Showing papers by "Bell Labs published in 1973"

Noiseless coding of correlated information sources

Abstract: Correlated information sequences \cdots ,X_{-1},X_0,X_1, \cdots and \cdots,Y_{-1},Y_0,Y_1, \cdots are generated by repeated independent drawings of a pair of discrete random variables X, Y from a given bivariate distribution P_{XY} (x,y) . We determine the minimum number of bits per character R_X and R_Y needed to encode these sequences so that they can be faithfully reproduced under a variety of assumptions regarding the encoders and decoders. The results, some of which are not at all obvious, are presented as an admissible rate region \mathcal{R} in the R_X - R_Y plane. They generalize a similar and well-known result for a single information sequence, namely R_X \geq H (X) for faithful reproduction.

An Effective Heuristic Algorithm for the Traveling-Salesman Problem

Abstract: This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem. The procedure is based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems. The procedure produces optimum solutions for all problems tested, "classical" problems appearing in the literature, as well as randomly generated test problems, up to 110 cities. Run times grow approximately as n2; in absolute terms, a typical 100-city problem requires less than 25 seconds for one case GE635, and about three minutes to obtain the optimum with above 95 per cent confidence.

Steady-State Motion of Magnetic Domains

Abstract: This paper introduces two integrals which simplify calculation of the dynamic properties of magnetic domains. These integrals, over quadratic functions of the spatial derivatives of the magnetization, yield forces acting on a domain which correspond to the gyroscopic and dissipative terms in the Gilbert equation. The force integral corresponging to the gyroscopic term is found to be even less sensitive to the details of the spin distribution than the dissipative drag integral. Hard magnetic bubble domains are considered as an illustrative example.

A computer program for designing optimum FIR linear phase digital filters

Abstract: This paper presents a general-purpose computer program which is capable of designing a large Class of optimum (in the minimax sense) FIR linear phase digital filters. The program has options for designing such standard filters as low-pass, high-pass, bandpass, and bandstop filters, as well as multipassband-stopband filters, differentiators, and Hilbert transformers. The program can also be used to design filters which approximate arbitrary frequency specifications which are provided by the user. The program is written in Fortran, and is carefully documented both by comments and by detailed flowcharts. The filter design algorithm is shown to be exceedingly efficient, e.g., it is capable of designing a filter with a 100-point impulse response in about 20 s.

Band Structures of Transition-Metal-Dichalcogenide Layer Compounds.

Abstract: The nonrelativistic augmented-plane-wave (APW) method is applied to calculate the electronic band structures of several transition-metal-dichalcogenide ($T{X}_{2}$) layer compounds, including materials with the $C6(1T\ensuremath{-}\mathrm{Hf}{\mathrm{S}}_{2},1T\ensuremath{-}\mathrm{Ta}{\mathrm{S}}_{2})$, $C27(2H\ensuremath{-}\mathrm{Ta}{\mathrm{S}}_{2},2H\ensuremath{-}\mathrm{Nb}{\mathrm{Se}}_{2})$, and $C7(2H\ensuremath{-}\mathrm{Mo}{\mathrm{S}}_{2})$ structure types These calculations involve crystal potentials that are derived from neutral-atom charge densities The results of these calculations confirm that the group-$\mathrm{IV}B$ ($1T\ensuremath{-}\mathrm{Hf}{\mathrm{S}}_{2}$) and group-$\mathrm{VI}B$ ($2H\ensuremath{-}\mathrm{Mo}{\mathrm{S}}_{2}$) compounds are semiconductors; the calculated indirect band gaps of 27 and 12 eV are in reasonable agreement with the observed values of 20 and 14 eV, respectively Metallic behavior is predicted for the intermediate group-$\mathrm{V}B$ compounds $1T\ensuremath{-}\mathrm{Ta}{\mathrm{S}}_{2}$, $2H\ensuremath{-}\mathrm{Ta}{\mathrm{S}}_{2}$, and $2H\ensuremath{-}\mathrm{Nb}{\mathrm{Se}}_{2}$ A novel feature of the metal $d$ bands in the $2H\ensuremath{-}T{X}_{2}$ compounds is the occurence of a 1-eV hybridization gap within the ${d}_{{z}^{2}}$ and ${d}_{xy}$, ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ manifolds This splits off a pair of hybridized $d$ bands which are half-filled in $2H\ensuremath{-}\mathrm{Ta}{\mathrm{S}}_{2}$ and $2H\ensuremath{-}\mathrm{Nb}{\mathrm{Se}}_{2}$ and completely filled in $2H\ensuremath{-}\mathrm{Mo}{\mathrm{S}}_{2}$ As a result of this hybridization gap, the valence or conduction bandwidths in each of these $2H\ensuremath{-}T{X}_{2}$ compounds are reduced to about 1 eV

