On the effect of gap width on the admittance of solid circularcylindrical dipoles

A center-fed, solid, circular cylindrical dipole of radius a with feed gap of width 2d radiating in a circular waveguide of radius b terminated in infinite ground planes is rigorously analyzed by applying both the conservation-of-complex-power technique and the multiple-reflections technique. The analysis begins by studying the dependence of the dipole admittance on its feed gap width and on its length, 2l, as well as on b, with ka (k=2π/λ is the number) as a parameter. From the decreasing amplitudes of the almost periodic oscillations of these input admittances as b/λ is increased, the input admittances of dipoles radiating in free space (b→∞) are estimated using a variable-bound approach. The effect of gap width (d/a⩽5) for different lengths of dipoles (0.2⩽2l/λ⩽1) in free space and for different thicknesses (ka⩽0.2) is then established. The feed gap dependence for a half-wave dipole is also examined in detail for d /a⩽10 and ka⩽0.14     

Secret key agreement by public discussion from common information

The problem of generating a shared secret key S by two parties knowing dependent random variables X and Y, respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable Z, jointly distributed with X and Y according to some probability distribution P_XYZ, can also receive all messages exchanged by the two parties over a public channel. The goal of a protocol is that the enemy obtains at most a negligible amount of information about S. Upper bounds on H(S) as a function of P_XYZ are presented. Lower bounds on the rate H (S)/N (as N→∞) are derived for the case in which X=[X₁, . . ., X _N], Y=[Y₁, . . ., Y_N] and Z=[Z₁, . . ., Z_N] result from N independent executions of a random experiment generating X_i, Y_i and Z_i for i=1, . . ., N. It is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels, even when the enemy's channel is superior to the other two channels     

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     

Statistical inference under multiterminal rate restrictions: adifferential geometric approach

A statistical inference problem for a two-terminal information source emitting mutually correlated signals X and Y is treated. Let sequences Xⁿ and Yⁿ of n independent observations be encoded independently of each other into message sets M_X and M_Y at rates R₁ and R ₂ per letter, respectively. This compression causes a loss of the statistical information available for testing hypotheses concerning X and Y. The loss of statistical information is evaluated as a function of the amounts R₁ and R ₂ of the Shannon information. A complete solution is given in the case of asymptotically complete data compression, R₁, R₂→0 as n→∞. It is shown that the differential geometry of the manifold of all probability distributions plays a fundamental role in this type of multiterminal problem connecting Shannon information and statistical information. A brief introduction to the dually coupled e-affine and m-affine connections together with e -flatness and m-flatness is given     

Binary [18,11]2 codes do not exist-Nor do [64,53]2 codes

A binary, linear block code C with block length n and dimension n is commonly denoted by [n, k] or, if its minimum distance is d, by [n, k,d]. The code's covering radius r(C) can be defined as the smallest number r such that any binary column vector of length (n-k) can be written as a sum of r or fewer columns of a parity-check matrix of C. An [n,k] code with covering radius r is denoted by [n,k]r. R.A. Brualdi et al., (1989) showed that l(m,r) is defined to be the smallest n such that an [n,n-m]r code exists. l(m,2) is known for m⩽6, while it is shown by Brualdi et al. that 17⩽l(7,2)⩽19. This lower bound is improved by A.R. Calderbank et al. (1988), where it is shown that [17,10]2 codes do not exist. The nonexistence of [18,11]2 codes is proved, so that l(7,2)=19. l[7.2)=19 is established by showing that [18,11]2 codes do not exist. It is also shown that [64,53]2 codes do not exist, implying that l(11,2)⩾65     

New minimum distance bounds for certain binary linear codes

Let an [n, k, d]-code denote a binary linear code of length n, dimension k, and minimum distance at least d. Define d(n, k) as the maximum value of d for which there exists a binary linear [n, k, d]-code. T. Verhoeff (1989) has provided an updated table of bounds on d(n, k) for 1⩽k⩽n⩽127. The authors improve on some of the upper bounds given in that table by proving the nonexistence of codes with certain parameters     

