Performance analysis of nonblocking packet switch with input andoutput buffers

The performance of nonblocking packet switches such as the knockout switch and Batcher banyan switch for high-speed communication networks can be improved as the switching capacity L per output increases; the switching capacity per output refers to the maximum number of packets transferred to an output during a slot. The N×N switch with L=N was shown to attain the best possible performance by M.J. Karol et al. (1987). Here a N×N nonblocking packet switch with input and output buffers is analyzed for an arbitrary number of L such that 1⩽L⩽N. The maximum throughput and packet loss probability at input are obtained when N=∞     

Grating degeneration technique and sandwich structures forholographic N×N passive star couplers

Design for an efficient N×N passive integrated optical star coupler are proposed. The concepts of grating degeneration and sandwich structures are presented. The techniques and their combinations can significantly reduce the number of gratings required by the coupler and thus make it possible to build holographic N×N star couplers with recording materials of a moderate dynamic range     

Computing local minima and maxima of digital images in pipelineimage processing systems equipped with hardware comparators

An efficient technique is presented for computing minima (maxima) values of gray levels of pixels within rectangular windows. It is suitable for pipeline image processing systems having processors equipped with hardware comparators. The complexity of computing the minima and/or maxima of gray levels within M×N windows is determined     

Recursive updating the eigenvalue decomposition of a covariancematrix

The author addresses the problem of computing the eigensystem of the modified Hermitian matrix, given the prior knowledge of the eigensystem of the original Hermitian matrix. Specifically, an additive rank-k modification corresponding to adding and deleting blocks of data to and from the covariance matrix is considered. An efficient and parallel algorithm which makes use of a generalized spectrum-slicing theorem is derived for computing the eigenvalues. The eigenvector can be computed explicitly in terms of the solution of a much-reduced (k ×k) homogeneous Hermitian system. The overall computational complexity is shown to be improved by an order of magnitude from O(N³) to O(N ²k), where N×N is the size of the covariance matrix. It is pointed out that these ideas can be applied to adaptive signal processing applications, such as eigen-based techniques for frequency or angle-of-arrival estimation and tracking. Specifically, adaptive versions of the principal eigenvector method and the total least squares method are derived     

An efficient communication structure for distributed commitprotocols

To maintain consistency in a distributed database environment, the transactions must be executed atomically. The standard algorithm for ensuring an atomic execution is called the distributed commit protocol. The two-phase commit protocol and its variations, the well-known protocols used for this purpose, are characterized by successive rounds of message exchange, among all the sites of the database, at the time a transaction enters into a completion phase. The performance of these protocols is given by a complexity measure that depends on the communication structure of the protocol. Given N sites, the worst-case complexity of a commit protocol is O(N²). A communication structure called maximal binomial structure (MBS) is presented, for which the complexity of the protocol is O(N×log³ N). A lower bound for this complexity is also given, which is O(N×log² N). Protocols using the MBS remain symmetric. A scheme for an arbitrary expansion of the MBS to allow communication among a large number of sites is proposed. For the expanded system, the protocol complexity is also shown to be O(N×log³ N ). These structures are shown to be superior to other known structures     

A multibus train communication (AMTRAC) architecture for high-speedfiber optic networks

A multibus train (ordered demand assignment) communication architecture, using the AMTRAC protocol (for efficient utilization of fiber-optic-based very-high-speed networks) is presented. Taking advantage of the emerging WDM (wavelength-division multiplexing) and FDM (frequency-division multiplexing) technologies, the proposed solution introduces a coordinated multichannel control combining the performance advantages of two known approaches for high-speed communication: multichannel and train protocols. As a result an AMTRAC-based high-speed network achieves channel utilization significantly higher than previous approaches. For a network consisting of N stations, with propagation delay to packet transmission time ratio given by a, the AMTRAC architecture reaches a capacity of 1/(1+a/N ²)     

The impedance matrix localization (IML) method for moment-methodcalculations

The impedance matrix localization (IML) method, a modification of the standard method of moments that can be implemented as a modification to existing computer programs, is examined. This modification greatly eases the excessive storage requirements and long computation times of moment-method approaches by using novel bases and testing function that localize the important interactions to only a small number of elements within the impedance matrix elements can be made so small (typically 10 ^-4 to 10^-6 in relative magnitude) that they may be approximated by zero. In the case of a two-dimensional body with unknowns on its surface, both analytical arguments and numerical calculations suggest that, for an N×N matrix, about 100N matrix elements will need to be kept, even for very large N. The resulting sparse matrix requires storage for only 100N complex numbers rather than for N² numbers. Similar results are expected in three dimensions. The structure of the resulting matrix problem allows the use of highly efficient solution methods. Results are given for one such possibility: iteration preconditioned by incomplete LU decomposition     