Stochastic Transport in a Disordered Solid. I. Theory

Abstract: A general theory of stochastic transport in disordered systems has been developed. The theory is based on a generalization of the Montroll-Weiss continuous-time random walk (CTRW) on a lattice. Starting from a general mobility formalism, specialized $\stackrel{\mathrm{\ifmmode\acute\else\textasciiacute\fi{}}}{\mathrm{t}}$o hopping conduction, an exact expression for the conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ for the CTRW process is derived. The frequency dependence of $\ensuremath{\sigma}(\ensuremath{\omega})$ is determined by the Fourier transform of the zeroth and second spatial moments of the function $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}},t)$, which is equal to the probability per unit time that the displacement and time between hops is $\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$, $t$. The conductivity corresponding to characteristically different types of hopping distributions is discussed, as well as the basic approximation in adopting a CTRW on a lattice to transport in disordered solids.

A Two's Complement Parallel Array Multiplication Algorithm

Abstract: An algorithm for high-speed, two's complement, m-bit by n-bit parallel array multiplication is described. The two's complement multiplication is converted to an equivalent parallel array addition problem in which each partial product bit is the AND of a multiplier bit and a multiplicand bit, and the signs of all the partial product bits are positive.

Injection locking of microwave solid-state oscillators

Abstract: Injection locking of microwave solid-state oscillators is discussed, based on the familiar theorem that the total impedance times the current is equal to the applied voltage. Both quasi-static and dynamic analyses of the locking range, large-signal injection, locking stability, and AM and FM noise are given, and recent experimental work is reviewed briefly. No applications of injection locking are discussed in detail.

A digital signal processing approach to interpolation

Abstract: In many digital signal precessing systems, e.g., vacoders, modulation systems, and digital waveform coding systems, it is necessary to alter the sampling rate of a digital signal Thus it is of considerable interest to examine the problem of interpolation of bandlimited signals from the viewpoint of digital signal processing. A frequency dmnain interpretation of the interpolation process, through which it is clear that interpolation is fundamentally a linear filtering process, is presented, An examination of the relative merits of finite duration impulse response (FIR) and infinite duration impulse response (IIR) digital filters as interpolation filters indicates that FIR filters are generally to be preferred for interpolation. It is shown that linear interpolation and classical polynomial interpolation correspond to the use of the FIR interpolation filter. The use of classical interpolation methods in signal processing applications is illustrated by a discussion of FIR interpolation filters derived from the Lagrange interpolation formula. The limitations of these filters lead us to a consideration of optimum FIR filters for interpolation that can be designed using linear programming techniques. Examples are presented to illustrate the significant improvements that are obtained using the optimum filters.

Mean-Value Point in the Brillouin Zone

Abstract: A new special point in the Brillouin zone is introduced. It is defined as the point such that the value which any given periodic function of wave vector assumes at this point is an excellent approximation to the average value of the same function throughout the Brillouin zone. This special point is termed the "mean-value point," and is dictated by the crystal symmetry. The coordinates of the mean-value point for cubic lattices are explicitly given.

Structure in aqueous solutions of nonpolar solutes from the standpoint of scaled-particle theory

Abstract: Underlying assumptions have been examined in scaled-particle theory for the case of a rigid-sphere solute in liquid water. As a result, it has been possible to improve upon Pierotti’s corresponding analysis in a way that explicitly incorporates measured surface tensions and radial-distribution functions for pure water. It is pointed out along the way that potential energy nonadditivity should create an orientational bias for molecules in the liquid-vapor interface that is peculiar to water. Some specific conclusions have been drawn about the solvation mode for the nonpolar rigid-sphere solute.

