Self-avoiding random loops

A random loop, or polygon, is a simple random walk whose trajectory is a simple Jordan curve. The study of random loops is extended in two ways. First, the probability P_n(x,y) that a random n-step loop contains a point (x,y) in the interior of the loop is studied, and (1/2, 1/2) is shown to be (1/2)-(1/ n). It is plausible that P_n(x,y) tends toward 1/2 for all ( x,y), but this is not proved even for (x,y)=(3/2,1/2) A way is offered to simulate random n-step self-avoiding loops. Numerical evidence obtained with this simulation procedure suggests that the probability P_n (3/2,1/2)≈(1/2)-(c/n), for some fixed c      

Block 2-D interpolation, efficient matrix factorization andapplication to signal processing

A block 2-D decomposition and a new block LU matrix factorization based on a Newton approach are presented for solving quickly and efficiently polynomial or exponential 2-D interpolation problems. The sample grids under consideration are described by the product representation {x₀, x₁, . . ., x_n} x{y₀, y ₁, . . ., y_m}, where the x grid and the y-grid are not necessarily uniformly spaced. The attractive features of the method are the inherent efficient parallelism, the reduced computational requirements needed for the LU decomposition, and the capability of implementation of 1-D fast and accurate algorithms. The proposed method can be used for modeling 2-D discrete signals, designing 2-D FIR filters, 2-D Fourier matrix factorization, 2-D DFT, etc     

Ga1-yInyAs/InAsxP1-1 (y>0.53, x>0) pin photodiodes for long wavelengthregions (λ>2 μm) grown by hydride vapour phase epitaxy

pin photodiodes with a 2.3 μm absorption edge are presented, using hydride vapour phase epitaxy. A Ga₁-_yIn_yAs (y=0.72) absorption layer, lattice-mismatched to the InP substrate, was grown on an InAs_xP_1-x (x=0-0.33) graded composition buffer layer. Typical dark current was 5 μA (0.03 A/cm²) at -6 V. Effective carrier lifetime of 0.05 μs was estimated from I/V characteristics     

A storage-efficient method for solving banded Toeplitz systems

A method is presented for solving the banded Toeplitz system Tx=y by decomposing T into its asymptotic upper and lower triangular factors (which are banded and Toeplitz) and a rank-p correction matrix, where p is the bandwidth of T. This way of representing T requires only O(p²) words of storage and allows computation of x in O(2Np) operations. A similar method is presented for the case in which T is bi-infinite and y is zero outside a finite region     

Bounding the capacity of saturation recording: the Lorentz modeland applications

The authors consider the problem of bounding the information capacity of saturation recording. The superposition channel with additive Gaussian noise is used as a model for recording. This model says that for a saturation input signal, x(t) (i.e., one that can assume only one of two levels), the output can be expressed as y(t)=x˜(t)+z(t ) where x˜(t) is a filtered version of the input x(t) and z(t) is additive Gaussian noise. The channel is described by the impulse response of the channel filter, h(t), and by the autocorrelation function of the noise. A specific example of such a channel is the differentiated Lorentz channel. Certain autocorrelation and spectrum expressions for a general Lorentz channel are derived. Upper and lower bounds on the capacity of saturation recording channels are described. The bounds are explicitly computed for the differentiated Lorentz channel model. Finally, it is indicated how the derived bounds can be applied in practice using physical measurements from a recording channel     

Polarization properties of fused fiber couplers and polarizingbeamsplitters

The polarization properties of fused taped fiber couplers were investigated experimentally by changing cross-sectional shapes at the coupler waist. The coupling difference between x and y polarized light was studied for many test fused fiber couplers with various cross-sectional shapes. On the basis of the experimental results, two polarizing beamsplitters with the aspect ratio of 1.1 and 1.8 were produced, and their chromatic characteristics were measured. It was evident that the aspect ratio should be more than 1.7 to manufacture polarizing beamsplitters with few power transfer cycles, i.e. long spectral period. Splitting ratios of polarizing beamsplitters with the aspect ratio of 1.1 and 1.8 were 17.6 and -12.7 dB for x polarized light and -16.1 and 11.7 dB for γ polarized light, respectively. Their losses were less than 0.6 and 0.3 dB     

