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)     

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     

The calculation of the probability of detection and the generalizedMarcum Q-function

A highly reliable, accurate, and efficient method of calculating the probability of detection, P_N(X,Y ), for N incoherently integrated samples, where X is the constant received signal-to-noise ratio of a single pulse and Y is the normalized threshold level, is presented. The useful range of parameters easily exceeds most needs. On a VAX/11 computer with double precision calculations, better than 13-place absolute accuracy is normally achieved. There is a gradual loss of accuracy with increasing parameter values. For example, for N=10⁹, and with both NX and Y near 10⁷, the accuracy can drop to ten places. The function P_N(X,Y ) can be equated to the generalized Marcum Q-function, Q_m(α,β). The corresponding limits on α and β are roughly 4500 for the 13-place accuracy and 60000 for ultimate (INTEGER×4) limit     

Gain measurements on the KrF(B→X), XeF(B→X), and XeF(C→A) lasertransitions in an XeF(C→A) laser gas mixture

Optimum energy extraction from an electron-beam-pumped XeF(C →A) laser is achieved with a five-component rare gas halide mixture. The characterization and modeling of laser action in such a gas mixture requires a knowledge of small-signal gain and absorption coefficients not only on the blue-green XeF(C→ A) transition, but also in the ultraviolet (UV) region for the competing XeF(B→X) and KrF(B→X ) transitions. The authors report gain measurements on the XeF(C→A) transition and small-signal gain and absorption coefficients at or near both the XeF(B→X ) (351 and 353 nm) and KrF(B→X) (248 nm) transitions. A study of the gain for the UV and visible transitions as a function of Kr and Xe partial pressure is reported, and its impact on the XeF(C→A) kinetics is discussed     

Bias in a stress-strength problem

The bias of the maximum likelihood estimator for R≠Pr{ X<Y} where X and Y are independent normal random variables with unknown parameters is discussed. The bias is an odd function with respect to δ=gauf^-1 (R), where gauf(·) is the Cdf of the standard normal distribution, so the study is restricted to R ⩾0.5, or equivalently, δ⩾0. There exists δ₀>0 such that the bias is positive in the interval 0<δ<δ₀. R has a positive bias at least in the interval 0.84<R<0.94     

Lower bounds for q-ary covering codes

The authors prove combinatorial lower bounds for K_q (n,R), the minimal cardinality of any q-ary code of length n and covering radius R. Tables of lower bounds for K_q(n,R) are presented for q=3, 4, 5     

Robustness of mean E{X} and R charts

The effect of nonnormality on E{X} and R charts is reported. The effect of departure from normality can be examined by comparing the probabilities that E{X} and R lie outside their three-standard-deviation and two-standard-deviation control limits. Tukey's λ-family of symmetric distributions is used because it contains a wide spectrum of distributions with a variety of tail areas. The constants required to construct E{X} and R charts for the λ-family are computed. Control charts based on the assumption of normality give inaccurate results when the tails of the underlying distribution are thin or thick. The validity of the normality assumption is examined by using a numerical example     

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     

A proposed chemically pumped laser based on theb→X transition in O2

Simple kinetics calculations demonstrate that the well-known electronic energy pooling reaction involving O₂(a ¹Δ) is capable of producing an effective population inversion in O₂(b¹Σ). The densities of O₂(a¹Δ) which are potentially achievable suggest that the extractable energy storage density of an O ₂(b→X) chemical laser might exceed 0.5 MJ/m³. The b→X emission lifetime measurements conducted under conditions of high relative O₂( b¹Σ) density reveal no evidence of rapid self-quenching effects which would be potentially detrimental to laser performance. The relatively long energy storage times predicted, together with freedom from reagent mixing requirements, make such a laser an attractive alternative to other existing and proposed short wavelength chemical lasers     

The (d,k) subcode of a linear block code

A simple technique employing linear block codes to construct (d,k) error-correcting block codes is considered. This scheme allows asymptotically reliable transmission at rate R over a BSC channel with capacity C_BSC provided R ⩽C_d,k-(1+C_BSC), where C_d,k is the maximum entropy of a (d,k ) source. For the same error-correcting capability, the loss in code rate incurred by a multiple-error correcting (d,k) code resulting from this scheme is no greater than that incurred by the parent linear block code. The single-error correcting code is asymptotically optimal. A modification allows the correction of single bit-shaft errors as well. Decoding can be accomplished using off-the-shelf decoders. A systematic (but suboptimal) encoding scheme and detailed case studies are provided     

Convergence of filters with applications to the Kalman-Bucy case

For each N, and each fixed time T, a signal X^N and a `noisy' observation Y^N are defined by a pair of stochastic difference equations. Under certain conditions (X^N, Y^N) converges in distribution to (X, Y, where dX(t)= f(t, X(t))dt+dV( t), dY(t)=g(t, X( t))dt+dW(t). Conditions are found under which convergence in distribution of the conditional expectations E{F(X^N)|Y^N} to E{F(X)|Y} follows, for every bounded continuous function F. The case in which the conditional expectations still converge but the limit is not E{ F(X)|Y} is also studied. In the situation where f and g are linear functions of X, an examination of this limit leads to a Kalman-Bucy-type estimate of X ^N which is asymptotically optimal and is an improvement on the usual Kalman-Bucy estimate     

