedure which dominates the computing time, only a few matrix manipulations are required to obtain {dβ/dV, dH_x/dV, dH_y/dV} and {d²β/dV², d²H_x/dV² , d²H_y/dV²}. Some numerical examples are examined to see the influence of different refractive index distributions with dips on the dispersions of the four nondegenerate LP ₁₁ modes for elliptical-core fibers     

Design optimization of stacked layer dielectrics for minimum gate leakage currents

An effective model to evaluate the leakage currents for different stacked gates deep submicron MOS transistors is presented. For a given equivalent oxide thickness of a stacked gate, the gate leakage current decreases with an increase of high-k dielectric thickness or a decrease of interlayer thickness. Turning points at high gate biases of the I–V curves are observed for Si₃N₄/SiO₂, Ta₂O₅/SiO₂, Ta₂O₅/SiO_2−yN_y, Ta₂O₅/Si₃N₄, and TiO₂/SiO₂ stacked gates except for Al₂O₃/SiO₂ structure. Design optimization for the stacked gate architecture to obtain the minimum gate leakage current is evaluated.     

Strongly consistent online forecasting of centered Gaussianprocesses

An estimator Eˆ(d_n,n) of the conditional expectation E[X_n+1|X_n,...,X(n-d_n+1)] in a centered, stationary, and ergodic Gaussian process {X_i}_i with absolutely summable Wold coefficients is constructed on the basis of having observed X₁,...,X_n . For a suitable choice of the length dn→∞ (n→∞) of the past covered by the conditional expectation, it is established that |Eˆ(d_n,n)-E[X_n+1|X_n ,...,X(n-d_n+1)]|→0 with probability 1. In addition, sufficient conditions for |E[X_n+1|X_n,X _n-1,...]-E[X_n+1|X_n,...,X(n-d_n +1)]| →0 to hold with probability 1 are given, that is, conditions under which Eˆ(d_n,n) can be used as a strongly consistent forecaster for |E[X_n+1|X_n,X _n-1,...]     

Single- and double-heterojunction pseudomorphic In0.5(Al0.3Ga0.7)0.5P/In0.2Ga0.8As high electron mobility transistors grown by gas sourcemolecular beam epitaxy

In_0.5(Al_0.3Ga_0.7)_0.5 P/In_0.2Ga_0.8As single- and double-heterojunction pseudomorphic high electron mobility transistors (SH-PHEMTs and DH-PHEMTs) on GaAs grown by gas-source molecular beam epitaxy (GSMBE) were demonstrated for the first time. SH-PHEMTs with a 1-μm gate-length showed a peak extrinsic transconductance g_m of 293 mS/mm and a full channel current density I_max of 350 mA/mm. The corresponding values of g_m and I_max were 320 mS/mm and 550 mA/mm, respectively, for the DH-PHEMTs. A short-circuit current gain (H₂₁) cutoff frequency f_T of 21 GHz and a maximum oscillation frequency f_max of 64 GHz were obtained from a 1 μm DH device. The improved device performance is attributed to the large ΔE_c provided by the In_0.5(Al_0.3Ga_0.7)_0.5P/In _0.2Ga_0.8As heterojunctions. These results demonstrated that In_0.5(Al_0.3Ga_0.7)_0.5P/In _0.2Ga_0.8As PHEMT's are promising candidates for microwave power applications     

In-circuit hot-carrier model and its application to inverter chainoptimization

An analytical in-circuit device lifetime model and design methodology for minimizing hot-carrier effects in an inverter chain are presented. Based on the model, in-circuit device lifetime, τ_AC , for hot-carrier induced degradation is given by τ_AC =τ_DC/R, R≡√π/2√Vcc/b√(T _rise.T_fall)/T_c where τ_DC is the device lifetime under a DC test, T_rise and T_fall are the rise time for input and fall time for output, T_C is cycle time and b is a constant. The model also shows that minimizing circuit delay in the inverter chain maximizes hot-carrier reliability     

Two-dimensional weight-constrained codes through enumeration bounds

For a rational α∈(0,1), let 𝒜_n×m,α be the set of binary n×m arrays in which each row has Hamming weight αm and each column has Hamming weight αn, where αm and αn are integers. (The special case of two-dimensional balanced arrays corresponds to α=1/2 and even values for n and m.) The redundancy of 𝒜_n×m,α is defined by ρ_n×m,α=nmH(α)-log₂|𝒜 _n×m,α| where H(x)=-xlog₂x-(1-x)log₂(1-x). Bounds on ρ_n×m,α are obtained in terms of the redundancies of the sets 𝒜_ℒ,α of all binary ℒ-vectors with Hamming weight αℒ, ℒ∈{n,m}. Specifically, it is shown that ρ_n×m,α⩽nρ_m,α+mρ _n,α where ρ_ℒ,α=ℒH(α)-log₂|𝒜 _ℒ,α| and that this bound is tight up to an additive term O(n+log m). A polynomial-time coding algorithm is presented that maps unconstrained input sequences into 𝒜_n×m,α at a rate H(α)-(ρ_m,α/m)     