Optical switch matrix with simplified N×Ntree structure

Optical switch matrices with compact size and excellent crosstalk characteristics are discussed. Novel architectures for optical switch matrices are obtained by condensing the structure of N× N tree structure. 4×4 switches fabricated on LiNbO₃ substrates are discussed     

Restoration of color images by multichannel Kalman filtering

A Kalman filter for optimal restoration of multichannel images is presented. This filter is derived using a multichannel semicausal image model that includes between-channel degradation. Both stationary and nonstationary image models are developed. This filter is implemented in the Fourier domain and computation is reduced from O(Λ ³N³M⁴) to O(Λ³N³M² ) for an M×M N-channel image with degradation length Λ. Color (red, green, and blue (RGB)) images are used as examples of multichannel images, and restoration in the RGB and YIQ domains is investigated. Simulations are presented in which the effectiveness of this filter is tested for different types of degradation and different image model estimates     

Analysis of N×N passive optical starcoupler based on the normal modes of N input waveguides

An integrated passive N×N optical star coupler on silicon wafer is described. Antiresonant reflecting optical waveguides (ARROWs) are analyzed and utilized as the input and output waveguides of the N×N coupler. Combining the exact solutions of the slab ARROW waveguide with the effective index method, a 5×5 coupler is analyzed. In the slab waveguide analysis, the input waveguides are coupled to their neighbors. The interaction of the waveguides is described in terms of the normal modes of propagation. The resultant field distribution is then diffracted into the free space region which separates the input and output sections. The radiation illuminates the receiving aperture from which the receiving N waveguides branch out, each output element obtaining equal power levels. Different types of loss such as spillover loss and mismatch loss were analyzed and estimated for N=5. A 5×5 star coupler with a transmission efficiency of 56% at a wavelength of 1.3 μm is achievable     

Efficient N×N star couplers using Fourier optics

A technique for constructing an efficient N×N star coupler with large N at optical frequencies is described. The coupler is realized in free space using two arrays, each connected to N single-mode fibers. The highest efficiencies are obtained using a planar arrangement of two linear arrays separated by a dielectric slab serving as free-space region. The coupler is suitable for mass production in integrated form, with efficiencies exceeding 35%     

Nonblocking property of reverse banyan networks

The authors present a new nonblocking property of the reverse banyan network under a particular input packet pattern at the input ports. The reverse banyan network is the mirror image of the banyan network. If the input packets of the N×N reverse banyan network have consecutive output address as modulo N, then the reverse banyan network is nonblocking. The routing of packets in the reverse banyan network is described, and the nonblocking property of the reverse banyan network is proved. A possible application of this property in the switching network is discussed     

Electromagnetic scattering of finite strip array on a dielectricslab

A feast recursive algorithm is used to compute the scattering properties of a finite array of strip gratings on a dielectric slab. this algorithm has a computational complexity of O(N log² N) for one incident angle and O(N ² log N) for N incident angles. It uses plane wave basis for expanding the incident wave and the scattered wave. The scattered wave is expanded in terms of a Sommerfeld-type integral with spectral distribution along a vertical branch cut, rendering its expansion very efficient. To validate the scattering solution obtained using the recursive algorithm, comparisons with the method of moments are illustrated. The current distributions on the strips and scattering patterns are both presented. Since this algorithm has reduced computational complexity and is fast compared to other conventional methods, it can be used to analyze very large strip arrays. Scattering solution of a 50-wavelength wide strip is illustrated     

Efficient N×N star coupler based on Fourieroptics

A technique for constructing an efficient N×N star coupler suitable for mass production in integrated form for large N at optical frequencies is discussed. The coupler can be realised using Si technology by means of two arrays of strip waveguides and a dielectric slab formed on a glass substrate. Power transfer between the two arrays is accomplished through radiation in the dielectric slab with theoretical efficiency exceeding 30% under optimised conditions     

