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     

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)     

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     

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     

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     

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     

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     

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     

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     

Polarisation independent switch and polarisation splitter employingΔβ and Δκ modulation

The authors report a novel type of polarisation independent directional coupler switch on X-cut, Y-propagating Ti:LiNbO₃, with modest fabrication tolerances. The device can also be used as a polarisation splitter. The principle of operation and experimental results are given     

Ti:LiNbO3 stripe waveguide Bragg reflector gratings

The first demonstration of Bragg reflector grating filters in Ti:LiNbO₃ single-mode channel guides is reported. Filter bandwidths as narrow as 0.14 nm centred at 1.476 μm have been achieved for TE polarisation in Y-cut (X-propagating) material     

A high-performance lateral bipolar transistor fabricated on SIMOX

Double-diffused, lateral n-p-n bipolar transistors were fabricated in a simple CMOS-like process using SIMOX silicon-on-insulator (SOI) substrates. Excellent device characteristics were achieved, with peak h_FE=120, BV_CEO=10 V, and peak f_t=4.5 GHz. The f_t versus BV _CEO trade-off was studied as a function of n ^- collector width. f_t>25 GHz is predicted for this structure with an improved device layout and optimized basewidth. This process may be easily extended in order to fabricate complementary BJTs in a C-BiCMOS thin-film SOI technology     

Simple proof of the concavity of the entropy power with respect toadded Gaussian noise

A very simple proof of M.H. Costa's result (see ibid., vol.IT-31, p.751-60, 1985) that the entropy power of X_t=X +N(O,tI) is concave in t, is derived as an immediate consequence of an inequality concerning Fisher information. This relationship between Fisher information and entropy is found to be useful for proving the central limit theorem. Thus, one who seeks new entropy inequalities should try first to find new equalities about Fisher information, or at least to exploit the existing ones in new ways     

Low-sidelobe weighted-coupled integrated acoustooptic tunablefilter using focused surface acoustic waves

A single-stage low-sidelobe weighted-coupled integrated acoustooptic tunable filter (IAOTF) operating at the optical wavelength of 1.31 μm has been realized on a Y-cut X-propagating LiNbO₃ substrate for the first time. The weighted-coupling, which enabled the achievement of low-sidelobe levels, was facilitated by focused surface acoustic waves generated by a curved interdigital transducer. First sidelobe levels as low as -17.6 dB have been obtained. Optical bandwidth of 4 nm and tuning range of 170 nm for an interaction length of 6 mm were also accomplished     

Effect of hot-electron injection of high-frequency characteristicsof abrupt In0.52(Ga1-xAlx)0.48As/InGaAs HBT's

The effect of hot-electron injection energy (E_i) into the base on the high-frequency characteristics of In_0/52(Ga_1-xAl_x)_0.48 As/InGaAs abrupt heterojunction bipolar transistors (HBTs) is investigated by changing the composition of the emitter. There exists an optimum E_i at which a maximum current gain cutoff frequency (ft) is obtained. Analysis of hot-electron transport in the base and collector by Monte Carlo simulation is carried out to understand the above phenomenon. The collector transit time (τ_c ) increases with E_i, because electrons with higher energy transfer from the Γ valley into the upper L and X valleys. At first, the base transit time (τ_b ) decreases with E_i at the low E_i region. However, τ_b does not decrease monotically with E_i, because of the nonparabolicity in the energy-band structure of InGaAs. Consequently, there exists a minimum in the sum of τ_b and τ_c , in other words a maximum f_t, at an intermediate value of E_i     

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     

Velocity saturation in the collector of Si/GexSi1-x/Si HBT's

The effects of velocity saturation on the unity gain-bandwidth product f_t and transconductance g_m of n-p-n and p-n-p heterojunction bipolar transistors (HBTs) with Ge_xSi_1-x bases are described and simulated. For the n-p-n device, velocity saturation combined with a valence-band offset at the base-collector junction causes accelerated g_m and f_t rolloff for current densities greater than the knee current for the Kirk effect. For the p-n-p device, the g_m and f_t are degraded for all current densities. These limitations combine with the limits imposed by dislocation formation due to strain in the pseudomorphic layer to impose constraints on the design of Si/Ge_x Si_1-x/Si HBTs     

Transistor design for predictable power gain at maximum frequency

Equations which define the neutral base width, collector doping, and epitaxial collector thickness of a bipolar transistor giving a specified unilateral power gain at the highest frequency, possible are derived. Emitter-base capacitance, emitter delay, emitter stripe width, base doping, and the operating base-collector voltage are assumed to be known and fixed. The hybrid-π equivalent circuit is assumed valid up to the transition frequency f_t. Peak f_max (maximum oscillation frequency) is examined as a function of the collector doping. Maximizing f_max at all costs leads to a design with an f_t which approaches zero. In designing a transistor, the two figures of merit must be traded off against each other. A simple expression giving maximum f_max/f_t is derived and used to define the transistor design which gives some specified power gain at the highest possible frequency