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     

More on the decoder error probability for Reed-Solomon codes

A combinatorial technique similar to the principle of inclusion and exclusion is used to obtain an exact formula for P_E (u), the decoder error probability for Reed-Solomon codes. The P_E(u) for the (255, 223) Reed-Solomon code used by NASA and for the (31, 15) Reed-Solomon code (JTIDS code) are calculated using the exact formula and are observed to approach the Qs of the codes rapidly as u gets large. An upper bound for the expression |P_E(u)/ Q-1| is derived and shown to decrease nearly exponentially as u increases     

A family of efficient burst-correcting array codes

A family of binary burst correcting array codes that are defined as follows is discussed: consider an n₁×n n₂ array with n₁=4u+ν+2 and n₂=6u+2ν+5, u⩾1, ν⩾0, ν≠1 where each row and column has even parity. The bits are read diagonally starting from the upper-left corner. The columns are viewed cyclically, i.e. the array is a cylinder. If one diagonal has been read out, one proceeds with the second diagonal preceding it. It is proven that the codes of this type can correct any burst of length up to n₁. The burst-correcting efficiency of this family tends to 4/5 as u→∞. As a comparison, the burst-correcting efficiency of other families of array codes tends to 2/3; the same is true for Fire codes. A simple decoding algorithm for the codes is also presented     

Asymptotic performance of M-ary orthogonal modulation ingeneralized fading channels

The asymptotic (M→∞) probability of symbol error P_e,_m for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E_b/N₀) and E_b is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E_b/N₀. These channels exist for all m⩾1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel     

Observation of a large number of new laser lines from12CD3F gas optically pumped with a continuouslytunable high-pressure pulsed CO2 laser

An observation is reported of a large number of new laser lines from ¹²CD₃F gas optically pumped with a continuously tunable high-pressure pulsed CO₂ laser. Making use of the coincidence of the 10 μm P and R branches of CO₂ with the v₃ and v₆ vibrational-rotational absorption bands of ¹²CD₃F, 180 laser lines were found in the wavenumber range between 8 and 55 cm^-1, all of them yet unknown; these lines are studied for characteristic properties of laser action. All laser lines are assigned as pure rotational transitions in the vibrational excited or ground states     

Upper bounds on capacity for a constrained Gaussian channel

A low-pass and a bandpass additive white Gaussian noise channel with a peak-power constraint imposed on otherwise arbitrary input signals are considered. Upper bounds on the capacity of such channels are derived. They are strictly less than the capacity of the channel when the peak-power constrain is removed and replaced by the average-power constraint, for which the Gaussian inputs are optimum. This provides the answer to an often-posed question: peak-power limiting in the case of bandlimited channels does reduce capacity, whereas in infinite bandwidth channels it does not, as is well known. For an ideal low-pass filter of bandwidth B, the upper bound is Blog 0.934P/(N₀B) for P/( N₀B)≫1, where P is the peak power of the input signal and N₀/2 is the double-sided power spectral density of the additive white Gaussian noise     

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     

On universal hypotheses testing via large deviations

A prototype problem in hypotheses testing is discussed. The problem of deciding whether an i.i.d. sequence of random variables has originated from a known source P₁ or an unknown source P₂ is considered. The exponential rate of decrease in type II probability of error under a constraint on the minimal rate of decrease in type I probability of error is chosen for a criterion of optimality. Using large deviations estimates, a decision rule that is based on the relative entropy of the empirical measure with respect to P₁ is proposed. In the case of discrete random variables, this approach yields weaker results than the combinatorial approach used by Hoeffding (1965). However, it enables the analysis to be extended to the general case of Rⁿ-valued random variables. Finally, the results are extended to the case where P₁ is an unknown parameter-dependent distribution that is known to belong to a set of distributions (P⁰₁, &thetas;∈Θ)     

Measurement of the characteristics of the optical-microwavedouble-resonance effect of the 87Rb D1line for application as an atomic frequency standard

The OMDR (optical-microwave double resonance) spectrum of ⁸⁷ Rb with the aim of using a frequency-stabilized GaAs semiconductor laser instead of an Rb lamp as a pumping source in a gas-cell-type Rb frequency standard. Natural isotope ⁸⁷Rb was sealed in a glass cell with buffer gases (Ar/N₂=1.2, total pressure=39 torr). The double resonance signal in the 5P_1/2(F=2)←5S_1/2( F=1) transition appearing at the resonance to the F=2←1 hyperfine transition of the 5S_1/2 state was detected. The optimum operational cell temperature was 56°C. The peak-to-peak frequency width of the atomic hyperfine resonance discriminator used to stabilize the microwave frequency shifts induced by detuning of the laser frequency, changes in the laser and microwave powers, and temperature drift of the cell were investigated     

Dependence of the frequency shift of the optical-microwave doubleresonance signal in the Cs D2 line on the pumpingfrequency and power of a GaAs semiconductor laser

The OMDR (optical-microwave double resonance) effect in the Cs D₂ line was studied for realizing a gas-cell-type Cs atomic frequency standard. A glass cell containing Cs with buffer gases (Ar/N₂=1.26, total pressure=39 torr) was placed in a TE₀₁₂ mode microwave cavity at a temperature of 45°C and was pumped using a GaAs semiconductor laser frequency locked to an external interferometer tuned to the 6P_3/2 (F=2,3,4)←6 S_1/2(F=3) transition. The OMDR signal appearing at the resonance to the F=4←3 hyperfine transition of the 6S_1/2 state shifted with detuning of the laser frequency and with change of the laser and microwave powers. The dependence of the shift on these variables around an optimum operating condition was obtained as, Δν_MW[Hz]=-(0.31±0.02) {1+(0.44±0.15) (ΔP_L/P_L)} Δν_L [MHz]-10(ΔV_MW/V _MW)     