Infrared Lattice Vibrations and Free-Electron Dispersion in GaN

Abstract: Infrared reflectivity and absorption measurements have been made on single-crystal epitaxial GaN on (0001) $\ensuremath{\alpha}\ensuremath{-}$${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ crystals. Analysis of the normal-incidence reflectance data on low-carrier-concentration layers using the Kramers-Kronig technique and dielectric oscillator fits yields the values ${\ensuremath{\omega}}_{\mathrm{TO}}^{\ensuremath{\perp}}=560$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and ${\ensuremath{\omega}}_{\mathrm{LO}}^{\ensuremath{\perp}}=746$ ${\mathrm{cm}}^{\ensuremath{-}1}$ for the optical mode frequencies at 300 K. Adopting ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}^{\ensuremath{\perp}}=5.35$ from a fit to Ejder's refractive-index data the additional quantities ${\ensuremath{\epsilon}}_{o}^{\ensuremath{\perp}}=9.5$ for the static dielectric constant, ${e}_{B}^{*\ensuremath{\perp}}=2.65e$ for the Born effective charge, and ${\ensuremath{\alpha}}^{\ensuremath{\perp}}=0.44$ for the polaron coupling constant are derived. Reflectivity measurements at 50\ifmmode^\circ\else\textdegree\fi{} incidence with $s$ and $p$ polarizations show that the longitudinal lattice mode is nearly isotropic. Using the value ${\ensuremath{\omega}}_{\mathrm{TO}}^{\ensuremath{\parallel}}=533$ ${\mathrm{cm}}^{\ensuremath{-}1}$ from Raman data the values ${\ensuremath{\omega}}_{\mathrm{LO}}^{\ensuremath{\parallel}}=744$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\epsilon}}_{o}^{\ensuremath{\parallel}}=10.4$, ${e}_{B}^{*\ensuremath{\parallel}}=2.82e$, and ${\ensuremath{\alpha}}^{\ensuremath{\parallel}}=0.49$ are obtained from oscillator fits to the 50\ifmmode^\circ\else\textdegree\fi{} incidence data. Information on the free-carrier effects in GaN was obtained by studying the normal-incidence reflectance as a function of carrier concentration in the 2\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 1\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ range. By fitting the reflectance minima versus concentration data, a value of $\frac{{m}^{*}}{m}=(0.20\ifmmode\pm\else\textpm\fi{}0.02)$ for the optical effective mass is obtained. Measurements at 50\ifmmode^\circ\else\textdegree\fi{} incidence show that the plasma frequency is isotropic within experimental precision.

Spherical Model of Shallow Acceptor States in Semiconductors

Abstract: The effective-mass approximation for shallow acceptor states in cubic semiconductors with degenerate valence bands is reformulated. The Hamiltonian is written as the sum of a spherical term and a cubic corection, thus pointing out the relevance of the spherical symmetry in the acceptor problem and the strong similarity to the case of atoms with the spin-orbit interaction. Without the introduction of any explicit representation of the Hamiltonian, the present formulation yields a meaningful classification of the acceptor states and reduces the eigenvalue problem to simple radial Hamiltonians. These radial Hamiltonians are explicitly given for the most improtant acceptor states and are shown to apply also to the description of the exciton problem. The variational method is used in the numerical calculation. The resulting eigenvalues, eigenfunctions, and related quantities are given as functions of the relevant parameters. The theoretical ionization energies are compared with available experimental data.

Fluctuation Effects at a Peierls Transition

Abstract: The effects of fluctuations on the Peierls transition in one dimension are calculated by taking a functional average over variations in the order parameter. It is found that the transition is suppressed to a temperature of approximately one quarter of the mean-field transition but remains fairly sharp. The coherence length and density of states are calculated as a function of temperature, and brief comparison is made to experimental systems.

Radiation Forces and Momenta in Dielectric Media

Abstract: There has existed a continuing dialogue concerning the proper identification of radiation forces and momenta in dielectric media. I argue herein that a sensible and consistent picture of these forces and momenta is available. That is, the density of electromagnetic momentum $\stackrel{\ensuremath{\rightarrow}}{\mathbf{G}}$ is given by $\stackrel{\ensuremath{\rightarrow}}{\mathbf{G}}=\frac{\stackrel{\ensuremath{\rightarrow}}{\mathbf{S}}}{{c}^{2}}$, where $\stackrel{\ensuremath{\rightarrow}}{\mathbf{S}}$ is Poynting's vector. The forces which are exerted on material objects in dielectric media are associated with changes in both the electromagnetic and mechanical momenta of the media. In fairly broad circumstances, such forces may be found from the rate of change in a pseudomomentum $\stackrel{\ensuremath{\rightarrow}}{\mathbf{K}}$ given by $\stackrel{\ensuremath{\rightarrow}}{\mathbf{K}}=\ensuremath{\epsilon}\stackrel{\ensuremath{\rightarrow}}{\mathbf{G}}$, where $\ensuremath{\epsilon}$ is the dielectric constant of the medium.

Electron and hole ionization rates in epitaxial silicon at high electric fields

Abstract: Ionization rates for electrons and holes are extracted from photomultiplication measurements on silicon p+n mesa diodes for electric fields of 2·0 × 105−7·7 × 105 V/cm at temperatures of 22, 50, 100 and 150°C. These results are particularly pertinent to the analysis of high-frequency (∼ 100 GHz) silicon IMPATT diodes. The rates obtained here are in reasonable agreement with previously published data of van Overstraeten and DeMan, although slightly larger in magnitude. Calculated curves of breakdown voltage vs background doping level are presented using the room temperature ionization rates. Also a comparison is made to previously reported rates. The new rates provide a closer agreement between predicted and measured breakdown voltages for breakdown voltages less than 70 V.