The Kolmogorov complexity, universal distribution, and codingtheorem for generalized length functions

A function h(w) is said to be useful for the coding theorem if the coding theorem remains to be true when the lengths |w| of codewords w in it are replaced with h(w). For a codeword w=a₀a₁...a_m-1 of length m and an infinite sequence Q=(q₀, q₁, q₂, ...) of real numbers such that 0n⩽½, let |w|_Q denote the value Σ_n=0^m-1 (if a_n =0 then -log₂q_n, else -log₂(1-q _n)), that is, -log₂, (the probability that flippings of coins generate x) assuming that the (i+1)th coin generates a tail (or 0) with probability q_i. It is known that if 0n→∞ q_n then |w|_Q is useful for the coding theorem and if lim_n→∞ q _n/(1/(2ⁿ))=0 then |w|_Q is not useful. We introduce several variations of the coding theorem and show sufficient conditions for h(w) not to be useful for these variations. The usefulness is also defined for the expressions that define the Kolmogorov complexity and the universal distribution. We consider the relation among the usefulness for the coding theorem, that for the Kolmogorov complexity, and that for the universal distribution     

ICP etching of SiC

A number of different plasma chemistries, including NF₃/O₂, SF₆/O₂, SF₆/Ar, ICl, IBr, Cl₂/Ar, BCl₃/Ar and CH₄/H₂/Ar, have been investigated for dry etching of 6H and 3C–SiC in an inductively coupled plasma tool. Rates above 2000 Å cm⁻¹ are found with fluorine-based chemistries at high ion currents. Surprisingly, Cl₂-based etching does not provide high rates, even though the potential etch products (SiCl₄ and CCl₄) are volatile. Photoresist masks have poor selectivity over SiC in F₂-based plasmas under normal conditions, and ITO or Ni is preferred.     

Electrical properties of rare earth silicides produced by channeled ion beam synthesis

Electrical measurements have been performed on ErSi_1.7, YSi_1.7 and Er_0.5Y_0.5Si_1.7, produced by channeled ion beam synthesis. The results have been compared with thin films of the same rare earth silicides produced by other methods. The room temperature resistivities of the ErSi_1.7, YSi_1.7 and Er_0.5Y_0.5Si_1.7 are 52, 69 and 87 μΩ cm, respectively, significantly higher than the reported values for MBE synthesised layers. The ErSi_1.7 shows evidence of magnetic ordering, but this is not observed in either the YSi_1.7 or the Er_0.5Y_0.5Si_1.7 down to 3 K.     

Emission cross sections and spectroscopy of Ho3+ laserchannels in KGd(WO4)2 single crystal

The spectroscopic properties of Ho³⁺ laser channels in KGd(WO₄)₂ crystals have been investigated using optical absorption, photoluminescence, and lifetime measurements. The radiative lifetimes of Ho³⁺ have been calculated through a Judd-Ofelt (JO) formalism using 300-K optical absorption results. The JO parameters obtained were Ω₂=15.35×10^-20 cm², Ω ₄=3.79×10^-20 cm², Ω₆ =1.69×10^-20 cm². The 7-300-K lifetimes obtained in diluted (8·10¹⁸ cm^-3) KGW:0.1% Ho samples are: τ(⁵F₃)≈0.9 μs, τ( ⁵S₂)=19-3.6 μs, and τ(⁵F₅ )≈1.1 μs. For Ho concentrations below 1.5×10²⁰ cm^-3, multiphonon emission is the main source of non radiative losses, and the temperature independent multiphonon probability in KGW is found to follow the energy gap law τ_ph ^-1(0)=βexp(-αΔE), where β=1.4×10^-7 s^-1, and α=1.4×10³ cm. Above this holmium concentration, energy transfer between Ho impurities also contributes to the losses. The spectral distributions of the Ho³⁺ emission cross section σ_EM for several laser channels are calculated in σ- and π-polarized configurations. The peak a σ_EM values achieved for transitions to the ⁵I₈ level are ≈2×10^-20 cm² in the σ-polarized configuration, and three main lasing peaks at 2.02, 2.05, and 2.07 μm are envisaged inside the ⁵I₇→⁵I₈ channel     

Propagation of lower-order modes in a radially anisotropiccylindrical waveguide with liquid crystal cladding

