Statistical inference under multiterminal rate restrictions: adifferential geometric approach

A statistical inference problem for a two-terminal information source emitting mutually correlated signals X and Y is treated. Let sequences Xⁿ and Yⁿ of n independent observations be encoded independently of each other into message sets M_X and M_Y at rates R₁ and R ₂ per letter, respectively. This compression causes a loss of the statistical information available for testing hypotheses concerning X and Y. The loss of statistical information is evaluated as a function of the amounts R₁ and R ₂ of the Shannon information. A complete solution is given in the case of asymptotically complete data compression, R₁, R₂→0 as n→∞. It is shown that the differential geometry of the manifold of all probability distributions plays a fundamental role in this type of multiterminal problem connecting Shannon information and statistical information. A brief introduction to the dually coupled e-affine and m-affine connections together with e -flatness and m-flatness is given     

Secret key agreement by public discussion from common information

The problem of generating a shared secret key S by two parties knowing dependent random variables X and Y, respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable Z, jointly distributed with X and Y according to some probability distribution P_XYZ, can also receive all messages exchanged by the two parties over a public channel. The goal of a protocol is that the enemy obtains at most a negligible amount of information about S. Upper bounds on H(S) as a function of P_XYZ are presented. Lower bounds on the rate H (S)/N (as N→∞) are derived for the case in which X=[X₁, . . ., X _N], Y=[Y₁, . . ., Y_N] and Z=[Z₁, . . ., Z_N] result from N independent executions of a random experiment generating X_i, Y_i and Z_i for i=1, . . ., N. It is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels, even when the enemy's channel is superior to the other two channels     

Determination of equivalent network parameters of short-gate-lengthmodulation-doped field-effect transistors

The small-signal intrinsic Y-parameters of millimeter-wave MODFETs are examined. These parameters were extracted from S-parameter data after removal of parasitics through a method of successive Z-to-Y and Y-to-Z transformations. This approach has yielded accurate values of all the parameters of an equivalent network model for the MODFETs tested, with the exception of some uncertainties in the determination of the intrinsic Y₂₁ phase-delay time constant. It is shown that accurate determination of the intrinsic carrier transit time (τ) is possible through the unity extrapolation of the intrinsic current gain ∥h₂₁∥, and this yields the related carrier average velocity (ν_av). Results obtained from three 0.25-μm-gate-length MODFETs, based on different heterostructures, and results obtained from a 0.15-μm-gate-length lattice-matched structure are presented     

A new method for on wafer noise measurement

A method for measuring the noise parameters of MESFETs and HEMTs is presented. It is based on the fact that three independent noise parameters are sufficient to fully describe the device noise performance. It is shown that two noise parameters, R_n and |Y_OPT|, can be directly obtained from the frequency variation of the noise figure F₅₀ corresponding to a 50 Ω generator impedance. By using a theoretical relation between the intrinsic noise sources as additional data, the F₅₀ measurement only can provide the four noise parameters. A good agreement with more conventional techniques is obtained     

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     

Capacitance allocation and its role in the performance ofdoubling-circuit pulsed gas lasers: its application to the N2laser

An investigation of the optical output for all possible combinations between the capacitances, C₁ and C ₂, in a doubling circuit N₂ laser is presented. It is shown that a maximum optical output appears when C ₁=C₂ for constant total capacitance. The maximum value increases when the total capacitance increases and the system approaches saturation for capacitance values higher than 20 nF each. This behavior of the optical energy is due to a similar behavior of the current, which becomes maximum when the best coupling of the two loops of the system is achieved through capacitance equality, and the oscillatory behavior of the system is minimized. When this equality is disturbed, either with weak (C₁>C₂ ) or strong (C₂<C₁) coupling of the system, the current and optical outputs decrease. In both cases, the undesirable oscillatory behavior of the system increases. The electric parameters R₁,L₁ of the spark-gap loop and R₂,L₂ of the laser channel loop are calculated     

Confidence bounds for Pr{X>Y} in 1-way ANOVArandom model

Approximate confidence bounds for reliability, R=Pr{X >Y|X,Y}, are obtained, where X and Y are independent normal (Gaussian) random variables, and X and Y are vectors of measurements for X and Y, respectively. Balanced 1-way ANOVA (analysis of variants) random effect models are assumed for the populations of X and Y. Confidence bounds are derived for R under three cases for standard deviations, σ_x and σ_y. An example shows how the results are used     