Stochastic Transport in a Disordered Solid. II. Impurity Conduction

Abstract: In a previous paper, the authors have developed a general theory of stochastic transport in disordered systems. In the present paper, the theory is applied, in detail, to a prototype of transport in a disordered system - impurity conduction in semiconductors. The complete frequency dependence of the real and imaginary part of the conductivity is calculated. In particular, the calculation details the transition from an ${\ensuremath{\omega}}^{s}$ dependence to essentially dc behavior (at a finite frequency), where $s\ensuremath{\sim}0.6\ensuremath{-}0.8$, depending on temperature and concentration. The theoretical results for frequency, temperature, and concentration dependence of the conductivity are shown to be in good agreement with the measurements of Pollak and Geballe (PG). In addition, the ac conductivity data of PG interpreted with the present theory yield experimental evidence for the existence of two-channel hopping in $n$-type Si.

Design of Totally Self-Checking Check Circuits for m-Out-of-n Codes

Abstract: The design of totally self-checking check circuits for m-out-of-n codes is described. Totally self-checking m-out-of-n checkers provide an error indication whenever the input is not an m-out-of-n code or whenever a fault occurs within the checker itself. Since the checker checks itself, there is no need for additional maintenance access or periodic exercise of the checker to verify its ability to detect errors. The basic structure of the checker relies on the use of majority detection circuits. Various gate level implementations for the majority detection circuits are also presented, although the self-checking capability of the checker does not depend on their particular implementation since they are exhaustively tested by code inputs. The self-testing checkers for k-out-of-2k codes are discussed in the most detail since the totally self-checking checkers for 1-out-of-n and arbitrary m-out-of-n codes are constructed by first translating the code to a k-out-of-2k code via a totally self-checking translator.

Bond-Charge Calculation of Nonlinear Optical Susceptibilities for Various Crystal Structures

Abstract: A simple localized-bond-charge model for the calculation of nonlinear optical susceptibilities is presented. We find that there are three important contributions to the nonlinearity, namely, the bond ionicity, the difference in atomic radii of the bonded atoms, and $d$-electron contributions. By including these effects we are able with one simple theory to accurately treat a wide variety of different types of compounds including ${A}^{\mathrm{III}}{B}^{\mathrm{V}}$ (e.g., GaAs, GaP, InSb), ${A}^{\mathrm{II}}{B}^{\mathrm{VI}}$ (e.g., ZnS, ZnO, BeO), ${A}^{\mathrm{I}}{B}^{\mathrm{VII}}$ (e.g., CuCl, CuBr, CuI), ${A}^{\mathrm{IV}}{B}_{2}^{\mathrm{VI}}$ (e.g., Si${\mathrm{O}}_{2}$), multibond crystals [e.g., ${A}^{\mathrm{I}}{B}^{\mathrm{III}}{C}_{2}^{\mathrm{VI}}$ (LiGa${\mathrm{O}}_{2}$, AgGa${\mathrm{S}}_{2}$, CuIn${\mathrm{S}}_{2}$, CuGa${\mathrm{Se}}_{2}$), ${A}^{\mathrm{II}}{B}^{\mathrm{IV}}{C}_{2}^{\mathrm{V}}$ (CdGe${\mathrm{P}}_{2}$, CdGe${\mathrm{As}}_{2}$, ZnGe${\mathrm{P}}_{2}$), ${A}^{\mathrm{III}}{B}^{\mathrm{V}}{C}_{4}^{\mathrm{VI}}$ (AIP${\mathrm{O}}_{4}$), also K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$], highly anisotropic crystals (e.g., HgS, Se, Te), as well as ferroelectrics (e.g., LiNb${\mathrm{O}}_{3}$, ${\mathrm{Ba}}_{2}$Na${\mathrm{Nb}}_{5}$${\mathrm{O}}_{15}$, LiTa${\mathrm{O}}_{3}$).

Inability of Humans to Discriminate between Visual Textures That Agree in Second-Order Statistics—Revisited

Abstract: In an earlier study by Julesz (1962) pairs of random textures were generated side-by-side using a Markov process with different third-order joint-probability distributions but identical first- and second-order distributions. Such texture pairs could not be discriminated from each other by the human visual system without scrutiny. Unfortunately, Markov processes are inherently one-dimensional while the general processes underlying visual texture discrimination are two-dimensional. Here three new methods are introduced that generate two-dimensional non-Markovian textures with different third-order but identical first- and second-order statistics. All three methods generate texture pairs that cannot be discriminated from each other.The lack of texture discrimination is the more astonishing since the individual elements that form the texture pair are clearly perceived as being very different. However, a counterexample was found that yields discrimination although the texture pair has approximately identical s...

