Binary images of cyclic codes over Z4

We determine all linear cyclic codes over Z₄ of odd length whose Gray images are linear codes (or, equivalently, whose Nechaev-Gray (1989) image are linear cyclic codes or are linear cyclic codes)     

Quasi-cyclic codes over Z4 and some new binarycodes

Previously, (linear) codes over Z₄ and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z ₄-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z₄ produces a new binary code, a (92, 2²⁴, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials     

On algebraic decoding of the Z4-linear Goethals-likecodes

The Z₄-linear Goethals-like code of length 2^m has 2^2m+1-3m-2 codewords and minimum Lee distance 8 for any odd integer m⩾3. We present an algebraic decoding algorithm for all Z₄-linear Goethals-like codes C_k introduced by Helleseth et al.(1995, 1996). We use Dickson polynomials and their properties to solve the syndrome equations     

Direct hardware solution to quadratic equation Z2⊕Z⊕β=0 in Galois fields based on normalbasis representation

Normal basis representation is considered to represent the elements of Galois fields. The quadratic equation, Z²⊕Z⊕β=0, is solved directly and a new, simple, regular and expandable hardware structure is introduced to solve this equation. The main advantage of this structure over the structures in non-normal basis representations is its independence from generating polynomial of the field     

Frequency-dependent FDTD methods using Z transforms

The frequency-dependent finite-difference time-domain method (FD) ²TD method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent. However, as researchers search for more elaborate applications, the formulation of the (FD)²TD methods becomes more complex. In this work, the mathematics of the (FD) ²TD method is developed using Z transform theory. This has the advantages of presenting a clearer formulation, and allowing researchers to draw on the literature of systems analysis and signal processing disciplines     

Analysis of erbium-doped fiber amplifiers pumped in the4I15/2-4I13/2 band

A theoretical model for the amplifiers predicts gain coefficients of around 2 dB per milliwatt of launched pump power, in close agreement with previously reported measurements. The model is also used to determine the optimal pump wavelength λ_opt that maximizes the amplifier gain. It is shown that the latter is insensitive to pump detuning near λ_opt=1.48 μm, within a 20 nm range, which indicates that broadband, multimode laser diode pump sources and pumps with narrow linewidths should yield identical gain performance     

Analysis of Z-invariant and Z-variantsemiconductor rib waveguides by explicit finite difference beampropagation method with nonuniform mesh configuration

An efficient and simple explicit finite difference beam propagation method (EFD-BPM) incorporating nonuniform mesh is described. The criteria for stability are developed, and it is shown that this algorithm is power conserving when the stability criteria are met. EFD-BPM is applied to the analysis of single and coupled semiconductor rib waveguides and its accuracy is confirmed by comparing the results with the reported results. Nonuniform mesh is found to improve the efficiency of the method significantly for the analysis of weakly guiding waveguide structures. Several coupled rib waveguide structures with curved input and output branching sections are analyzed using both three-dimensional EFD-BPM and two-dimensional finite difference BPM combined with effective index approximation     

An algorithm for computing the inverse Z transform

The authors determine an infinite impulse response of a causal system via a sampling algorithm applied to the transform on the unit circle     

Proton-exchanged optical waveguides in Z-cut LiNbO3 using phosphoric acid

Proton-exchanged Z-cut LiNbO₃ planar waveguides formed using phosphoric acid were characterized optically. The refractive index profile and the diffusion parameters were studied systematically. These waveguides have propagation losses of less than 1 dB/cm and exhibit properties that are different from those obtained using benzoic acid. The index profile is not a simple step function and can be modeled accurately by a polynomial expression. A maximum surface index increase of 0.145 was measured at a 0.633-μm wavelength. The diffusion constant D₀ and the activation energy Q for the proton-exchange process using this acid were found to be 6.43×10⁸ μm²/h and 82.91 kJ/mol, respectively. The annealing properties of these waveguides were also established, and the effects of annealing on surface index change and waveguide depth increase were found to follow a power-law relationship     

Thermal shifts of the spectral lines in the 4F3/2 to 4I11/2 manifold of anNd:YAG Laser

A report is presented of the thermal shifts of eleven of the twelve lines from the ⁴F_3/2 Stark energy levels to the ⁴I_11/2 energy levels in an Nd:YAG laser for a temperature change from 20-200°C. The thermal shift difference between the Stark sublevels R₁, R₂ in ⁴F_3/2 is found to be about -0.6±0.6 cm^-1/100°C. Within experimental uncertainty, all of the lasing lines either moved to longer wavelength or remained unchanged with increasing temperature     

Image restoration by convex projections using adaptive constraintsand the L1 norm

A new projection method based on the row action projection (RAP) algorithm for image restoration is presented. The new implementation is computationally attractive and facilitates local adaption of projection operators. The local mean and the least L₁ norm set of solutions are used as constraints. Computer simulations illustrate the new methods to be very competitive in restoring missing spectral components of a degraded image     

Optimal pump wavelength in the4I15/2-4I13/2 absorption band for efficient Er3+-doped fiberamplifiers

