Entropy and the law of small numbers

Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when S/sub n/=/spl Sigma//sub i=1//sup n/X/sub i/ is the sum of the (possibly dependent) binary random variables X/sub 1/,X/sub 2/,...,X/sub n/, with E(X/sub i/)=p/sub i/ and E(S/sub n/)=/spl lambda/, then D(P(S/sub n/)/spl par/Po(/spl lambda/)) /spl les//spl Sigma//sub i=1//sup n/p/sub i//sup 2/+[/spl Sigma//sub i=1//sup n/H(X/sub i/)-H(X/sub 1/,X/sub 2/,...,X/sub n/)] where D(P(S/sub n/)/spl par/Po(/spl lambda/)) is the relative entropy between the distribution of S/sub n/ and the Poisson (/spl lambda/) distribution. The first term in this bound measures the individual smallness of the X/sub i/ and the second term measures their dependence. A general method is outlined for obtaining corresponding bounds when approximating the distribution of a sum of general discrete random variables by an infinitely divisible distribution. Second, in the particular case when the X/sub i/ are independent, the following sharper bound is established: D(P(S/sub n/)/spl par/Po(/spl lambda/))/spl les/1//spl lambda/ /spl Sigma//sub i=1//sup n/ ((p/sub i//sup 3/)/(1-p/sub i/)) and it is also generalized to the case when the X/sub i/ are general integer-valued random variables. Its proof is based on the derivation of a subadditivity property for a new discrete version of the Fisher information, and uses a recent logarithmic Sobolev inequality for the Poisson distribution.     

Power allocation and routing in multibeam satellites with time-varying channels

We consider power and server allocation in a multibeam satellite downlink which transmits data to N different ground locations over N time-varying channels. Packets destined for each ground location are stored in separate queues and the server rate for each queue, i, depends on the power, p/sub i/(t), allocated to that server and the channel state, c/sub i/(t), according to a concave rate-power curve /spl mu//sub i/(p/sub i/,c/sub i/). We establish the capacity region of all arrival rate vectors (/spl lambda//sub 1/,...,/spl lambda//sub N/) which admit a stabilizable system. We then develop a power-allocation policy which stabilizes the system whenever the rate vector lies within the capacity region. Such stability is guaranteed even if the channel model and the specific arrival rates are unknown. Furthermore, the algorithm is shown to be robust to arbitrary variations in the input rates and a bound on average delay is established. As a special case, this analysis verifies stability and provides a performance bound for the choose-the-K-largest-connected-queues policy when channels can be in one of two states (ON or OFF ) and K servers are allocated at every timestep (K相似文献   

High-speed (/spl ges/1 GHz) electrical and optical adding, mixing, and processing of square-wave signals with a transistor laser

This letter reports the common-emitter operation (gain /spl beta/=/spl Delta/I/sub C///spl Delta/I/sub B/>1, 20/spl deg/C, I/sub B/=36 mA, /spl lambda/=970 nm) of a dual-input transistor laser, arranged with a separate base contact on either side of a single emitter, that adds, mixes, and processes high-speed square-wave electrical inputs and delivers separate electrical and optical outputs. Applying a square-wave electrical input X/sub 1/(t) to one base contact and X/sub 2/(t) at a second base input, we obtain, with the pulsewidth modulated because of mixing, an electrical output proportional to /spl beta//spl times/[X/sub 1/(t)+X/sub 2/(t)] and a laser output tracking the electrical output (h/spl nu//spl times/f[X/sub 1/(t)+X/sub 2/(t)]) and exceeding it in bandwidth (pulse sharpness).     

