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     

Modulatable orthogonal sequences and their application to SSMAsystems

A set of N-1 orthogonal sequences of period N ² is proposed, where N is a natural number. Each orthogonal sequence proposed can be modulated by N complex numbers of absolute value 1, so the modulated sequence is also orthogonal. When N is an odd prime number, the absolute value of the cross-correlation function between any two of the N-1 orthogonal sequences is constant and satisfies the mathematical lower bound. This property of the cross-correlation function is not changed when each of the two orthogonal sequences is modulated by N complex numbers of absolute value 1. Two spread-spectrum multiple-access (SSMA) systems using these sequences are proposed. One system is an asynchronous SSMA system, using the proposed sequences unmodulated. The cochannel interference peak between any two channels in this system realizes the mathematical lower bound for an asynchronous SSMA system using a set of orthogonal sequences. The other system is a synchronous SSMA system without cochannel interference which uses the modulated form of the proposed sequences     

The inductance matrix of a multiconductor transmission line inmultiple magnetic media

A simple relationship between the inductance matrix and the auxiliary capacitance matrix is given. For a multiconductor transmission line consisting of N_c conducting cylinders in inhomogeneous media consisting of N_d homogeneous regions with permeabilities μ_i and permittivities ϵ _i, the inductance matrix [L] for the line is obtained by solving the magnetostatic problem of N_c conductors in N_d regions with permeabilities μ _i. The capacitance matrix [C] for the line is obtained by solving the electrostatic problem of N_c conductors in N_d regions with permittivities ϵ _i. It is shown that [L]=μ₀ϵ₀[C^'] ^-1, where [C^'] is the capacitance matrix of an auxiliary electrostatic problem of N_c conductors in N_d regions with relative permittivities set equal to the reciprocals of the relative permeabilities of the magnetostatic problem, i.e. ϵ^' _i/ϵ₀=μ₀/μ_i     

A parametric modeling of ionic channel current fluctuations usingthird-order statistics and its application to estimation of the kineticparameters of single ionic channels

The case where third-order cumulants of stationary ionic-channel current fluctuations (SICFs) are nonzero, and where SICFs are corrupted by an unobservable additive colored Gaussian noise that is independent of SICFs is considered. First, a virtual synthesizer that yields an output whose third-order cumulants are equivalent to those of SICFs on a specific slice is constructed. The synthesizer output is expressed by the sum of N_s-1 first-order differential equation systems, where N_s denotes the number of states of single ionic channels. Next, discretizing the synthesizer output, a discrete autoregressive [AR(N_s-1)] process driven by the sum of N_s-1 moving average (MA(N_s -2)) processes is derived. Then the AR coefficients are explicitly related to the kinetic parameters of single ionic channels, implying that the kinetic parameters can be estimated by identifying the autoregressive moving-average coefficients using the third-order cumulants. In order to assess the validity of the proposed modeling and the accuracy of parameter estimates, Monte Carlo simulation is carried out in which the closed-open and closed-open-blocked schemes are treated as specific examples     

A novel multilevel coherent optical system: 4-quadrature signaling

A novel multilevel coherent optical system is proposed. It is based on the exploitation of the property that the electromagnetic field propagating in a single-mode optical fiber can be represented by a four-dimensional vector whose components are the phase and quadrature terms of the two polarization components of the electrical field. This allows a wider use of the resources of the electromagnetic field for information transmission in order to obtain a spectrally efficient modulation format with a limited end. The net performance gain with respect to multilevel amplitude and phase modulation (N-APK) and N-PSK increases with an increase in the number of levels N. For instance, for N=32 the gain is 1.6 and 7.7 dB with respect to N-APK and N-PSK systems. The effect of laser phase noise on the system performance is evaluated     