Effects on Correlation Between Two Mobile Radio Base-Station Antennas

Abstract: The correlation between signals received by two mobile radio base-station antennas is investigated to determine spacing requirements for space diversity. Measurements of the fading of UHF signals received by two base-station horn antennas oriented at different angles with respect to the incoming mobile radio signal were made for different antenna spacings. The experimental results are compared with an analytical expression derived in this paper; they agree fairly well. A further experiment was made after removing the possible local scatterers surrounding the base station. Comparing these two experimental results, we find that the following are true. 1) Propagation in the direction of a line connecting the two base-station antennas is the critical case and requires a large separation of 70 wavelengths. As soon as the incoming wave is 10° away from the inline axis, the spacing requirement drops to 30 wavelengths. 2) Local scatterers at the base station tend to decrease the correlation between signals received at the two antennas. We conclude that an upper limit to the spacing of antennas used for diversity can be obtained and that it is within the achievable range.

Quantum Dielectric Theory of Electronegativity in Covalent Systems. III. Pressure-Temperature Phase Diagrams, Heats of Mixing, and Distribution Coefficients

Abstract: Electronegativity difference was redefined in Paper I of this series as a scaling parameter which combines the concepts of valence and size differences. A procedure has been developed for its evaluation in terms of a two-band model. In Paper II of this series it was shown that this model describes and predicts the ionization potentials and electronic interband gaps of binary ${A}^{N}{B}^{8\ensuremath{-}N}$ compounds and their alloys. Here the energy of this model semiconducting-insulating solid is evaluated relative to a free-electron gas, i.e., an idealized metal, as a function of composition, pressure, and temperature. Using this highly simplified scaling approach, we obtain suprisingly accurate predictions for the heat of fusion, melting point, and pressure-temperature phase diagrams of these materials. A revised method of calculating the excess heat of mixing of a substitutional alloy is presented. This calculation is extended to the case of an arbitrary dilute impurity in an arbitrary semiconducting host; the distribution coefficient at the melting point of the host is obtained.

Masking in Visual Recognition: Effects of Two-Dimensional Filtered Noise

Abstract: It is difficult to recognize portraits that have been coarsely sampled and quantized. Blurring such images improves recognition. A simple, straightforward explanation is that high-frequency noise introduced by the sampling and quantizing must be removed by low-pass filtering to improve the signal-to-noise ratio and hence signal detectability or recognition. Experiments reported here, suggested on the basis of a different model, show instead that noise bands that are spectrally adjacent to the picture's spectrum are considerably more effective in suppressing recognition.

Metal-Insulator Transitions in Pure and Doped V 2 O 3

Abstract: The addition of ${\mathrm{Ti}}^{3+}$ and ${\mathrm{Mg}}^{2+}$ to ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ leads to the suppression of the antiferromagnetic insulating phase; whereas the addition of ${\mathrm{Ti}}^{4+}$, ${\mathrm{Zr}}^{4+}$, and ${\mathrm{Fe}}^{3+}$ results in a first-order transition from a metallic to an insulating state. The effect of impurity ions is discussed in terms of the changes they cause in the bandwidth in analogy with the effect of pressure. The Hall coefficient of metallic ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ at 4.2 \ifmmode^\circ\else\textdegree\fi{}K and 20 kbar is ${R}_{H}=+(3.5\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{3}$/C which is close to the value measured at 150 \ifmmode^\circ\else\textdegree\fi{}K and 1 atm. The residual resistivity of metallic ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ is strongly impurity dependent (140 \ensuremath{\mu}\ensuremath{\Omega} cm/at.% Cr and 35 \ensuremath{\mu}\ensuremath{\Omega} cm/at.% Ti). These results are not completely consistent with current theories for the metal-insulator transition in ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ but the best available model still seems to involve a localized-to-nonlocalized transition within the $d$ band primarily involving orbitals in the basal plane.

Radiation Pressure on a Free Liquid Surface

Abstract: The force of radiation pressure on the free surface of a transparent liquid dielectric has been observed using focused pulsed laser light. It is shown that light on either entering or leaving the liquid exerts a net outward force at the liquid surface. This force causes strong surface lens effects, surface scattering, and nonlinear absorption. The data relate to the understanding of the momentum of light in dielectrics.