Asymptotic capacity of two-dimensional channels with checkerboard constraints

A checkerboard constraint is a bounded measurable set S/spl sub/R/sup 2/, containing the origin. A binary labeling of the Z/sup 2/ lattice satisfies the checkerboard constraint S if whenever t/spl isin/Z/sup 2/ is labeled 1, all of the other Z/sup 2/-lattice points in the translate t+S are labeled 0. Two-dimensional channels that only allow labelings of Z/sup 2/ satisfying checkerboard constraints are studied. Let A(S) be the area of S, and let A(S)/spl rarr//spl infin/ mean that S retains its shape but is inflated in size in the form /spl alpha/S, as /spl alpha//spl rarr//spl infin/. It is shown that for any open checkerboard constraint S, there exist positive reals K/sub 1/ and K/sub 2/ such that as A(S)/spl rarr//spl infin/, the channel capacity C/sub S/ decays to zero at least as fast as (K/sub 1/log/sub 2/A(S))/A(S) and at most as fast as (K/sub 2/log/sub 2/A(S))/A(S). It is also shown that if S is an open convex and symmetric checkerboard constraint, then as A(S)/spl rarr//spl infin/, the capacity decays exactly at the rate 4/spl delta/(S)(log/sub 2/A(S))/A(S), where /spl delta/(S) is the packing density of the set S. An implication is that the capacity of such checkerboard constrained channels is asymptotically determined only by the areas of the constraint and the smallest (possibly degenerate) hexagon that can be circumscribed about the constraint. In particular, this establishes that channels with square, diamond, or hexagonal checkerboard constraints all asymptotically have the same capacity, since /spl delta/(S)=1 for such constraints.     

Composite right/left-handed transmission line based compact resonant antennas for RF module integration

Several electrically small resonant antennas employing the composite right/left-handed transmission line (CRLH-TL) are presented for integration with portable RF modules. The proposed antenna designs are based on the unique property of anti-parallel phase and group velocity of the CRLH-TL at its fundamental mode. In this mode, the propagation constant increases as the frequency decreases, therefore, a small guided wavelength can be obtained at a lower frequency to provide the small /spl lambda//sub g//2 resonant length used to realize a compact antenna design. Furthermore, the physical size and the operational frequency of the antenna depend on the unit cell size and the equivalent transmission line model parameters of the CRLH-TL, including series inductance, series capacitance, shunt inductance and shunt capacitance. Optimization of these parameters as well as miniaturization techniques of the physical size of unit cell is investigated. A four unit-cell resonant antenna is designed and tested at 1.06 GHz. The length, width and height of the proposed antenna are 1/19/spl lambda//sub 0/, 1/23/spl lambda//sub 0/ and 1/83/spl lambda//sub 0/, respectively. In addition, a compact antenna using a 2-D three by three mushroom like unit cell arrangement is developed at 1.17 GHz, showing that an increased gain of 0.6 dB and higher radiation efficiency can be achieved over the first prototype antenna. The same design is applied in the development of a circularly polarized antenna operating at 2.46 GHz. A 116/spl deg/ beamwidth with axial ratio better than 3 dB is observed. The physical size of the proposed mushroom type small antenna and the circularly polarized antenna is 1/14/spl lambda//sub 0/ by 1/14/spl lambda//sub 0/ by 1/39/spl lambda//sub 0/ and 1/10/spl lambda//sub 0/ by 1/10/spl lambda//sub 0/ by 1/36/spl lambda//sub 0/, respectively.     

Compression mappings on primitive sequences over Z/(p/sup e/)

Let Z/(p/sup e/) be the integer residue ring with odd prime p/spl ges/5 and integer e/spl ges/2. For a sequence a_ over Z/(p/sup e/), there is a unique p-adic expansion a_=a_/sub 0/+a_/spl middot/p+...+a_/sub e-1//spl middot/p/sup e-1/, where each a_/sub i/ is a sequence over {0,1,...,p-1}, and can be regarded as a sequence over the finite field GF(p) naturally. Let f(x) be a primitive polynomial over Z/(p/sup e/), and G'(f(x),p/sup e/) the set of all primitive sequences generated by f(x) over Z/(p/sup e/). Set /spl phi//sub e-1/ (x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,1/(x/sub 0/, x/sub 1/,...,x/sub e-2/) /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,2/(x/sub 0/,x/sub 1/,...,x/sub e-2/) where /spl eta//sub e-2,1/ and /spl eta//sub e-2,2/ are arbitrary functions of e-1 variables over GF(p) and 2/spl les/k/spl les/p-1. Then the compression mapping /spl phi//sub e-1/:{G'(f(x),p/sup e/) /spl rarr/ GF(p)/sup /spl infin// a_ /spl rarr/ /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) is injective, that is, a_ = b_ if and only if /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl phi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/). Furthermore, if f(x) is a strongly primitive polynomial over Z/(p/sup e/), then /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl psi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) if and only if a_ = b_ and /spl phi//sub e-1/(x/sub 0/,...,x/sub e-1/) = /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/).     