A binary analog to the entropy-power inequality

Let {X_n}, {Y_n} be independent stationary binary random sequences with entropy H( X), H(Y), respectively. Let h(ζ)=-ζlogζ-(1-ζ)log(1-ζ), 0⩽ζ⩽1/2, be the binary entropy function and let σ(X)=h^-1 (H(X)), σ(Y)=h^-1 (H(Y)). Let z_n=X_n⊕Y_n , where ⊕ denotes modulo-2 addition. The following analog of the entropy-power inequality provides a lower bound on H(Z ), the entropy of {Z_n}: σ(Z)⩾σ(X)*σ(Y), where σ(Z)=h^-1 (H(Z)), and α*β=α(1-β)+β(1-α). When {Y _n} are independent identically distributed, this reduces to Mrs. Gerber's Lemma from A.D. Wyner and J. Ziv (1973)     

A multiple-state memory cell based on the resonant tunneling diode

The device consists primarily of several molecular-beam-epitaxy (MBE-) grown GaAs/(AlGa)As resonant tunneling diodes connected in parallel. This device exhibits multiple peaks in the I-V characteristic. When a load resistor is connected, the circuit can be operated in a multiple stable mode. With this concept, implementation of three-state and four-state memory cells are made. In the three-state case the operating points at voltages V₀=0.27 V , V₁=0.42 V, and V₂=0.53 V represent the logic levels 0, 1, and 2. Similarly for the four-state memory cell the logic levels voltages are V₀=0.35 V, V₁=0.42 V, V₂=0.54 V, and V ₃=0.59 V. A suggestion of an integrated device structure using this concept is also presented     

Input filter design criteria for switching regulators usingcurrent-mode programming

Design criteria are developed for a constant-frequency current-programmed switching DC-to-DC converter with an input filter to ensure stability and prevent performance degradation. The criteria are given in terms of the filter voltage transfer function H_S , output admittance Y_s, and the y-parameter model of the switching converter. The criteria are listed as four inequalities and illustrated graphically. The criteria may be summarized as follows: assuming a converter that satisfies its loop gain T, line-to-output transfer function A_gf , and output impedance Z_of requirement is given, an input filter with H_s and Y_s can be used to attenuate the noise emissions from the converter without adversely affecting the converter if H_s⩽1 (may be relaxed to 3-6 dB), and Y _s is larger than the curves of the graphical illustration, perhaps using 6 dB as a rule-of-thumb minimum separation     

The bandwidth performance of a two-element adaptive array withtapped delay-line processing

The bandwidth performance of a two-element adaptive array with a tapped delay line behind each element is examined. It is shown how the number of taps and the delay between taps affect the bandwidth performance of the array. An array with two weights and one delay behind each element is found to yield optimal performance (equal to that obtained with continuous-wave interference) for any value of intertap delay between zero and T₉₀/B, where T ₉₀ is a quarter-wavelength delay time and B is the fractional signal bandwidth. Delays less that T₉₀ yield optimal performance but result in large array weights. Delays larger than T₉₀/B yield suboptimal signal-to-interference-plus-noise ratio when each element has only two weights. For delays between T₉₀/B and 4T₉₀/B , the performance is suboptimal with only two taps but approaches the optimal if more taps are added to each element. Delays larger than T₉₀/B result in suboptimal performance regardless of the number of taps used     

Focused codes for channels with skewed errors

Consider a channel with inputs and outputs in the field F _q(q>2). It is said that the channel is skewed on a set B⊂F_q* if the additive noise generated by the channel is likely to lie in B, i.e. B is a set of common errors. The concern is the construction of focused codes that are appropriate for such channels. It is said that a code is (t₁,t₂)-focused on B if it can correct up to t₁+t₂ errors provided at most t₁ of those errors lie outside of B; the strategy is to offer different levels of protection against common and uncommon errors and so provide novel tradeoffs between performance and rate. Techniques for constructing focused codes and bounds on their rates are described     

Absolute and relative nonlinear optical coefficients of KDP, KD*P,BaB2O4, LiIO3, MgO:LiNbO3,and KTP measured by phase-matched second-harmonic generation

Both absolute and relative nonlinear optical coefficients of six nonlinear materials measured by second-harmonic generation are discussed. A single-mode, injection-seeded, Q-switched Nd:YAG laser with spatially filtered output was used to generate the 1.064-μm fundamental radiation. The following results were obtained: d₃₆(KD*P)=0.38 pm/V, d₃₆(KD*P)=0.37 pm/V, |d₂₂(BaB ₂O₄)|=2.2 pm/V, d₃₁(LiIO₃ )=-4.1 pm/V, d₃₁(5%MgO:MgO LiNbO₃)=-4.7 pm/V, and d_eff(KTP)=3.2 pm/V. The accuracy of these measurements is estimated to be better than 10%     