The authors report the measured gain of a highly efficient erbium-doped fiber amplifier pumped at wavelengths between 1.46 and 1.51 μm. The optimal pump wavelength, λ_opt, was determined to be 1.475 μm. At this wavelength, the maximum gain coefficients for signals at 1.531 and 1.544 μm were 2.3 and 2.6 dB/mW, respectively. At λ_opt, high gains ranging from 32 dB at pump power P_p=20 mW up to 40 dB at P _p=80 mW were obtained. These modest pump powers are within the capabilities of currently available 1.48-μm diode lasers. The width about λ_opt for 3-dB gain variation exceeded 27 nm for P_p=10 mW and 40 nm for P_p >20 mW. With this weak dependence on pump wavelength, single-longitudinal-mode lasers do not have a significant advantage over practical Fabry-Perot multimode pump lasers     

Simplified Z-propagating DC bias stable TE-TM modeconvertor fabricated in Y-cut lithium niobate

A TE-TM mode converter, useful at either 0.632 or 0.840 μm, has been fabricated on y-cut LiNbO₃ by Ti indiffusion with the channel waveguide placed parallel to the z-axis. For TE polarized input, the maximum TM modulation depth is 97 percent at 0.632 μm with a 5-V (pp) drive and 99 percent at 0.840 μm with a 12-V (pp) drive. A similar device operating at 1.3 μm displays 98-percent TE-TM switching at 68 V. Operation involves only coplanar electrodes placed alongside the channel acting on the r₆₁ electrooptic coefficient. A separately deposited buffer layer is unnecessary. Testing indicates a substantially greater tolerance to electrode misalignment than afforded by similar structures formed in x-cut substrates. Data illustrating immunity to photorefractive drift in the presence of a DC bias voltage is presented for 0.840-μm wavelength operation     

The ZπM algorithm: a method for interferometric imagereconstruction in SAR/SAS

This paper presents an effective algorithm for absolute phase (not simply modulo-2-pi) estimation from incomplete, noisy and modulo-2pi observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2-pi-periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss-Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step (Z-step), implemented by network programming techniques and an iterative conditional modes (ICM) step (pi-step). Accordingly, the algorithm is termed ZpiM, where the letter M stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2pi-multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low-pass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach.     

Measurement of the stimulated emission cross section for the 4F3/2-4I13/2transition of Nd3+ in YAlO3 crystal

A method for the simultaneous measurement of the stimulated emission cross section and fluorescence lifetime by studying the relation between laser parameters and the laser relaxation oscillation frequency is discussed. The stimulated emission cross section for the ⁴F_3/2-⁴I_13/2 transition of Nd³⁺ ion in YAP crystal was measured to be (22±1)×10^-20 cm²     

Quarter-micrometer gate ion-implanted GaAs MESFET's with an f1 of 126 GHz

The fabrication and characterization of a 0.25-μm-gate, ion-implanted GaAs MESFET with a maximum current-gain cutoff frequency f_t of 126 GHz is reported. Extrapolation of current gains from bias-dependent S-parameters at 70-100% of I _dss yields f₁'s of 108-126 GHz. It is projected that an f₁ of 320 GHz is achievable with 0.1-μm-gate GaAs MESFETs. This demonstration of f₁'s over 100 GHz with practical 0.25-μm gate length substantially advances the high-frequency operation limits of short-gate GaAs MESFETs     

On the number of points on shells for shiftedZ4n lattices

A conjecture is proven on the number of points on shells for the shifted Z⁴ and the shifted Z⁸ lattices. Furthermore, the results are extended to any shifted Z⁴ⁿ lattice (n=0, 1, . . .). These results provide an easy way to compute the number of points on shells for the type of lattices used in the design of multidimensional signal sets or in vector coding     

Closest coset decoding of |u|u+v| codes

The general concept of closest coset decoding (CCD) is presented, and a soft-decoding technique for block codes that is based on partitioning a code into a subcode and its cosets is described. The computational complexity of the CCD algorithm is significantly less than that required if a maximum-likelihood detector (MLD) is used. A set-partitioning procedure and details of the CCD algorithm for soft decoding of |u|u+v| codes are presented. Upper bounds on the bit-error-rate (BER) performance of the proposed algorithm are combined, and numerical results and computer simulation tests for the BER performance of second-order Reed-Muller codes of length 16 and 32 are presented. The algorithm is a suboptimum decoding scheme and, in the range of signal-to-noise-power-density ratios of interest, its BER performance is only a few tenths of a dB inferior to the performance of the MLD for the codes examined     

A single-hop F2 propagation model forfrequencies above 30 MHz and path distances greater than 4000 km

Standard textbook explanations of ionosphere propagation suggest that 30 MHz and 4000 km are the limiting frequency and distance for single-hop communications. During the peak of sunspot cycle 22, however, there have been hundreds of reports of F₂ communications exceeding great-circle distance of 4200 km at 50 MHz. It is shown that parabolic F₂ ionospheric models explain this propagation irregularity, although textbooks and reference books fail to show that such long distances at VHF are possible     

2-D quasi m-arrays and Gold code arrays

Two-dimensional quasi-maximal-area arrays (quasi-m-arrays) are proposed. These quasi-m-arrays are so named because their cyclic correlation properties are very close to those of the m-arrays. These arrays are generated by modulo-2 addition of maximal length sequences. The cyclic autocorrelation of any quasi-m-array is close to the delta-function. In addition, the cyclic cross-correlation is small compared with the cyclic autocorrelation peak. Two-dimensional Gold code arrays generated by the same construction method are also studied. Correlation properties of these Gold code arrays are similar to those of the quasi-m-arrays. The Gold code arrays provide families of arrays in which any two arrays have the bound on their cyclic cross-correlation. These arrays are also shown to have the quasi-orthogonal property