Phase-noise-free coherent optical communication system utilizingdifferential polarization shift keying (DPolSK)

An optical communication system utilizing differential polarization modulation, which is free from phase noise, is discussed. The system proved to be immune to essentially all phase jitter. Separate square operations for the x and y channels, followed by multiplication of the two-channel outputs, effectively removed phase jitter. The delay-and-multiply circuit was directly incorporated in the paths of the frequency shifter and the coupler to the local oscillator laser, minimizing the optical power loss     

Average and randomized communication complexity

The communication complexity of a two-variable function f(x,y) is the number of information bits two communicators need to exchange to compute f when, initially, each knows only one of the variables. There are several communication-complexity measures corresponding to whether (1) the worst case or average number of bits is considered, (2) computation errors are allowed and (3) randomization is allowed. Tight bounds are provided for the typical behavior of all bounded-error communication-complexity measures of Boolean functions. In the present work, the authors formally define the deterministic model. They describe randomized protocols and compare them to deterministic ones. They both survey previous work and describe original results     

A novel binarily detectable high-speed optical position-sensitivedevice (BPSD)

A binary position sensitive device (BPSD) which can be used to detect the position of optical illumination in the binary form is described. This device consists of a p-i-n structure, sandwiched with two-axis (x and y) stripelike electrodes. For preliminary laboratory demonstration, a test device with an active area of 1 cm² including 8×8 elements was fabricated using an a-SiC:H single heterostructure. The fabricated device showed a high-speed response of 0.3 μs for the pulsive input illumination and high quantum efficiency over more than unity having a dark current of 10 pA/element. Output signal uniformity was ±5%, which is suitable for digital applications. In this demonstration, it was found that the response limitation depends on the computer processing time     

Numerical evaluation of parabolic cylinder functions

The numerical evaluation of the parabolic cylinder functions D _p(z) in two cases is described. Case I is for the argument z=xe^-iπ/4, with x real, and the order p=-1/2+iy, with y real. Case II is for z arbitrary, but p an integer. These cases are of special importance in the analysis of wave scattering from a parabolic cylinder. Expressions for D_p(z) are presented which are numerically accurate and efficient     

Schottky diodes of Au on GaAs1-xSbx/GaAs n-Nheterostructures grown by MBE

Au Schottky barrier heights on molecular-beam-epitaxial grown n-GaAs_1-xSb_x/N-GaAs heterostructures with x up to 0.26 have been studied. It was found that φ_bn=0.9-1.77x+2.89x², or φ_bn≈0.77E_g-0.20 for x<0.26. The pinning position of the Fermi level with respect to the valence-band edge for x<0.26 takes the form of E _pin=-0.52x+0.53 eV, which also appears to be valid for an x value up to 1.0     

Dark current analysis and characterization ofInxGa1-xAs/InAsyP1-y gradedphotodiodes with x>0.53 for response to longer wavelengths(>1.7 μm)

The dark current properties of In_xGa_1-xAs photodiodes, where x is varied from 0.53 to 0.82 for extending the long wavelength cutoff from 1.7 to 2.6 μm, are described. Detailed analyses of optoelectrical parameters of In_0.82Ga _0.1As photodiodes are presented. Dark current, which is a critical parameter and limits the operation of the photodiode, is analyzed and compared with the experimental values. Typical characteristics of photodiodes with cutoff wavelengths of 1.7 μm (x=0.53), 2.2 μm (x=0.72), and 2.6 μm (x=0.82) are presented. The typical and best values of the dark currents obtained are presented     

A new single-polarization optical fiber

In the single-polarization optical fiber, two isolated stress-applying parts contribute to radiate one of the two orthogonal polarization modes due to the asymmetrical geometric-index effect in addition to a stress-induced birefringence effect without bending the fiber. The loss spectra for x- and y-polarizations and the length dependence of the crosstalk show that the present fiber exhibits single-polarization characteristics     