Efficient fiber-optic structure with applications to sensor arrays

A fiber-optic structure which performs the functions of sensing and telemetry with a minimum of components and with efficient utilization of optical power is described. This structure, referred to as a recursive lattice array, requires N+1 couplers and N fiber sensing loops to realise N sensors. It is shown that for pulsed operation, the duty cycle approaches 100% and the maximum sampling rate is 1/(N+1)T, with T denoting the transit time of a single sensing loop. In the ideal (lossless) case, the power returned to the receiver from any sensor is -10 log 2N referred to the input, compared with previously reported, nonrecursive structures for which this figure-of-merit is -20 log N. Expressions for the optimum coupler tap ratios for two different cases of interest are derived: first, for the case in which all the coupler tap ratios are equal, and second, for the case where they may assume different values. The magnitudes of decaying recirculating terms which add noise to the desired primary returns from each sensor are estimated. Methods for reducing the magnitudes of the undesired terms are outlined     

A linear lightwave Benes network

The authors consider linear lightwave networks with a single waveband that have N inputs, each with a transmitter, and N outputs, each with a receiver, interconnected by optical links, broadcast stars, and wavelength-independent 2×2 switches. The transmitters and receivers can tune to C different wavelengths. The authors describe a rearrangeably nonblocking network that is a modification of the Benes network and uses transmitters that are fixed tuned and switches with two states. The network uses [1+o(1)] N/log₂(N/C) switches, which is shown to be nearly the minimum number. It is also shown that, if C =o(log N), then a rearrangeably nonblocking network requires [1+o(1)]Nlog₂N switches even if the switches have more than two states     

Fast cosine transform of Toeplitz matrices, algorithm andapplications

A fast algorithm for the discrete cosine transform (DCT) of a Toeplitz matrix of order N is derived. Only O(N log N)+O(M) time is needed for the computation of M elements. The storage requirement is O(N). The method carries over to other transforms (DFT, DST) and to Hankel or circulant matrices. Some applications of the algorithm are discussed     

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     

On minimizing the peak-to-average power ratio for the sum of N sinusoids

A new derivation is presented of a previously known relationship for phasing N equal-amplitude, equally spaced (in frequency) sinusoids so that the peak-to-average power ratio of their sum is 2.6 dB. The method of derivation provides intuitive insight into why this result is possible, and shows that the 2.6 dB figure is obtained independently of N as long as N is large. Any phase or frequency modulation can be applied simultaneously to all N sinusoids without altering this result     

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     

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=∞     

Edge-connected, crossed-electrode array for two-dimensionalprojection and beamforming

A novel geometry for planar structures which allows simpler implementation and construction while trading off higher signal processing costs and possible reduced performance is introduced. A geometry for array construction which uses two sets of orthogonal striped electrodes is discussed. The basic operation principles of the geometry are given. While obtaining N² intersecting points in a two-dimensional structure, only 2N control points are required. Thus, N² active elements are controlled with 2N degrees of freedom, which simplifies both implementation and data handling. This gain in simplicity is traded off against reduced performance when used as a projector and increased signal processing when used in beamforming if the process is carried out in a two-step process. The limitations of the crossed-electrode geometry and discussed, and a theory for operation as a projector and a receiver is presented     

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     

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%     

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     

Systolic arrays for the discrete Hartley transform

Recently, R.N. Bracewell (1983) introduced the discrete Hartley transform (DHT) as an alternative to the discrete Fourier transform (DFT). Two linear systolic array models for the (DHT) are derived. One model requires O(2N-1) in the computational phase and O(N) in the preloading phase. The other model requires O(2N-1) in the computational phase and O(N) in the output phase. A square systolic array for two-dimensional DHT is also constructed by combining the individual advantages of each model. The CORDIC algorithm is proposed as an alternative to conventional multipliers. To speed up the systolic array, two-level pipelining with CORDIC is also possible     

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     

A selective ARQ protocol with a finite-length buffer

Of the automatic-repeat-request (ARQ) techniques commonly used in communication systems, selective protocols, while the most efficient, have the notable drawback of requiring large buffers at the receiver side. A selective ARQ protocol with a finite-length buffer is described. If N is the number of codewords transmittable in the round-trip delay, the protocol requires a buffer length N+N_a , N_a⩾2 being an integer. A lower bound on the throughput of the protocol is derived. It achieves higher throughputs than similar schemes giving results comparable to those for selective protocols with infinite-length buffer for high error rates in the communication channel     

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