A chemically driven visible laser transition using fastnear-resonant energy transfer

Evidence is obtained which demonstrates the potential for developing purely chemical visible lasers based on rapid near-resonant energy transfer from metastable excited triplet states of germanium and silicon monoxide (a³Σ⁺,b ³Π) to select metal atoms. In this study, the Group IIIA metal atoms were chosen as the energy receptors for the energy transfer-pump sequence. Excited triplet states were generated from the Ge-O₃, Ge-N₂, Si-N₂O, and Si-NO₂ reactions; the bulk of the experimental results was obtained with a germanium-based system. The energy stored in the long-lived triplet states is transferred to pump X²P_1/2 thallium, indium, and gallium atoms to their lowest lying ² S_1/2 states. The authors observe a system of temporal behavior which suggests the creation of a population inversion producing a gain condition and forming the basis for full cavity oscillation on the Tl 7²S_1/2-6P _3/2 transition at 535 nm     

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     

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     

Automatic decision threshold level control in direct-sequencespread-spectrum systems

An algorithm for automatic decision threshold-level control in direct-sequence spread-spectrum systems is presented and analyzed. Using this algorithm, instantaneous setting of the threshold is possible. An additional loop called a threshold loop is used to improve the system performance. This loop is based on a constant false alarm rate (CFAR) criterion. The purpose of the algorithm is to set a decision threshold in the system which will provide a small probability of false alarm (P₃→0) and a large probability of signal detection (P_d→1) at the same time. The analysis has shown that the threshold probability distribution function (PDF) is narrower (equaling better performance) in the case of the CFAR algorithm, but this comes at the cost of a considerably larger integration time for the system (the system time response is slower). As a compromise, the instantaneous algorithm is modified so that k successive samples of the signal are used to determine the value of the threshold. This permits better control of the shape and position of the threshold PDF with respect to the P₃ and P _d curves. At the same time, the time response of the system is good and can be easily controlled     

A maintenance policy for repairable systems based on opportunisticfailure-rate tolerance

An opportunistic hazard rate replacement policy for a repairable system with several types of units is presented. A unit is repaired at failure when the hazard rate falls in (0, L-u). A unit is replaced at failure when the hazard rate falls in (L-u , L). An operating unit is replaced when its hazard rate reaches L. When a unit is replaced because its hazard rate reaches L, all operating units with their hazard rates falling in (L-u, L) are replaced. The long-run mean cost rate as a function of L and u is derived. Optimal L and u are obtained to minimize the total maintenance cost rate. Application and analysis of results are demonstrated through a numerical example. The maintenance model is designed for a system with multitype units. Each type has its own increasing hazard rate. Units are repaired or replaced depending on their hazard rate at a failure or active replacement of another unit. The repair interval, replacement limit, and replacement tolerance are determined to yield the optimal total maintenance cost rate     

Anomalous gain in an isotopically mixed CO2 laser andapplication to absolute wavelength calibration

Measurements are reported on a grating-tuned CO₂ laser, containing an isotopic mixture of ¹⁶O¹²C¹⁶ O, ¹⁶O¹²C¹⁸O, and ¹⁸O ¹²C¹⁸O. The P₆ and R ₁₄ lines of ¹⁶O¹²C¹⁶O were found to have anomalously high intensities. These anomalies are produced by the near coincidence of the transition frequencies in two distinct isotopes, permitting them to act as a single indistinguishable population. These two lines can be used to identify the rotational quantum numbers in the P and R branch spectra, thereby permitting absolute wavelength calibration to be achieved     

Predicted curvature of a glass fiber from the measured curvature ofits coating

An analytical stress model is developed to evaluate the elastic curve of a glass fiber whose coating has a constant (measured or imposed) bend radius. It is shown that in order to predict the bending behavior of a coated glass fiber subjected to bending a parameter u should be computed which depends, in addition to Young's modulus and diameter of the glass fiber itself, also on the length of the curved area and Young's modulus and outer diameter of the (primary) coating. In the range 0<u<2.365, the maximum curvature of the glass fiber occurs at the midpoint of the curved area. If the calculated u value is greater than (7π/4)=5.50, the curvature of the glass fiber in the midportion of the glass-coating composite is practically not different from the coating curvature. Within the range 2.365<u<5.50, the maximum curvature of the glass fiber is greater than the observed curvature of the coating     

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     

A model for fast switching transients in power systems: the nearzone concept

The author presents a simple time-domain model which makes it possible to predict the order of magnitude of the highest di/ dt values generated by closing switches in electrical power systems. The model is based on traveling-wave analysis. It is demonstrated that two different approaches must be applied, according to whether (a) the closing time, T_s, of the switch is faster than twice the traveling time to the first reflection point or (b) T_s is much slower. Under condition (b) the well-known quasistationary approach di/dt_max=U₀/L can be used, where U₀ is the switched voltage and L is the self-inductance of the line between the stray capacitances located to the left and the right of the switching device. Under condition (a) a new formula must be applied: di/dt _max≈2 U₀/ZT_s, where Z is the line impedance of the line in which the switching device is installed and T_s is the time during which the voltage across the switch collapses from U₀ to zero. Experimental results are given from both fast and slow closing switches