Multireception probabilities for FH/SSMA communications

Exact expressions for the probabilities P(l,m-l/k) of l correct packet receptions and m-l erroneous ones, out of total k packets contending in a slot, are presented for the case of frequency-hopped spread-spectrum random-access slotted networks employing random frequency hopping patterns. These expressions are difficult to evaluate numerically for values of m>3. However, their numerical analysis indicates that under light traffic conditions these probability values are very close to the ones provided by the independent receiver operation assumption, under which the distribution of multireception obeys the binomial law     

Asymptotic results for partial concentrators

Various switching network construction advantageously use modules known as partial concentrators. A partial concentrator is an n-input, m-output, single-stage switching device in which each input has access to some but not all of the outputs. A partial concentrator is said to have capacity c, if, for any k⩽c inputs, there exist k disjoint paths from the k inputs to some set of k outputs. Here, capacity values achievable for large n when each input has access to exactly M outputs, are considered. For a partial concentrator in which each input has access to exactly M outputs, it is shown that the cost ratio can be made arbitrarily small for any fixed M⩾2. In addition, it is shown that the rate of decrease of the cost ratio with increasing n is logarithmic for M=2, and polynomial for M⩾3     

The aperture admittance of a circumferential slot in a circularcylinder

A circumferential slot in an infinitely long cylinder when fed with a tangential electric field is considered. Parseval's theorem, in which Fourier integrals appear, is used to express the aperture admittance as the integral from zero to infinity of an infinite series. Recognizing that the first two terms of this infinite series have a nonintegrable singularity when the variable of integration w is equal to the wavenumber k, the authors distort slightly the contour of integration to avoid k. The terms of the infinite series are then approximated when w is close to k. A combination of numerical and analytical schemes employing both large and small argument approximations of Hankel functions is used to perform the integration. It has been found that these integration schemes work very well, and a simple and fast algorithm has resulted     

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=∞     

On the influence of coding on the mean time to failure fordegrading memories with defects

The application of a combined test-error-correcting procedure is studied to improve the mean time to failure (MTTF) for degrading memory systems with defects. The degradation is characterized by the probability p that within a unit of time a memory cell changes from the operational state to the permanent defect state. Bounds are given on the MTTF and it is shown that, for memories with N words of k information bits, coding gives an improvement in MTTF proportional to (k/n) N(d_min^-2)/(d_min ^-1), where d_min and (k/n) are the minimum distance and the efficiency of the code used, respectively. Thus the time gain for a simple minimum-distance-3 is proportional to N^-1. A memory word test is combined with a simple defect-matching code. This yields reliable operation with one defect in a word of length k+2 at a code efficiency k/(k+2)     

Admittance of an isolated waveguide-fed slot radiating betweenbaffles using a spectrum of two-dimensional solutions

An efficient method of computing resonant length and admittance characteristics of an isolated broad-wall shunt slot radiating between baffles of finite height is presented. The outer three-dimensional (3D) field problem associated with this geometry is reduced to a two-dimensional (2D) one via a Fourier transformation with respect to the longitudinal z direction. For each value of the longitudinal wave number k_z an integral equation is solved for the E field in the mouth of the plates using the method of moments. This procedure is repeated for several discrete values of k_z, to obtain a spectrum of 2D solutions which are then inverse-transformed to construct the 3D solution in the spatial domain for the exterior baffle region and the half space. The slot aperture field is determined by the conventional moment method solution to the integral equation that enforces the continuity of the H field across the slot. Scattering properties of the slot are then deduced. Numerical results for the resonant length and resonant conductance are presented. Computer results are found to be in good agreement with experimentally measured data     

Optimal designs of{k,n-k+1}-out-of-n:F systems(subject to 2 failure modes)

The problem of achieving optimal system size (n) for {k,n-k+1}-out-of-n systems, assuming that failure may take either of two forms, is studied. It is assumed that components are independently identically distributed (i.i.d.) and that the two kinds of system failures can have different costs. The optimal k or n that maximizes mean system-profit is determined, and the effect of system parameters on the optimal k or n is studied. It is shown that there does not exist a pair (k,n) maximizing the mean system-profit     

An efficient non-recursive algorithm for computing the reliabilityof k-out-of-n systems

An algorithm for computing the reliability of k-out-of- n systems is proposed. It is simple, easy to implement on a computer, time and memory efficient, and good for numerical computation. The memory complexity is O(n-k), and for a given value of n-k the computation time is proportional to n . Its FORTRAN implementation is presented     

A replacement policy maximizing MTTF of a system with several spareunits

A replacement policy is considered that maximizes mean time-to-failure (MTTF) of a system with N spare units. The optimum replacement time of a system with k spares (k=1, 2, ..., N) is derived successively from MTTF with k-1 spares by induction. The maximum MTTF is approximately given by a reciprocal of the hazard rate     

