Achievable key rates for universal simulation of random data with respect to a set of statistical tests

We consider the problem of universal simulation of an unknown source from a certain parametric family of discrete memoryless sources, given a training vector X from that source and given a limited budget of purely random key bits. The goal is to generate a sequence of random vectors {Y/sub i/}, all of the same dimension and the same probability law as the given training vector X, such that a certain, prescribed set of M statistical tests will be satisfied. In particular, for each statistical test, it is required that for a certain event, /spl epsiv//sub /spl lscr//, 1 /spl les/ /spl lscr/ /spl les/ M, the relative frequency /sup 1///sub N/ /spl Sigma//sub i=1//sup N/ 1/sub /spl epsiv//spl lscr//(Y/sub i/) (1/sub /spl epsiv//(/spl middot/) being the indicator function of an event /spl epsiv/), would converge, as N /spl rarr/ /spl infin/, to a random variable (depending on X), that is typically as close as possible to the expectation of 1/sub /spl epsiv//spl lscr/,/ (X) with respect to the true unknown source, namely, to the probability of the event /spl epsiv//sub /spl lscr//. We characterize the minimum key rate needed for this purpose and demonstrate how this minimum can be approached in principle.     

Time-frequency localisation of Shannon wavelet packets

It is well known that the 2/spl pi/ minimally supported frequency scaling function /spl phi//sup /spl alpha//(x) satisfying /spl phi//spl circ//sup /spl alpha//(/spl omega/)=/spl chi//sub (-/spl alpha/,2/spl pi/-/spl alpha/)/(/spl omega/), 0相似文献   

Microwave Characterization of Partially Magnetized Ferrites

In order to assist the microwave engineer in predicting the performance of partially magnetized devices, we have characterized the microwave permeability of partially magnetized materials. The real part of the tensor permeability elements, /spl mu/, /spl kappa/, and /spl mu//sub z/, depends primarily on the parameters /spl gamma/4/spl pi/M//spl omega/ and /spl gamma/4/spl pi/M/sub s/ / /spl omega/. Empirical formulas have been developed which show the dependence. At frequencies sufficiently below /spl omega/ = /spl pi/4/spl pi/M/sub s/, the loss can be characterized by the value of /spl mu/' at 4/spl pi/M = 0./spl mu/, /spl kappa/, and /spl mu//sub z/ depend weakly on composition, whereas /spl mu/' (4/spl pi/M = 0) does depend upon the chemical composition.     

A Catalog of Low Power Loss Parameters and High Power Thresholds for Partially Magnetized Ferrites

The low power loss and high power threshold properties have been measured on a number of candidate ferrite phase-shifting materials. The low power loss is characterized by /spl mu//sub 0/', the imaginary part of the diagonal component of the permeability tensor for the completely demagnetized state. /spl mu/sub 0/' was measured from 3.0 to 16.8 GHz. The high power properties are characterized by the parallel pump threshold at a bias field correspontig to H/sub i/ /spl equiv/ 0 and to 4/spl pi/M /spl equiv/ 4/spl pi/M/sub s/. The threshold was measured between 3.0 and 16.8 GHz. For the purposes of computer calculation /spl mu//sub 0/' and h/sub crit/ were fit to an equation of the form A (/spl gamma/4/spl pi/M/sub s/ / /spl omega/)/sup N/. Translating /spl mu//sub 0/' and h/sub crit/ to /spl Delta/H/sub eff/ and /spl Delta/H/sub k/ gives the YIG plus Al as the lowest loss and lowest threshold materials followed by the Gd garnets and MgMn spinels. The Ni spinels are very Iossy.     

Guided Waves in Inhomogeneous Focusing Media Part III: Wall Effects, Losses, and the Transition from Fast to Slow Waves

This paper is concerned with the determination of field patterns, propagation constants, and losses for axially propagating modes guided by an enclosed circular cylindrical, radially inhomogeneous dielectric of the type discussed in Parts I and II. The homogeneous outer medium (/spl gamma/ /spl ges/ /a) is assumed to have a large relative permittivity /spl epsiv//sub 2/, and the analysis includes the perfect conductor case /spl epsiv//sub 2/ /spl rarr/ /spl infin/. The transition to trapped waves as the binding effect increases is demonstrated. Propagation constants in the case with loss are determined using a perturbation technique.     