Dependence of the neodymium random laser threshold on the diameter of the pumped spot

We experimentally studied the dependence of the threshold energy density E/sub th//S in Nd/sub 0.5/La/sub 0.5/Al/sub 3/(BO/sub 3/)/sub 4/ random laser on the diameter of the pumped spot d and found that at d/spl ges/130/spl mu/m, E/sub th//S is proportional to 1/d+const. This functional dependence is different from the one commonly expected in the case of diffusion, /spl prop/1/d/sup 2/+const. However, the obtained experimental dependence does not mean the failure of the diffusion model. Calculating the mean photon's residence time /spl tau//sub res//sup p/ (which photons, making their diffusion-like random walks, spend inside the gain volume) as the function of d and further assuming that E/sub th//S/spl prop/(/spl tau//sup p//sub res/)/sup -1/, we predicted the experimentally obtained functional dependence, /spl prop/1/d+const. The major difference between our model and that of and was in the boundary conditions.     

Order estimation of Markov chains

Estimators /spl chi//sub n/(X/sub 0/, X/sub 1/, ..., X/sub n/), are described which, when applied to an unknown stationary process taking values from a countable alphabet /spl chi/, converge almost surely to k in case the process is a kth-order Markov chain and to infinity otherwise.     

Broadband 180/spl deg/ bit phase shifter using a /spl lambda//2 coupled line and parallel /spl lambda//8 stubs

In this paper, a broadband 180/spl deg/ bit phase shifter using a new switched-network was presented. The new network is composed of a /spl lambda//2 coupled line and parallel /spl lambda//8 open and short stubs, which are shunted at the edge points of a coupled line, respectively. According to a desired phase shift, it provides a controllable phase dispersive characteristic by the proper determination of Z/sub m/,Z/sub s/, and R values. The 180/spl deg/ bit phase shifter operated at 3 GHz was fabricated and experimented using design graphs which provide the required Z/sub m/,Z/sub s/ values, and I/O match and phase bandwidths. The experimental performances showed broadband characteristics.     

Continuous-wave dual-wavelength lasing in a two-section vertical-cavity laser

A vertical-cavity surface-emitting laser with two monolithically grown cavities is presented. The three-terminal device allows current injection into the active regions of both cavities. Under various injection conditions, the device lases continuous wave on either one of the two longitudinal modes supported by the cavity, or on both wavelengths simultaneously. By using a constant injection current in the bottom cavity, and adjusting the current in the top cavity, the device shows all four possible emission states. These are the off states, lasing at the short wavelength /spl lambda//sub S/, at the long wavelength /spl lambda//sub L/, and at both /spl lambda//sub S/ and /spl lambda//sub L/ at the same time.     

A cavity-backed rectangular aperture antenna with application to a tilted fan beam array antenna

A rectangular aperture of A/sub x//spl times/A/sub y/, cut in the top conducting plate of a triplate transmission line and backed by a cavity, radiates a tilted beam off the direction normal to the aperture. The mechanism of the radiation is explained using the Poynting vector distribution above the aperture and the phase distribution of the electric field over the aperture. The tilt angle is calculated as a function of side length A/sub x/ for a representative value of A/sub y/=18 mm=0.747/spl lambda//sub 12.45/, where /spl lambda//sub 12.45/ is the wavelength at a test frequency of 12.45 GHz. A tilted beam of approximately 27/spl deg/ is realized at A/sub x//A/sub y/=8/9 with a gain of approximately 8 dB. Using this value of A/sub x//A/sub y/, an array antenna composed of rectangular cavity-backed aperture elements is investigated. The array forms a tilted fan beam without phase shifters. The frequency responses of the gain and input impedance are discussed.     