A WDM cross-connected star topology for multihop lightwave networks

The authors propose a star topology for multihop lightwave networks in which the conventional N×N passive star coupler is replaced by fixed wavelength division multiplexed (WDM) cross connects. The proposed topology overcomes three major limitations of the conventional star topology. First, it reduces the number of wavelengths needed in a (p,k) ShuffleNet from kp ^k+1 wavelengths in the conventional topology to p wavelengths in the proposed one. Second, the signal power loss due to the 1/N power splitting at the star coupler no longer exists in the WDM cross connects and, therefore, the restriction on the supported number of users by the star network is alleviated. Third, it completely eliminates the need for wavelength filtering at the input to the receivers as is the case in the conventional star topology     

A multiple scattering solution for the effective permittivity of asphere mixture

A recursive algorithm for calculating the exact solution of a random assortment of spheres is described. In this algorithm, the scattering from a single sphere is expressed in a one-sphere T matrix. The scattering from two spheres is expressed in terms of two-sphere T matrices, which are related to the one-sphere T matrix. A recursive algorithm to deduce the (n+1)-sphere T matrix from the n-sphere T matrix is derived. With this recursive algorithm, the multiple scattering from a random assortment of N spheres can be obtained. This results in an N² algorithm rather than the normal N³ algorithm. As an example, the algorithm is used to calculate the low-frequency effective permittivity of a random assortment of 18 dielectric spheres. The effective permittivity deviates from the Maxwell-Garnett result for high contrast and high packing fraction. With a high packing fraction, dielectric enhancement at low frequency is possible     

Trellis-coded multidimensional phase modulation

A 2L-dimensional multiple phase-shift keyed (L×MPSK) signal set is obtained by forming the Cartesian product of L two-dimensional MPSK signal sets. A systematic approach to partitioning L×MPSK signal sets that is based on block coding is used. An encoder system approach is developed. It incorporates the design of a differential precoder, a systematic convolutional encoder, and a signal set mapper. Trellis-coded L×4PSK, L×8PSK, and L×16PSK modulation schemes are found for 1⩽L⩽4 and a variety of code rates and decoder complexities, many of which are fully transparent to discrete phase rotations of the signal set. The new codes achieve asymptotic coding gains up to 5.85 dB     

Power-efficient layout of a fiber-optic multistar that permits log2 N concurrent baseband transmissions among N stations

A passive, single-hop, fiber-optic interconnection among N stations, each with two transmitters and one receiver, and a round-robin transmission schedule for it, which jointly permit log ₂ N concurrent noninterfering transmissions on a single wavelength, has recently been described. This is a substantial improvement over the previously known limit of two concurrent transmissions, but the layout of this interconnection poses a challenge in terms of both wiring complexity and path loss. A power-efficient implementation of this interconnection using several stages of balanced fiber-optic star couplers is presented here. With lossless components, path loss is N, the same as that of a single-star interconnection that permits only a single transmission at a time. Consequently, the high degree of parallelism translates into higher capacity. The required number of (2×2) star couplers is also very similar to that required for implementing a single N×X star     

Recursive algorithms for calculating the scattering from Nstrips or patches

Using the definition of recursive relations for the reflection operator for N strips or patches, two easily programmable recursive algorithms are developed to calculate the electromagnetic scattering by N strips or patches. One algorithm is for arbitrary excitation, and the other is for a fixed excitation. The recursive algorithms require the inversion of small matrices at each stage and hence are suitable for programming on smaller computers. If the N strips or patches are identical and equally spaced, symmetry can be exploited to speed up the algorithms. A program was developed to calculate scattering by N strips, and the result is shown to converge to scattering by a large strip when the N strips are contiguous     

On the Hamming distance properties of group codes

Under certain mild conditions, the minimum Hamming distance D of an (N, K, D) group code C over a non-abelian group G is bounded by D⩽N -2K+2 if K⩽N/2, and is equal to 1 if K>N/2. Consequently, there exists no (N, K, N-K+1) group code C over an non-abelian group G if 1<K<N. Moreover, any normal code C with a non-abelian output space has minimum Hamming distance equal to D=1. These results follow from the fact that non-abelian groups have nontrivial commutator subgroups. Finally, if C is an (N, K, D) group code over an abelian group G that is not elementary abelian, then there exists an (N, K, D) group code over a smaller elementary abelian group G'. Thus, a group code over a general group G cannot have better parameters than a conventional linear code over a field of the same size as G