An approximate performance analysis of interconnected token-passingrings

An analysis of the performance, in terms of average message delay, is presented for a system of interconnected ring networks. The system is hierarchical, with local rings served by a high-speed backbone ring through gateway queues. In both the local and the backbone rings, the access technique employed is token passing. Service disciplines, with and without priority, have been studied. In the former, priority is given to inter-ring traffic over local traffic. The study makes use of certain results on average delay in systems where the customer initiating a busy period receives special service for the M/G/1 queue with nonpreemptive priority and for the G/G/1 queue. The analysis, which involved several approximations, was verified by simulation     

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     

When are two geometric Goppa codes equal?

Sufficient and necessary conditions are obtained for which the geometric Goppa codes C(D,G) and C( D,H) are equal for two divisors G and H . In particular, it is proven that if G and H are two effective divisors of the same degree smaller than n-1, then C(D,G) and C(D,H ) are equal, if and only if G=H     

Counting the number of minimum cuts in undirected multigraphs

The problem of counting the number of cuts with the minimum cardinality in an undirected multigraph arises in various applications, such as testing the super-λ-ness of a graph, as described by F.T. Boesch (1986), and calculating upper and lower bounds on the probabilistic connectedness of a stochastic graph G in which edges are subject to failure. It is shown that the number |C( G)| of cuts with the minimum cardinality λ(G) in a multiple graph G=(V,E) can be computed in O(|E|+λ(G)|V|² +λ(G)|C(G)||V|) time     

Index system and separability of constant weight Gray codes

A number system is developed for the conversion of natural numbers to the codewords of the Gray code G(n,k) of length n and weight k, and vice versa. The focus is on the subcode G(n,k) of G(n) consisting of those words of G(n) with precisely k 1-bits, 0<k<n. This code is called the constant weight Gray code of length n and weight k. As an application sharp lower and upper bounds are derived for the value of |i-j|, where i and j are indices of codewords g_i and g_j of G(n,k) such that they differ in precisely 2 m bits     

Analysis of a modified Hebbian rule

A modified Hebbian rule using the matrix G=sgn(X ^TX) to induce a certain mapping is discussed. This mapping g is specified as soon as one has chosen the m×n matrix X over U to construct G by use of the above expression. The analysis of g relies on simple counting arguments and on the use of Stirling's approximation to obtain asymptotic results     

Performance of time diversity/convolutional coding scheme

A rate R=1/3 coding scheme, comprising a time diversity delay line and an R=2/3 convolutional code, is investigated. The bit error rate performance of the scheme on a binary symmetric channel and a burst error channel is presented     

Recent results in art galleries [geometry]

Two points in a polygon are called if the straight line between them lies entirely inside the polygon. The art gallery problem for a polygon P is to find a minimum set of points G in P such that every point in P is visible from some point of G. The author provides an introduction to art gallery theorems and surveys the recent results of the field. The emphasis is on the results rather than the techniques. Several new problems that have the same geometric flavor as art gallery problems are also examined     

Performance of a coded band-limited spread-spectrum multiple-accessscheme using channel sensing

The authors introduce and study the message delay and channel throughput behavior of a channel-sense multiple access/spread-spectrum (CSMA/SS) scheme. It is assumed that each net station can gain information as to whether the total number of ongoing transmissions exceeds a given threshold, M, or not. This entails, for example, the availability of an ancillary low-rate out-of-band or in-band signaling channel. A transmitting station will abort its transmission upon the reception of a signaling message indicating that the current number of transmissions exceeds the prescribed threshold. A random-access scheme is used to control the access of messages to the channel. Using derived performance equations, numerical results are presented illustrating the delay-throughout performance of such a CSMA/SS scheme. Key parameters involved in this performance analysis include: channel bandwidth, error-correction code capability, and propagation delay. Given an average message length, an activity threshold level M can be selected to yield the best delay-throughput performance characteristics     

A new interpretation of the average matched filter for MSK-typereceivers

The minimum-mean-square-error approximation to a generalized minimum-shift-keying (MSK) signal using an offset quadrature phase-shift keying waveform with an elementary pulse, g(t), is considered. It is shown that the optimum shape of G(t), γ(t), coincides with the average pulse of the generalized MSK signal. Therefore, γ(-t) is the impulse response of the corresponding average matched fiber     

Bayes estimation of reliability under a random environment governedby a Dirichlet prior

The reliability function of a component whose lifetime is exponentially distributed with a known parameter λ>0 is R (t|λ)=exp (-λt). If an environmental effect multiplies the parameter by a positive factor η, then the reliability function becomes R(t|η,λ)=exp(-ηλt). The authors assume that η itself is random, and its uncertainty is described by a Dirichlet process prior D(α) with parameter α=MG₀, where M>O represents an intensity of assurance in the prior guess, G₀, of the (unknown) distribution of η. Under squared error loss, the Bayes estimator of R(t|η,λ) is derived both for the no-sample problem and for a sample of size n. Using Monte Carlo simulation, the effects of n, M, G₀ on the estimator are studied. These examples show that: (a) large values of n lead to estimates where the data outweigh the prior, and (b) large values of M increase the contribution of the prior to the estimates. These simulation results support intuitive ideas about the effect of environment and lifetime parameters on reliability     