Characteristics of a new BBOS with an AlGaAs-/spl delta/(n/sup +/)-GaAs-InAlGaP collector structure

Two-terminal switching performances are observed in a new AlGaAs-GaAs-InAlGaP npn bulk-barrier optoelectronic switch (BBOS) with an AlGaAs-/spl delta/(n/sup +/)-GaAs-InAlGaP collector structure. The device shows that the switching action takes place from a low-current state to a high-current state through a region of negative differential resistance (NDR). The transition from either state to the other may be induced by an appropriate optical or electrical input. It is seen that the effect of illumination increases the switching voltage V/sub s/, holding voltage V/sub H/, and holding current I/sub H/, and decreases the switching current I/sub S/, which is quite different from other results reported. In addition, it possesses obvious NDR even up to 160/spl deg/C. This high-temperature performance provides the studied device with potential high-temperature applications.     

Reliable method for computing the phase shift of multiline LRL calibration technique

In this paper, a new method for computing the phase shift of lines used in the multiline line-reflect-line (m) calibration technique is presented. The new method is based on a matrix approach to determine the traveling wave /spl lambda/ and uses a reliable criterion to compute the constants a/c and b. The new method overcomes the problem of sign ambiguity of the eigenvalues /spl lambda//sub 1/ and /spl lambda//sub 2/, inherent to the classical method. Another advantage of the new method of computing the phase shift is that the physical length of lines is not needed. The new method computes the line phase shift from the knowledge of the traveling wave /spl lambda/, that is, without previous knowledge of the wave propagation constant.     

More results on the weight enumerator of product codes

We consider the product code C/sub p/ of q-ary linear codes with minimum distances d/sub c/ and d/sub r/. The words in C/sub p/ of weight less than d/sub r/d/sub c/+max(d/sub r//spl lceil/(d/sub c//g)/spl rceil/,d/sub c//spl lceil/(d/sub r//q)/spl rceil/) are characterized, and their number is expressed in the number of low-weight words of the constituent codes. For binary product codes, we give an upper bound on the number of words in C/sub p/ of weightless than min(d/sub r/(d/sub c/+/spl lceil/(d/sub c//2)/spl rceil/+1)), d/sub c/(d/sub r/+/spl lceil/(d/sub r//2)/spl rceil/+1) that is met with equality if C/sub c/ and C/sub r/ are (extended) perfect codes.     

Cyclic codes over GR(4/sup m/) which are also cyclic over /spl Zopf//sub 4/

Let GR(4/sup m/) be the Galois ring of characteristic 4 and cardinality 4/sup m/, and /spl alpha/_={/spl alpha//sub 0/,/spl alpha//sub 1/,...,/spl alpha//sub m-1/} be a basis of GR(4/sup m/) over /spl Zopf//sub 4/ when we regard GR(4/sup m/) as a free /spl Zopf//sub 4/-module of rank m. Define the map d/sub /spl alpha/_/ from GR(4/sup m/)[z]/(z/sup n/-1) into /spl Zopf//sub 4/[z]/(z/sup mn/-1) by d/spl alpha/_(a(z))=/spl Sigma//sub i=0//sup m-1//spl Sigma//sub j=0//sup n-1/a/sub ij/z/sup mj+i/ where a(z)=/spl Sigma//sub j=0//sup n-1/a/sub j/z/sup j/ and a/sub j/=/spl Sigma//sub i=0//sup m-1/a/sub ij//spl alpha//sub i/, a/sub ij//spl isin//spl Zopf//sub 4/. Then, for any linear code C of length n over GR(4/sup m/), its image d/sub /spl alpha/_/(C) is a /spl Zopf//sub 4/-linear code of length mn. In this article, for n and m being odd integers, it is determined all pairs (/spl alpha/_,C) such that d/sub /spl alpha/_/(C) is /spl Zopf//sub 4/-cyclic, where /spl alpha/_ is a basis of GR(4/sup m/) over /spl Zopf//sub 4/, and C is a cyclic code of length n over GR(4/sup m/).     