Compression mappings on primitive sequences over Z/(p/sup e/)

Let Z/(p/sup e/) be the integer residue ring with odd prime p/spl ges/5 and integer e/spl ges/2. For a sequence a_ over Z/(p/sup e/), there is a unique p-adic expansion a_=a_/sub 0/+a_/spl middot/p+...+a_/sub e-1//spl middot/p/sup e-1/, where each a_/sub i/ is a sequence over {0,1,...,p-1}, and can be regarded as a sequence over the finite field GF(p) naturally. Let f(x) be a primitive polynomial over Z/(p/sup e/), and G'(f(x),p/sup e/) the set of all primitive sequences generated by f(x) over Z/(p/sup e/). Set /spl phi//sub e-1/ (x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,1/(x/sub 0/, x/sub 1/,...,x/sub e-2/) /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,2/(x/sub 0/,x/sub 1/,...,x/sub e-2/) where /spl eta//sub e-2,1/ and /spl eta//sub e-2,2/ are arbitrary functions of e-1 variables over GF(p) and 2/spl les/k/spl les/p-1. Then the compression mapping /spl phi//sub e-1/:{G'(f(x),p/sup e/) /spl rarr/ GF(p)/sup /spl infin// a_ /spl rarr/ /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) is injective, that is, a_ = b_ if and only if /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl phi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/). Furthermore, if f(x) is a strongly primitive polynomial over Z/(p/sup e/), then /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl psi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) if and only if a_ = b_ and /spl phi//sub e-1/(x/sub 0/,...,x/sub e-1/) = /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/).     

Temperature dependence of permittivity and loss tangent of lithium tantalate at microwave frequencies

Lithium tantalate (LiTaO/sub 3/) exhibits excellent electro-optical, piezoelectric, and pyroelectric properties and a very low thermal expansion. In this paper, we report measurements of loss tangent and the real part of the relative permittivity /spl epsiv//sub r/spl perp// measured in c-axis LiTaO/sub 3/ crystals in the temperature range from 14 K to 295 K at a frequency of 11.4 and 10 GHz. Microwave properties of LiTaO/sub 3/ were determined by measurements of the resonance frequency and the unloaded Q/sub o/ factor of a TE/sub 011/ mode cylindrical cavity containing the sample under test and accounting for uncalibrated cables and adaptors inside the cryocooler. The permittivity of LiTaO/sub 3/ was found to increase from 38.9 to 41.1 and the loss tangent to change from 1.1/spl times/10/sup -4/ to 6.5/spl times/10/sup -4/ over the full temperature range. Due to its low loss and relatively high permittivity, LiTaO/sub 3/ is suitable for microwave applications.     

On the Theory and Application of the Dielectric Post Resonator (Short Papers)

This short paper deals with the modes of the dielectric post resonator when epsilon/sub r/ is large. The normalized frequency F/sub 0/ = (pi D/lambda/sub 0/) /spl radic/ as a function of D/L is discussed. The simple approximate expressions for the resonant frequencies of the lower order modes are given. The properties of the TE/sub 011/, mode are discussed in detail from the point of view of its application to the measurement of the complex permittivity of microwave dielectrics. Curves and expressions for fast and simple determination of the maximum measurement errors are given.     