Chemically produced XeF(B) electronic excited state

Ultraviolet (UV) emission has been observed in the reactions of XeF₂+F₂+SiH₄ and XeF₂+F₂+F+B₂H₆. The emission spectra have been identified with the B²Σ→X²Σ transition of XeF. The emission intensity has also been examined as functions of the XeF₂, F₂, SiH₄, and Ar concentrations. Possible mechanisms of XeF(B) production are discussed     

Worst-case interactive communication. I. Two messages are almostoptimal

The reduction in communication achievable by interaction is investigated. The model assumes two communicators: an informant having a random variable X, and a recipient having a possibly dependent random variable Y. Both communicators want the recipient to learn X with no probability of error, whereas the informant may or may not learn Y. To that end, they alternate in transmitting messages comprising finite sequences of bits. Messages are transmitted over an error-free channel and are determined by an agreed-upon, deterministic protocol for (X,Y) (i.e. a protocol for transmitting X to a person who knows Y). A two-message protocol is described, and its worst case performance is investigated     

Multiterminal source encoding with one distortion criterion

The authors unify earlier investigations concerning the encoding of two correlated sources {X_k}, {Y_k } by means of separate encoders. Decoding is done by a single decoder which receives the outputs from both encoders. The reconstruction of {X_k} is required to be perfect in the usual Shannon sense. The authors determine the admissible rate region R (D), where D is the distortion of the reconstruction of {Y_k}. The binary Hamming case is investigated explicitly     

Characterization of inverse-Gaussian and gamma distributionsthrough their length-biased distributions

For the case where Y is a length-biased random variable corresponding to a random variable X having an inverse-Gaussian or gamma distribution, it is shown that Y can be written as a linear combination of X and a chi-square random variable and, conversely, X can be characterized through this relationship. Finally, the Wald distribution is characterized     

Correlation between 1/f noise and hFElong-term instability in silicon bipolar devices

Accelerated life tests with high-temperature storage and electric aging for n⁺-p-n silicon planar transistors were carried out. Current gain h_FE increases monotonously with time during the tests, and the h_FE drift is correlated with initial measured 1/f noise in the transistors, i.e. the drift amount significantly increases with the increase of noise level. The correlation coefficient of relative drift Δh_FE /h_FE and 1/f noise spectral density S_iB(f) is far larger than that of Δ h_FE/h_FE and initial DC parameters of the transistors. A quantitative theory model for the h _FE drift has been developed and explains the h _FE drift behavior in the tests, which suggests that the h _FE drift and 1/f noise can be attributed to the same physical origin, and both are caused by the modulation of the oxide traps near the Si-SiO₂ interface to Si surface recombination. 1/f noise measurement, therefore, may be used as a fast and nondestructive means to predict the long-term instability in bipolar transistors     

Light-to-input nonlinearities in an R-LED series network

The light-to-current (L-I) and light-to-voltage (L-V) differential nonlinearities in the simple network of a customary LED and an external resistor R in series are analyzed and calculated theoretically and compared with experimental data. Particular emphasis is placed on the influence of the log-arithmetic slope ν of the L-I characteristic and the bias current I upon the ratio of the corresponding nonlinearity parameters. It is thus deduced that, for a given optical power P, over superlinear portions of the L-I curve (ν>1) the L-I linearity is typically better than its corresponding L-V linearity. On the contrary, when the L-I dependence is sublinear (ν<1) the voltage driving scheme may ensure for the R-LED network, or the LED alone, a local L-V response much more linear than the L-I response, provided that appropriate (optimum) I and/or R values are chosen     

Stripline resonator measurements of Zs versus Hrf in YBa2Cu3O7-x thin films

A report is presented on measurements of the surface impedance, Z_S, of YBa₂Cu₃O_7-x thin films using a stripline resonator. The films were deposited on LaAlO₃ substrates by off-axis magnetron sputtering. The authors obtained Z_S as a function of frequency from 1.5 to 20 GHz, as a function of temperature from 4 K to the transition temperature (~90 K), and as a function of the RF magnetic field from zero to 300 Oe. At low temperatures the surface resistance, R _S, of the films shows a very weak dependence on the magnetic field up to 225 to 250 Oe. At 77 K, R_S is proportional to the square of the field. The penetration depth shows a much weaker dependence on the field than does R_S. The origins of the magnetic field dependence of Z_S are also discussed     

Power-efficient layout of a fiber-optic multistar that permits log2 N concurrent baseband transmissions among N stations

A passive, single-hop, fiber-optic interconnection among N stations, each with two transmitters and one receiver, and a round-robin transmission schedule for it, which jointly permit log ₂ N concurrent noninterfering transmissions on a single wavelength, has recently been described. This is a substantial improvement over the previously known limit of two concurrent transmissions, but the layout of this interconnection poses a challenge in terms of both wiring complexity and path loss. A power-efficient implementation of this interconnection using several stages of balanced fiber-optic star couplers is presented here. With lossless components, path loss is N, the same as that of a single-star interconnection that permits only a single transmission at a time. Consequently, the high degree of parallelism translates into higher capacity. The required number of (2×2) star couplers is also very similar to that required for implementing a single N×X star