Reliability of a consecutivek-out-of-r-from-n:F system

The reliability of the consecutive k-out-of-r-from-n:F system is studied. For k=2 an explicit solution is given for n components in line or in cycle in the i.i.d. case. For k⩾3 sharp lower and upper bounds are given for the reliability of the system and demonstrated for different values of n, k, r, p. These bounds are exact for r=n, n-1, n-2, n-3, and for these values the exact analytic solution is also given     

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     

Pseudocyclic maximum-distance-separable codes

The (n, k) pseudocyclic maximum-distance-separable (MDS) codes modulo (xⁿ- a) over GF(q) are considered. Suppose that n is a divisor of q+1. If n is odd, pseudocyclic MDS codes exist for all k. However, if n is even, nontrivial pseudocyclic MDS codes exist for odd k (but not for even k) if a is a quadratic residue in GF(q), and they exist for even k (but not for odd k) if a is not a quadratic residue in GF(q). Also considered is the case when n is a divisor of q-1, and it is shown that pseudocyclic MDS codes exist if and only if the multiplicative order of a divides (q-1)/n, and that when this condition is satisfied, such codes exist for all k. If the condition is not satisfied, every pseudocyclic code of length n is the result of interleaving a shorter pseudocyclic code     

Calculation of the binomial survivor function [reliabilityapplications]

A method is presented for calculating the binomial SF (cumulative binomial distribution), binfc(k;p,n), especially for a large n, beyond the range of existing tables, where conventional computer programs fail because of underflow and overflow, and Gaussian or Poisson approximations yield insufficient accuracy for the purpose at hand. This method is used to calculate and sum the individual binomial terms while using multiplication factors to avoid underflow; the factors are then divided out of the partial sum whenever it has the potential to overflow. A computer program uses this technique to calculate the binomial SF for arbitrary inputs of k, p, and n. Two other algorithms are presented to determine the value of p needed to yield a specified SF for given values of k and n and calculate the value where p=SF for a given k and n. Reliability applications of each algorithm/program are given, e.g. the value of p needed to achieve a stated k-out-of-n :G system reliability and the value of p for which k -out-of-n:G system reliability equals p     

New lower bounds for covering codes

Some new lower bounds on |C| for a binary linear [n, k]R code C with n+1=t(R +1)-r(0⩽r<R+1, t>2 odd) or with n+1=t(R+1)-1(t>2 even) are obtained. These bounds improve the sphere covering bound considerably and give several new values and lower bounds for the function t[n, k], the smallest covering radius of any [n, k] code     

Optimum codes of dimension 3 and 4 over GF(4)

n_q(k,d), the length of a q-ary optimum code for given k and d, for q=4 and k=3, 4 is discussed. The problem is completely solved for k=3, and the exact value of n₄(4,d) is determined for all but 52 values of d     

Markov-modulated flow model for the output queues of a packetswitch

The output queues of an M×N packet switch are studied using a Markov-modulated flow model. The switching element is a central server which sequentially routes packets from the inputs to the outputs. The focus is on systems in which the server speed is such that the bulk of the queuing takes place in the output queues. The conventional point process approach neglects the impact of switching and transmission time. An attempt is made to account for these finite system speeds by using a Markov-modulated continuous flow to approximate the arrival process to an output queue. This model captures the dependency between arrivals at different outputs and reflects the fact that packet arrivals and departures are not instantaneous. The output queue content distribution is obtained, for both infinite and finite buffer systems, from the spectral expansion of the solution of a system of differential equations. Numerical examples and comparisons with the results of an M/M/1 approximation are presented     

On the optimal design of k-out-of-n:G subsystems

For a k-out-of-n:G subsystem, the mathematical determination of the most economical number of components in the subsystem is sought. Optimal values of k (for fixed n) and n (for fixed k), which minimize the mean total cost of k-out-of-n:G subsystems, are given. A numerical example illustrates the results     

Coset correlation of m-sequences

It is well-known that there exists a unique shift l of the m-sequence S(k) such that the value of S₀(k)=S(k+l) is only determined by the cyclotomic coset to which k belongs. A measure called the `coset correlation' is introduced. It is proven that the shift l can be determined by the coset correlation     

Distribution of the lifetime of consecutive k-within-m-out-of-n:F systems

The distribution of the lifetime (MTTF) of any consecutive k -within-m-out-of-n:F system, with independent exponentially distributed component lifetimes, is shown to be a convex combination of the distributions (MTTFs) of several convolutions of independent random variables, where each convolution represents a distinct path in the evolution of the system's history, and where in each convolution all but the last random variable is exponential. The last random variable in each convolution is either a zero lifetime or the lifetime of several disjoint consecutive k_i within m_i-out-of-n:F systems in series with each k_i<k, each m_i<m, and each n_i<n. This enables the calculations to proceed recursively. Calculations are facilitated by the symmetric nature of the convex combination