Asymptotic properties on codeword lengths of an optimal FV code for general sources

This correspondence is concerned with asymptotic properties on the codeword length of a fixed-to-variable length code (FV code) for a general source {X/sup n/}/sub n=1//sup /spl infin// with a finite or countably infinite alphabet. Suppose that for each n /spl ges/ 1 X/sup n/ is encoded to a binary codeword /spl phi//sub n/(X/sup n/) of length l(/spl phi//sub n/(X/sup n/)). Letting /spl epsiv//sub n/ denote the decoding error probability, we consider the following two criteria on FV codes: i) /spl epsiv//sub n/ = 0 for all n /spl ges/ 1 and ii) lim sup/sub n/spl rarr//spl infin///spl epsiv//sub n/ /spl les/ /spl epsiv/ for an arbitrarily given /spl epsiv/ /spl isin/ [0,1). Under criterion i), we show that, if X/sup n/ is encoded by an arbitrary prefix-free FV code asymptotically achieving the entropy, 1/nl(/spl phi//sub n/(X/sup n/)) - 1/nlog/sub 2/ 1/PX/sup n/(X/sup n/) /spl rarr/ 0 in probability as n /spl rarr/ /spl infin/ under a certain condition, where P/sub X//sup n/ denotes the probability distribution of X/sup n/. Under criterion ii), we first determine the minimum rate achieved by FV codes. Next, we show that 1/nl(/spl phi//sub n/(X/sup n/)) of an arbitrary FV code achieving the minimum rate in a certain sense has a property similar to the lossless case.     

Theory of Direct-Coupled-Cavity Filters

A new theory is presented for the design of direct-coupled-cavity filters in transmission line or waveguide. It is shown that for a specified range of parameters the insertion-loss characteristic of these filters in the case of Chebyshev equal-ripple characteristic is given very accurately by the formula P/sub 0/ / /P/sub L/ = 1+h/sup 2/T/sub n//sup 2/[/spl omega//sub 0/ / /spl omega/ sin(/spl pi/ /spl omega/ / /spl omega//sub 0/) / sin/spl theta//sub 0/'] where h defines the ripple level, T/sub n/ is the first-kind Chebyshev polynomial of degree n, /spl omega/ / /spl omega//sub 0/ is normalized frequency, and /spl theta//sub 0/' is an angle proportional to the bandwidth of a distributed lowpass prototype filter. The element values of the direct-coupled filter are related directly to the step impedances of the prototype whose values have been tabulated. The theory gives close agreement with computed data over a range of parameters as specified by a very simple formula. The design technique is convenient for practical applications.     

On the scaling limit of ultrathin SOI MOSFETs

In this paper, a detailed study on the scaling limit of ultrathin silicon-on-insulator (SOI) MOSFETs is presented. Due to the penetration of lateral source/drain fields into standard thick buried oxide, the scale-length theory does not apply to thin SOI MOSFETs. An extensive two-dimensional device simulation shows that for a thin gate insulator, the minimum channel length can be expressed as L/sub min//spl ap/4.5(t/sub Si/+(/spl epsiv//sub Si///spl epsiv//sub I/)t/sub I/), where t/sub Si/ is the silicon thickness, and /spl epsiv//sub I/ and t/sub I/ are the permittivity and thickness of the gate insulator. With t/sub Si/ limited to /spl ges/ 2 nm from quantum mechanical and threshold considerations, a scaling limit of L/sub min/=20 nm is projected for oxides, and L/sub min/=10 nm for high-/spl kappa/ dielectrics. The effect of body doping has also been investigated. It has no significant effect on the scaling limit.     

On the /spl theta/-coverage and connectivity of large random networks

Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed, the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for /spl theta/-coverage is found for wireless networks modeled as n points uniformly distributed in a unit square, with every node connecting to its /spl phi//sub n/ nearest neighbors. A network is called /spl theta/-covered if every node, except those near the boundary, can find one of its /spl phi//sub n/ nearest neighbors in any sector of angle /spl theta/. For all /spl theta//spl isin/(0,2/spl pi/), if /spl phi//sub n/=(1+/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, it is shown that the probability of /spl theta/-coverage goes to one as n goes to infinity, for any /spl delta/>0; on the other hand, if /spl phi//sub n/=(1-/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, the probability of /spl theta/-coverage goes to zero. This sharp characterization of /spl theta/-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if /spl phi//sub n/=(1+/spl delta/)log/sub 2/n. Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed.     