Quadtree-structured recursive plane decomposition coding of images

The approximation of two-dimensional highly correlated grey value functions can be performed using a linear model of the type f( x, y)=a+bx+cy. The set of plane parameters (PPs) [a, b, c] can be determined in the least squares sense for a block of size N×N pixels, for example. Starting with a block size of 2×2 pixels, it is shown that the PPs obey a recursive law such that the PPs of a 2N×2N block can be computed recursively when only the PPs of the four adjacent subblocks of size N×N in the lower decomposition level are known. This concept of recursive plane decomposition (RPD) is embedded in a quadtree data structure to obtain a new variable block size image coding algorithm that offers a high performance at a low computational cost. Extensive comparisons to other state-of-the-art image coding algorithms are reported     

Reply to comments on Wait's `In defense of J.A. Stratton'

The author points out that M.G.M. Hussain (ibid., vol.31, no.3, p.202, May 1989), in his comments on the author's paper (ibid., vol.30, no.4, p.590, Nov. 1988) says that equation (4) is not valid at y=0. He notes that he stated that y>0. Even if the source were a current sheet in the plane y=0, it would still be possible to alloy y to approach zero from positive values     

AlInGaAs-AlGaAs strained single-quantum-well diode lasers

Diode lasers with a strained AlInGaAs active layer and AlGaAs confining and cladding layers are reported. Broad-stripe devices were fabricated in graded-index separate-confinement heterostructures grown by organometallic vapor-phase epitaxy on GaAs substrates and containing a single Al_yIn_xGa_1-x-yAs quantum well with 0.12⩽x⩽0.14 and five values of y between 0.05 and 0.17. With increasing Al content the emission wavelength decreases from 890 to 785 nm. The threshold current density J _th is less than 200 A-cm^-2, with one exception, and the differential quantum efficiency ranges from 78 to 81%. A preliminary reliability test was made on a saw-cut, uncoated broad-area device, with an Al_0.17In_0.12Ga_0.71As active layer, that was fabricated without using special precautions to minimize damage and was mounted junction side up. After 20 h of CW operations at a constant current of 1.125 times threshold, J _th has increased by only 3.5%     

Evaluating programmable logic devices

The use of the combinational/register coordinate system as a graphical way of measuring programmable logic devices (PLDs) in terms of gates and registers is reviewed. It is assumed that the I/O resources of the PLD, which constitute a third axis, are adequate. This allows the analysis to be restricted to an x-y plane fixed along the z-axis. The device's application area, which is the area bounded by its combinational and register capability, is discussed, and methods for calculating the application range are described. Three brief examples demonstrate the ways in which the coordinate system might be used in CAD tools that automate the PLD design process     

On the competitive optimality of Huffman codes

Let X be a discrete random variable drawn according to a probability mass function p(x), and suppose p(x), is dyadic, i.e., log(1/p(x)) is an integer for each x. It is shown that the binary code length assignment l(x)=log(1/p(x)) dominates any other uniquely decodable assignment l'(x) in expected length in the sense that El(X)<El'(X), indicating optimality in long run performance (which is well known), and competitively dominates l'(x), in the sense that Pr{ l (X)<l'(X)}>Pr{l ( X)>l'(X)}, which indicates l is also optimal in the short run. In general, if p is not dyadic then l=[log 1/p] dominates l'+1 in expected length and competitivity dominates l'+1, where l' is any other uniquely decodable code     

Pipelined recursive filter with minimum order augmentation

Pipelining is an efficient way for improving the average computation speed of an arithmetic processor. However, for an M-stage pipeline, the result of a given operation is available only M clock periods after initiating the computation. In a recursive filter, the computation of y(n) cannot be initiated before the computations of y(n-1) through y(n-N) are completed. H.B. Voelcker and E.E. Hartquist (1970) and P.M.Kogge and H.S. Stone (1973) independently devised augmentation techniques for resolving the dependence problem in the computation of y(n). However, the augmentation required to ensure stability may be excessively high, resulting in a very complex numerator realization. A technique which results in a minimum order augmentation is presented. The complexity of the resulting filter design is very much lower. Various pipelining architectures are presented. It is demonstrated by an example that when compared to the prototype filter, the augmented filter has a lower coefficient sensitivity and better roundoff noise performance