A minimum cost heterogeneous sensor network with a lifetime constraint

We consider a heterogeneous sensor network in which nodes are to be deployed over a unit area for the purpose of surveillance. An aircraft visits the area periodically and gathers data about the activity in the area from the sensor nodes. There are two types of nodes that are distributed over the area using two-dimensional homogeneous Poisson point processes; type 0 nodes with intensity (average number per unit area) /spl lambda//sub 0/ and battery energy E/sub 0/; and type 1 nodes with intensity /spl lambda//sub 1/ and battery energy E/sub 1/. Type 0 nodes do the sensing while type 1 nodes act as the cluster heads besides doing the sensing. Nodes use multihopping to communicate with their closest cluster heads. We determine them optimum node intensities (/spl lambda//sub 0/, /spl lambda//sub 1/) and node energies (E/sub 0/, E/sub 1/) that guarantee a lifetime of at least T units, while ensuring connectivity and coverage of the surveillance area with a high probability. We minimize the overall cost of the network under these constraints. Lifetime is defined as the number of successful data gathering trips (or cycles) that are possible until connectivity and/or coverage are lost. Conditions for a sharp cutoff are also taken into account, i.e., we ensure that almost all the nodes run out of energy at about the same time so that there is very little energy waste due to residual energy. We compare the results for random deployment with those of a grid deployment in which nodes are placed deterministically along grid points. We observe that in both cases /spl lambda//sub 1/ scales approximately as /spl radic/(/spl lambda//sub 0/). Our results can be directly extended to take into account unreliable nodes.     

Active-redundancy allocation in systems

An effective way of improving the reliability of a system is the allocation of active redundancies. Let X/sub 1/, X/sub 2/ be s-independent lifetimes of the components C/sub 1/ and C/sub 2/, respectively, which form a series system. Let us denote U/sub 1/ = min(max(X/sub 1/,X),X/sub 2/) and U/sub 2/ = min(X/sub 1/, max(X/sub 2/, X)), where X is the lifetime of a redundancy (say R) s-independent of X/sub 1/ and X/sub 2/. That is, U/sub 1/(U/sub 2/) denote the lifetime of a system obtained by allocating R to C/sub 1/(C/sub 2/) as an active redundancy. Singh and Misra (1994) considered the criterion where C/sub 1/ is preferred to C/sub 2/ for the allocation of R as active redundancy if P(U/sub 1/ > U/sub 2/) /spl ges/ P(U/sub 2/ > U/sub 1/). In this paper, we use the same criterion of Singh and Misra (1994). We investigate the allocation of one active redundancy when it differs depending on the component with which it is to be allocated. We also compare the allocation of two active redundancies (say R/sub 1/ and R/sub 2/) in two different ways; that is, R/sub 1/ with C/sub 1/ & R/sub 2/ with C/sub 2/, and viceversa. For this case, the hazard rate order plays an important role. We furthermore consider the allocation of active redundancy to k-out-of-n: G systems.     

Order statistics from a logistic distribution and applications to survival and reliability analysis

Joint moments involving arbitrary powers of order statistics are the main concern. Consider order statistics u/sub 1/ /spl les/ u/sub 2/ /spl les/ /spl middot//spl middot//spl middot/ /spl les/ u/sub k/ coming from a simple random sample of size n from a real continuous population where u/sub 1/ = x/sub r(1):n/ is order-statistic #r/sub 1/, u/sub 2/ = x/sub r(1)+r(2):n/ is order statistic #(r/sub 1/ + r/sub 2/), et al., and u/sub k/ = x/sub r(1)+/spl middot//spl middot//spl middot/+r(k):n/ is order statistic #(r/sub 1/ +/spl middot//spl middot//spl middot/+ r/sub k/). Product moments are examined of the type E[u/sub 1//sup /spl alpha/(1)/ /spl middot/ u/sub 2//sup /spl alpha/(2)//sub /spl middot/ /spl middot//spl middot//spl middot//spl middot//u/sub k//sup /spl alpha/(k)/] where /spl alpha//sub 1/, ..., /spl alpha//sub k/ are arbitrary quantities that might be complex numbers, and E[/spl middot/] denotes the s-expected value. Some explicit evaluations are considered for a logistic population. Detailed evaluations of all integer moments of u/sub 1/ and recurrence relations, recurring only on the order of the moments, are given. Connections to survival functions in survival analysis, hazard functions in reliability situations, real type-1, type-2 /spl beta/ and Dirichlet distributions are also examined. Arbitrary product moments for the survival functions are evaluated. Very general results are obtained which can be used in many problems in various areas.