The propagation behavior of the four lower-order modes, HE₁₁ , TE₀₁, TM₀₁, and HE₂₁, in a radially anisotropic cylindrical waveguide with liquid crystal cladding is studied both theoretically and experimentally. The cylindrical waveguide is a doubly-clad fiber with an isotropic core and inner cladding and a radially anisotropic outer cladding made of nematic liquid crystal. Theoretically, the propagation and decay constants for the TE₀₁ and TM₀₁ modes are obtained by solving the wave equations exactly, while those for the HE₁₁ and HE ₂₁ modes are derived using perturbation techniques under the weakly guiding approximation. It is predicted that in such a structure the guided TE₀₁ mode can be separated from the leaky HE₁₁, TM₀₁, and HE₂₁ modes. The theoretical results show good agreement with the experimental observations for a 3 cm long fiber cell with a 5 μm inner cladding radius     

Temperature-dependent Sellmeier coefficients and chromaticdispersions for some optical fiber glasses

Temperature-dependent Sellmeier coefficients are necessary to optimize optical design parameters of the optical fiber transmission system. These coefficients are calculated for fused silica (SiO₂ ), aluminosilicate, and Vycor glasses for the first time to find the temperature dependence of chromatic dispersion at any wavelength from UV to 1.7 μm. The zero dispersion wavelength λ₀ (1.273 μm for SiO₂, 1.393 μm for aluminosilicate, and 1.265 μm for Vycor glasses at 26°C) varies linearly with temperature, and dλ₀/dT is 0.03 nm/K for aluminosilicate and Vycor glasses, whereas for SiO₂ it is 0.025 nm/K. This study interprets the recently observed experimental value of dλ₀/dT for two dispersion shifted optical fibers; and the dominantly material origin of dλ₀/dT is confirmed here as a fundamental property of the optical fiber glasses     

Nested input-constrained codes

An input-constrained channel, or simply a constraint, is a set S of words that is generated by a finite labeled directed graph. An encoder for S maps, in a lossless manner, sequences of unconstrained input blocks into sequences of channel blocks, the latter sequences being words of S. In most applications, the encoders are finite-state machines and, thus, presented by state diagrams. In the special case where the state diagram of the encoder is (output) deterministic, only the current encoder state and the current channel block are needed for the decoding of the current input block. In this work, the problem of designing coding schemes that can serve two constraints simultaneously is considered. Specifically, given two constraints S₁ and S ₂ such that S₁⊆S₂ and two described rates, conditions are provided for the existence of respective deterministic finite-state encoders ε₁ and ε₂ , at the given rates, such that (the state diagram of) ε₁ is a subgraph of ε₂ Such encoders are referred to as nested encoders. The provided conditions are also constructive in that they imply an algorithm for finding such encoders when they exist. The nesting structure allows to decode ε₁ while using the decoder of ε₂. Developments in optical recording suggest a potential application that can take a significant advantage of nested encoders     

The relevance of fT and fmax for the speed ofa bipolar CE amplifier stage

Expressions relating the bandwidth of a common-emitter (CE) amplifier stage and the small-signal CML gate delay time to directly measurable transistor parameters, such as f_T, f_max, and input bandwidth f_υ, are presented. They are valid for an arbitrary division of the base resistance and base-collector depletion capacitance into internal and external components. No resistance measurements are needed. It is shown that the transistor input bandwidth f_υ is an important figure of merit for the speed of a CE stage. Under a given bias condition, f_υ is determined by the base resistance and the cut-off frequency. In most cases the value of the maximum oscillation frequency f_max is only of minor importance. It would therefore be more meaningful to present besides f_T also f_υ instead of f_max as a figure of merit for transistors for high-speed, low-power analog and digital circuits     

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     

Line impedance and propagation coefficient of narrowsuperconducting coplanar lines made of YBaCuO

The microwave properties of coplanar waveguides with line widths from 1 μm to 40 μm made of superconducting YBaCuO films with a thickness t=180 nm on LaAlO₃ are investigated. The line impedance Z_L and the normalized propagation coefficient β/β₀ of these waveguides are measured between 45 MHz and 26.5 GHz at temperatures between 77.4 K and 92 K. The ratio of the line width w to the distance of the ground layers d is constant with w/d=0.2. Therefore, Z_L and β/β₀ are independent of w for perfectly conducting waveguides. For superconducting waveguides it is found that Z_L and β/β₀ differ from the values of perfectly conducting waveguides. They increase for smaller line widths at a constant temperature. At w=1 μm and T=80 K, Z_L and β/β ₀ are nearly twice as high as calculated for perfect conductors. Furthermore, Z_L and β/β₀ increase with the temperature. It is shown that these effects are attributed to an increase of the inductance per unit length L' due to the superconducting material, whereas the capacitance per unit length C' behaves like C' of perfectly conducting waveguides. Using these results, the dimensions of the superconducting waveguides, which are necessary to obtain a desired Z_L at a given line width w, are calculated