Analysis and Evaluation of a Method of Measuring the Complex Permittivity and Permeability Microwave Insulators

Theory and experimental results are presented to show the possibility of using a resonant post technique for characterizing dielectric and magnetic materials at microwave frequencies. Results of the temperature dependence of the relative dielectric constant of nonmagnetic materials with /spl epsilon//sub r/, varying from 4 to 60 are presented and also loss tangent measurements at room temperature. The complex permittivity and permeability of a number of garnet materials has also been measured with 4/spl pi//spl gamma/M/sub s/ / /spl omega/ varying from 0.25 to 0.8. The measured real part of the permeability is in good agreement with the theoretical predictions of Schlomann and the imaginary part of the permeability agrees with measurements by Green et al. on similar materials.     

A highly threshold Voltage-controllable 4T FinFET with an 8.5-nm-thick Si-fin channel

Highly threshold voltage (V/sub th/)-controllable four-terminal (4T) FinFETs with an aggressively thinned Si-fin thickness down to 8.5-nm have successfully been fabricated by using an orientation-dependent wet-etching technique, and the V/sub th/ controllability by gate biasing has systematically been confirmed. The V/sub th/ shift rate (/spl gamma/=-/spl delta/V/sub th///spl delta/V/sub g2/) dramatically increases with reducing Si-fin thickness (T/sub Si/), and the extremely high /spl gamma/=0.79 V/V is obtained at the static control gate bias mode for the 8.5-nm-thick Si-fin channel device with the 1.7-nm-thick gate oxide. By the synchronized control gate driving mode, /spl gamma/=0.46 V/V and almost ideal S-slope are achieved for the same device. These experimental results indicate that the optimum V/sub th/ tuning for the high performance and low-power consumption very large-scale integrations can be realized by a small gate bias voltage in the ultrathin Si-fin channel device and the orientation-dependent wet etching is the promising fabrication technique for the 4T FinFETs.     

Mode Propagation in a Nonuniform Cylindrical Medium (Correspondence)

A simplified form of the coupling coefficient C(/spl beta//sub p/, /spl beta//sub q/) resulting from a coupled mode theory analysis of wave propagation in a nonuniform medium is derived. It is found for most situations of interest that C(/spl beta//sub p/, /spl beta//sub q/) is proportional to 1/(/spl beta//sub p/-/spl beta//sub q/) and the power transfer between two modes is proportional to 1/(/spl beta//sub p/ - /spl beta//sub q/)/sup 4/. /spl beta//sub p/ and /spl beta//sub q/ are the two different modal propagation constants. For a dielectric rod C(/spl beta//sub p/, /spl beta//sub q/) is a simple line integral around the rod boundary. Approximate forms are presented for optical waveguides.     

List decoding from erasures: bounds and code constructions

We consider the problem of list decoding from erasures. We establish lower and upper bounds on the rate of a (binary linear) code that can be list decoded with list size L when up to a fraction p of its symbols are adversarially erased. Such bounds already exist in the literature, albeit under the label of generalized Hamming weights, and we make their connection to list decoding from erasures explicit. Our bounds show that in the limit of large L, the rate of such a code approaches the "capacity" (1 - p) of the erasure channel. Such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good binary linear codes of rate /spl Omega/(/spl epsiv//sup 2//log(1//spl epsiv/)) that can be efficiently list-decoded using lists of size O(1//spl epsiv/) when an adversarially chosen (1 - /spl epsiv/) fraction of symbols are erased, for arbitrary /spl epsiv/ > 0. This improves previous results in this vein, which achieved a rate of /spl Omega/(/spl epsiv//sup 3/log(1//spl epsiv/)).     