A linear-time algorithm to compute the reliability of planarcube-free networks

A planar graph G=(V,E) is a cube-free graph (CF graph) if it has no subgraph homomorphic to the cube. The cube is the graph whose vertices and edges are the vertices and edges of the three dimensional geometric cube. The all-terminal reliability of a graph G whose edges can fail (with known probabilities) is the probability that G is connected. The problem of computing the all-terminal reliability of a general graph is NP-hard. An O(| V|) time algorithm for computing the all-terminal reliability of CF graphs is presented     

An approximate analysis of a buffered CSMA/CD

A continuous-time carrier-sense multiple access with collision detection (CSMA/CD) system with a finite number of homogeneous stations, each possessing an infinite buffer, is analyzed. The system and each station is treated approximately as an independent M/G/1 queuing system. Since stations are mutually dependent, the interference from other stations is taken into account, in terms of the service-time distribution. With this analysis, the mean message delay can be numerically obtained. The stability of the system is also discussed. In addition, the upper-bound condition for the transmission interval is presented that keeps the system stable. It is concluded that the stability of the system becomes more sensitive to the retransmission interval as the number of stations increases     

On the design and performance of a 6-18 GHz three-tier matrixamplifier

A 3×3 matrix amplifier for the 6-18-GHz frequency band has been developed. Using MESFETs fabricated on VPE (vapor-phase epitaxial) material, gains of G=23.5±0.5 dB with a maximum reflection loss of RL=-10 dB were obtained from 5.2 to 18.7 GHz. Gain improvement to G=29.1±1.1 dB at a worst-case reflection loss of RL=-7.5 dB between 4.6 and 18.3 GHz when MBE (molecular-beam epitaxial) material was used for the MESFETs. In addition to the experimental results, important design considerations, especially in regard to the termination impedances of the idle ports, are discussed     

Performance analysis of the Josephson DC flip-flop

A linear analytical model of the Josephson DC flip-flop is proposed. The model describes both the Baechtold's and Hebard's flip-flops. The output signal line is treated as either a single inductance or a transmission line with a finite impedance. The former leads to the lumped model, while the latter leads to the distributed model. The lumped model gives the load condition for successful reset. This is given as a relationship between the CR and L/ R time constant, where C is the device capacitance, L is the load inductance, and R is the load resistance. The switching delay is also described as a linear function of the CR and L/R. With the distributed circuit model, the load condition for successful reset is Z₀⩾R. Minimum delay is obtained at Z₀=R. Grounding one end of the output signal line reduces the delay more than the nongrounded configuration. The scalar relationship of the switching delay and the power consumption to the design rule is discussed     

Perturbation analytic methodologies for design and optimization ofcommunication networks

Perturbation analysis (PA) is a technique for estimating performance sensitivities of queuing networks from direct observation of a single stochastic realization. It is used here to address such problems for communication networks. For a G/G/1 link model, it is shown that efficient PA algorithms can be used to estimate online the marginal delay of messages due to incoming flow perturbations. This information is used in a minimum-delay distribution algorithm to optimize routing. PA algorithms are extended to estimate throughput and mean delay sensitivities with respect to link capacities, including blocking phenomena due to finite queues. A window-flow-control model is considered, and experimental results of PA estimates for throughput sensitivities are provided. these estimates are seen to be accurate under heavy-load conditions, but, in general, enhanced PA techniques are required to incorporate more-complicated dynamic flow control and routing policies     

The bandwidth performance of a two-element adaptive array withtapped delay-line processing

The bandwidth performance of a two-element adaptive array with a tapped delay line behind each element is examined. It is shown how the number of taps and the delay between taps affect the bandwidth performance of the array. An array with two weights and one delay behind each element is found to yield optimal performance (equal to that obtained with continuous-wave interference) for any value of intertap delay between zero and T₉₀/B, where T ₉₀ is a quarter-wavelength delay time and B is the fractional signal bandwidth. Delays less that T₉₀ yield optimal performance but result in large array weights. Delays larger than T₉₀/B yield suboptimal signal-to-interference-plus-noise ratio when each element has only two weights. For delays between T₉₀/B and 4T₉₀/B , the performance is suboptimal with only two taps but approaches the optimal if more taps are added to each element. Delays larger than T₉₀/B result in suboptimal performance regardless of the number of taps used     

Decoding algebraic-geometric codes up to the designed minimumdistance

A simple decoding procedure for algebraic-geometric codes C _Ω(D,G) is presented. This decoding procedure is a generalization of Peterson's decoding procedure for the BCH codes. It can be used to correct any [(d*-1)/2] or fewer errors with complexity O(n³), where d * is the designed minimum distance of the algebraic-geometric code and n is the codelength     

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     

On the semiconductor laser logarithmic gain-current densityrelation

The simplified relation, α=G₀ In (η _iJ/J₀), between material gain α and current density J is shown to be a very good shape approximation, for quantum wells and bulk materials, essentially independent of the type of recombination processes present. Simulations show that for a given material system, G₀ decreases by only about 30% from pure electron-hole-recombination-dominated to pure Auger-recombination-dominated. A generic quantum-well situation is explored to reveal the density of states and recombination coefficient dependence of G₀ and to formulate simple estimates for G₀. The results were tested against published data for eight quantum-well diode lasers. The predicted values of G ₀ were generally found to be in agreement with experiments only for the wider gap diodes. The discrepancies were attributed in part to carrier induced absorption, and it is shown that the formalism can be modified in selected cases to incorporate this without changing the basic form of the gain. A new expression which relates the temperature dependence of the measured parameters to the characteristic temperature, T₀, is provided