The Zak transform and some counterexamples in time-frequencyanalysis

It is shown how the Zak transform can be used to find nontrivial examples of functions f, g∈L²(R) with f×g≡0≡F×G, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, k∈L²(R), h≠k, such that |h|=|k|, |H |=|K|. A similar construction is used to find an abundance of nontrivial pairs of functions h, k∈L² (R), h≠k, with |A_h |=|A_k| or with |W_h|=|W _k| where A_h, A_k and W_h, W_k are the ambiguity functions and Wigner distributions of h, k, respectively. One of the examples of a pair of h, k∈L²(R), h≠k , with |A_h|=|A_k| is F.A. Grunbaum's (1981) example. In addition, nontrivial examples of functions g and signals f₁≠f₂ such that f₁ and f₂ have the same spectrogram when using g as window have been found     

An improved inverse filtering method for parametric spectralestimation

For a wide-sense stationary process x(k), it is well known that its power spectrum P_xx(f) can be estimated by whitening the data with the inverse filter, V (z)=1/H(z), of the assumed minimum-phase rational model H(z) associated with x(k ). However, the initial conditions for computing the output e (k) of the recursive filter V(z) are unknown and must be preassigned. An improved inverse filtering method which simultaneously estimates the coefficients of V(z) as well as the initial conditions is proposed. The resultant power spectral estimator, with the initial conditions being estimated, outperforms that with the initial conditions wrongly set to zero as the time constant of V(z) is comparable to the number of data. Some simulation results which support the superior performance of the former are presented     

Asymptotic distortion spectrum of clipped, DC-biased, Gaussiannoise [optical communication]

Consider a zero-mean, stationary Gaussian process g(t ), to which a large positive constant A has been added. Define a distortion process h_A(t) as equal to g(t)+A when the latter is negative and equal to zero otherwise. The author calculates the power spectrum of the process h_A(t) asymptotically as A becomes large. The results have application for estimating the nonlinear-distortion power in the recovered signal when many frequency-multiplexed subcarriers collectively modulate a laser's output power, as would be the case for CATV transmission over an optical fiber. The process h_A(t) then models the nonlinear distortion caused by occasional clipping of the DC-biased laser input     

Identities and approximations for the weight distribution of q-ary codes

An explicit formula is derived that enumerates the complete weight distribution of an (n, k, d) linear code using a partially known weight distribution. An approximation formula for the weight distribution of q-ary linear (n, k , d) codes is also derived. It is shown that, for a given q-ary linear (n, k, d) code, the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q=q ^-(n-k) as u becomes large. The error term is a decreasing function of the minimum weight of the dual. The results are also valid for nonlinear (n, M, d) codes with the minimum weight of the dual replaced by the dual distance     

A general decoding technique applicable to replicated filedisagreement location and concatenated code decoding

Code symbols are treated as vectors in an r-dimensional vector space F^r over a field F. Given any ( n, k) linear block code over F with minimum distance d, it is possible to derive an (n, k) code with symbols over F^r, also with minimum distance d, which can correct any pattern of d-2 or fewer symbol errors for which the symbol errors as vectors are linearly independent. This is about twice the bound on the number of errors guaranteed to be correctable. Furthermore, if the error vectors are linearly dependent and d-2 or fewer in number, the existence of dependence can always be detected. A decoding techinque is described for which complexity increases no greater than as n ³, for any choice of code. For the two applications considered, situations are described where the probability of the error patterns being linearly dependent decreases exponentially with r     

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     

Asymptotic performance of M-ary orthogonal modulation ingeneralized fading channels

The asymptotic (M→∞) probability of symbol error P_e,_m for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E_b/N₀) and E_b is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E_b/N₀. These channels exist for all m⩾1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel     

1/f noise in MODFETs at low drain bias

The 1/f noise in normally-on MODFETs biased at low drain voltages is investigated. The experimentally observed relative noise in the drain current S_I/I² versus the effective gate voltage V_G=V_GS-V_off shows three regions which are explained. The observed dependencies are S_I/I²∝V_G ^m with the exponents m=-1, -3, 0 with increasing values of V_G. The model explains m =-1 as the region where the resistance and the 1/f noise stem from the 2-D electron gas under the gate electrode; the region with m=0 at large V_G or V_GS≅0 is due to the dominant contribution of the series resistance. In the region at intermediate V_G , m=-3, the 1/f noise stems from the channel under the gate electrode, and the drain-source resistance is already dominated by the series resistance     