Expansions for the capacitance of a cross concentric with a squarewith an identity

Two series for the geometrical capacitance C₀ of a coaxial structure which have certain theoretical and practical advantages are given. Not only do the series give the limiting behavior of C₀, they also permit the direct calculation of C₀ with sufficient accuracy for most engineering applications without resorting to elliptic functions     

Phase-difference distribution for a narrow-band non-Gaussian noiseand related statistics

A probability density function _Pm(R₁,R₂,Δ) is presented for a narrowband noise process in which R₁ and R₂ are two envelope samples and Δ is the phase difference. For m=1 the process is Gaussian, but for m=2,3, etc., it is non-Gaussian. New second-order statistical properties are identified for it as well as the density function for the resulting envelope when a signal is added to the noise. These results are given, though the major concern is with the density of the phase difference Δ and the density of &thetas;, the response of an FM detector fed with the noise     

A dispersion formula satisfying recent requirements in microstripCAD

A dispersion formula ϵ^*_eff(f)=ϵ^* -{ϵ^*-ϵ^*_eff(0)}/{1+( f/f₅₀)^m}, for the effective relative permittivity ϵ^*_eff(f) of an open microstrip line is derived for computer-aided design (CAD) use. The 50% dispersion point (the frequency f₅₀ at which ϵ^*_eff(f₅₀)={ϵ ^*+ϵ^*_eff(0)}/2}) is used a normalizing frequency in the proposed formula, and an expression for f₅₀ is derived. To obtain the best fit of ϵ ^*_eff(f) to the theoretical numerical model, the power m of the normalized frequency in the proposed formula is expressed as a function of width-to-height ratio w/ h for w/h⩾0.7 and as a function of w /h, f₅₀, and f for w/h⩽0.7. The present formula has a high degree of accuracy, better than 0.6% in the range 0.1<w/h⩽10, 1<ϵ^*⩽128, and any height-to-wavelength ratio h/λ₀     

On the semiconductor laser logarithmic gain-current densityrelation

The simplified relation, α=G₀ In (η _iJ/J₀), between material gain α and current density J is shown to be a very good shape approximation, for quantum wells and bulk materials, essentially independent of the type of recombination processes present. Simulations show that for a given material system, G₀ decreases by only about 30% from pure electron-hole-recombination-dominated to pure Auger-recombination-dominated. A generic quantum-well situation is explored to reveal the density of states and recombination coefficient dependence of G₀ and to formulate simple estimates for G₀. The results were tested against published data for eight quantum-well diode lasers. The predicted values of G ₀ were generally found to be in agreement with experiments only for the wider gap diodes. The discrepancies were attributed in part to carrier induced absorption, and it is shown that the formalism can be modified in selected cases to incorporate this without changing the basic form of the gain. A new expression which relates the temperature dependence of the measured parameters to the characteristic temperature, T₀, is provided     

Maximum heat-sink temperature for CW operation of adouble-heterostructure semiconductor injection laser

Assuming that the temperature dependence of the threshold current for pulsed operation is known, an analytical expression for the maximum heat-sink temperature, T_hm, for CW operation of the laser can be derived. The maximum heat-sink temperature is expressed in terms of the characteristic temperature T₀, the room-temperature threshold current for pulsed operation I₀ , the equivalent effective thermal resistance &thetas;, and the equivalent effective series electrical resistance r of the device. It is shown that the values of T_hm can be enhanced by increasing the value of T₀ or by decreasing the values of I₀, &thetas;, and r     

Dispersion of bound electron nonlinear refraction in solids

A two-hand model is used to calculate the scaling and spectrum of the nondegenerate nonlinear absorption. From this, the bound electronic nonlinear refractive index n₂ is obtained using a Kramers-Kronig transformation. The authors include the effects of two-photon and Raman transitions and the AC Stark shift (virtual band blocking). The theoretical calculation for n₂ shows excellent agreement with measured values for a five-order-of-magnitude variation in the modulus of n₂ in semiconductors and wide-gap optical solids. Beam distortion methods were used to measure n₂ in semiconductors. The observations result in a comprehensive theory that allows a prediction of n₂ at wavelengths beneath the band edge, given only the bandgap energy and the linear index of refraction. Some consequences for all-optical switching are discussed, and a wavelength criterion for the observation of switching is derived