Measurements of effective dielectric permittivity of microstrip-line-type liquid crystal devices using inductive coupled ring resonator

The effective dielectric permittivity of microstrip-line-type liquid crystal devices was determined in the 3-33 GHz frequency range by using a newly developed inductive coupled ring resonator. The frequency performance of /spl epsiv/'/sub /spl par// and /spl epsiv/'/sub /spl perp// can be obtained from the measured and simulated resonant frequencies of an inductive coupled ring resonator with or without a DC electric field E/sub 0/.     

Prime-length real-valued polynomial residue division algorithms

One class of efficient algorithms for computing a discrete Fourier transform (DFT) is based on a recursive polynomial factorization of the polynomial 1-z/sup -N/. The Bruun algorithm is a typical example of such algorithms. Previously, the Bruun algorithm, which is applicable only when system lengths are powers of two in its original form, is generalized and modified to be applicable to the case when the length is other than a power of two. This generalized algorithm consists of transforms T/sub d,f/ with prime d and real f in the range 0/spl les/f<0.5. T/sub d,0/ computes residues X(z)mod(1-z/sup -2/) and X(z)mod(1-2 cos(/spl pi/k/d)z/sup -1/+z/sup -2/), k=1, 2, ..., d-1, and T/sub d,f/ (f /spl ne/0) computes residues X(z)mod(1-2cos(2/spl pi/(f+k)/d)z/sup -1/+z/sup -2/), k=0, 1, ..., d-1 for a given real signal X(z) of length 2d. The purpose of this paper is to find efficient algorithms for T/sub d,f/. First, polynomial factorization algorithms are derived for T/sub d,0/ and T/sub d,1/4/. When f is neither 0 nor 1/4, it is not feasible to derive a polynomial factorization algorithm. Two different implementations of T/sub d,f/ for such f are derived. One implementation realizes T/sub d,f/ via a d-point DFT, for which a variety of fast algorithms exist. The other implementation realizes T/sub d,f/ via T/sub d, 1/4/, for which the polynomial factorization algorithm exists. Comparisons show that for d/spl ges/5, these implementations achieve better performance than computing each output of T/sub d,f/ separately.     

High-speed silicon electrooptic Modulator design

An electrically driven Mach-Zehnder waveguide modulator based on high-index contrast silicon split-ridge waveguide technology and electronic carrier injection is proposed. The excellent optical and carrier confinement possible in high-index contrast waveguide devices, together with good thermal heat sinking and forward biased operation, enables high-speed modulation with small signal modulation bandwidths beyond 20 GHz, a V/sub /spl pi// times length figure of merit of V/sub /spl pi//L=0.5 V/spl middot/cm and an insertion loss of about 4 dB. The modulator can be fabricated in a complementary metal-oxide-semiconductor compatible way.     

Loss characteristics of high-/spl epsiv//sub r/ microstrip lines fabricated by an etchable thick-film on ceramic MCM technology

Etchable thick-film multi-chip-module (MCM) technology has led to the possibility of fabricating microwave integrated circuits (MICs) with performance similar to MICs produced using more expensive conventional thin-film MCM-D techniques. However, little data is available on the loss characteristics of the technology at microwave frequencies. This paper describes an experimental investigation into the loss properties of high-definition etchable thick-film MCM microstrip lines formed on a variety of high dielectric constant (high-/spl epsiv//sub r/) ceramic substrates. Substrates investigated comprise 96% alumina (/spl epsiv//sub r/=9.5), (Zr,Sn)TiO/sub 4/(/spl epsiv//sub r/=36.6) and BaO-PbO-Nd/sub 2/O/sub 3/-TiO/sub 2/ (/spl epsiv//sub r/=90.9). Microstrip loss properties are determined by fabricating a series of loosely coupled half-wave resonators on each substrate, with a range of characteristic impedance values. Measurements to 6 GHz are compared to those for similar lines fabricated using conventional thin-film MCM-D technology. The results demonstrate that etchable thick-film MCM technology provides many of the advantages of thin-film MCM-D technology, such as low-loss and high-definition conductors, and is suitable for the cost-effective fabrication of miniaturised high-performance microstrip MICs in high volume.