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     

A dispersion formula satisfying recent requirements in microstripCAD

A dispersion formula ϵ^*_eff(f)=ϵ^* -{ϵ^*-ϵ^*_eff(0)}/{1+( f/f₅₀)^m}, for the effective relative permittivity ϵ^*_eff(f) of an open microstrip line is derived for computer-aided design (CAD) use. The 50% dispersion point (the frequency f₅₀ at which ϵ^*_eff(f₅₀)={ϵ ^*+ϵ^*_eff(0)}/2}) is used a normalizing frequency in the proposed formula, and an expression for f₅₀ is derived. To obtain the best fit of ϵ ^*_eff(f) to the theoretical numerical model, the power m of the normalized frequency in the proposed formula is expressed as a function of width-to-height ratio w/ h for w/h⩾0.7 and as a function of w /h, f₅₀, and f for w/h⩽0.7. The present formula has a high degree of accuracy, better than 0.6% in the range 0.1<w/h⩽10, 1<ϵ^*⩽128, and any height-to-wavelength ratio h/λ₀     

Bounding the capacity of saturation recording: the Lorentz modeland applications

The authors consider the problem of bounding the information capacity of saturation recording. The superposition channel with additive Gaussian noise is used as a model for recording. This model says that for a saturation input signal, x(t) (i.e., one that can assume only one of two levels), the output can be expressed as y(t)=x˜(t)+z(t ) where x˜(t) is a filtered version of the input x(t) and z(t) is additive Gaussian noise. The channel is described by the impulse response of the channel filter, h(t), and by the autocorrelation function of the noise. A specific example of such a channel is the differentiated Lorentz channel. Certain autocorrelation and spectrum expressions for a general Lorentz channel are derived. Upper and lower bounds on the capacity of saturation recording channels are described. The bounds are explicitly computed for the differentiated Lorentz channel model. Finally, it is indicated how the derived bounds can be applied in practice using physical measurements from a recording channel     

Evaluation of the quantization error in denominator-separable 2-Drecursive filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the computation of the infinite square sum J=Σ^∞_m=φΣ ^∞_n=φy² (m, n). A simple method is presented for evaluating J based on partial fraction expansion and using the residue method provided the Z-transform Y(Z₁, Z₂) of the sequence y(m, n) having quadrant support is a causal bounded input, bounded output (BIBO) stable denominator-separable rational function. The value of J is expressed as a sum of simple integrals which can easily be evaluated. The simple integrals are tabulated for ready reference. The proposed method is suitable for analytical as well as numerical computation and can easily be programmed     

Convergence of filters with applications to the Kalman-Bucy case

For each N, and each fixed time T, a signal X^N and a `noisy' observation Y^N are defined by a pair of stochastic difference equations. Under certain conditions (X^N, Y^N) converges in distribution to (X, Y, where dX(t)= f(t, X(t))dt+dV( t), dY(t)=g(t, X( t))dt+dW(t). Conditions are found under which convergence in distribution of the conditional expectations E{F(X^N)|Y^N} to E{F(X)|Y} follows, for every bounded continuous function F. The case in which the conditional expectations still converge but the limit is not E{ F(X)|Y} is also studied. In the situation where f and g are linear functions of X, an examination of this limit leads to a Kalman-Bucy-type estimate of X ^N which is asymptotically optimal and is an improvement on the usual Kalman-Bucy estimate     

New multilevel codes over GF(q)

Set partitioning is applied to multidimensional signal spaces over GF(q), i.e., GFⁿ¹(q) (n1⩽q ), and it is shown how to construct both multilevel block codes and multilevel trellis codes over GF(q). Multilevel (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d_min⩾d are presented. These codes use Reed-Solomon codes as component codes. Longer multilevel block codes are also constructed using q-ary block codes with block length longer than q+1 as component codes. Some quaternary multilevel block codes are presented with the same length and number of information symbols as, but larger distance than, the best previously known quaternary one-level block codes. It is proved that if all the component block codes are linear. the multilevel block code is also linear. Low-rate q-ary convolutional codes, word-error-correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multilevel trellis codes over GF(q) or binary-to-q-ary trellis codes