On single-sample robust detection of known signals with additive unknown-mean amplitude-bounded random interference--II: The randomized decision rule solution (Corresp.)

A randomized decision rule is derived and proved to be the saddlepoint solution of the robust detection problem for known signals in independent unknown-mean amplitude-bounded noise. The saddlepoint solutionphi^{0}uses an equaUy likely mixed strategy to chose one ofNBayesian single-threshold decision rulesphi_{i}^{0}, i = 1,cdots , Nhaving been obtained previously by the author. These decision rules are also all optimal against the maximin (least-favorable) nonrandomized noise probability densityf_{0}, wheref_{0}is a picket fence function withNpickets on its domain. Thee pair(phi^{0}, f_{0})is shown to satisfy the saddlepoint condition for probability of error, i.e.,P_{e}(phi^{0} , f) leq P_{e}(phi^{0} , f_{0}) leq P_{e}(phi, f_{0})holds for allfandphi. The decision rulephi^{0}is also shown to be an eqoaliir rule, i.e.,P_{e}(phi^{0}, f ) = P_{e}(phi^{0},f_{0}), for allf, with4^{-1} leq P_{e}(phi^{0},f_{0})=2^{-1}(1-N^{-1})leq2^{-1} , N geq 2. Thus nature can force the communicator to use an {em optimal} randomized decision rule that generates a large probability of error and does not improve when less pernicious conditions prevail.     

An estimate of the variation of a band-limited process

Upper and lower bounds are established for the mean-square variation of a stationary processX(t)whose power spectrum is bounded byomega_{c}, in terms of its average powerP_{0}and the average powerP_{1}of its derivative. It is shown thatleft( frac{2}{pi} right)^{2} P_{1} tau^{2} leq E {|X(t+tau )-X(t)|^{2}} leq P_{1} tau^{2} leq omega_{c}^{2}P_{0}tau^{2}where the upper bounds are valid for anytauand the lower bound fortau < pi / omega_{c}. These estimates are applied to the mean-square variation of the envelope of a quasi-monochromatic process.     

An approximation to the weight distribution of binary primitive BCH codes with designed distances 9 and 11 (Corresp.)

Recently Kasami {em et al.} presented a linear programming approach to the weight distribution of binary linear codes [2]. Their approach to compute upper and lower bounds on the weight distribution of binary primitive BCH codes of length2^{m} - 1withm geq 8and designed distance2t + 1with4 leq t leq 5is improved. From these results, the relative deviation of the number of codewords of weightjleq 2^{m-1}from the binomial distribution2^{-mt} left( stackrel{2^{m}-1}{j} right)is shown to be less than 1 percent for the following cases: (1)t = 4, j geq 2t + 1andm geq 16; (2)t = 4, j geq 2t + 3and10 leq m leq 15; (3)t=4, j geq 2t+5and8 leq m leq 9; (4)t=5,j geq 2t+ 1andm geq 20; (5)t=5, j geq 2t+ 3and12 leq m leq 19; (6)t=5, j geq 2t+ 5and10 leq m leq 11; (7)t=5, j geq 2t + 7andm=9; (8)t= 5, j geq 2t+ 9andm = 8.     

Bent-function sequences

In this paper we construct a new family of nonlinear binary signal sets which achieve Welch's lower bound on simultaneous cross correlation and autocorrelation magnitudes. Given a parameternwithn=0 pmod{4}, the period of the sequences is2^{n}-1, the number of sequences in the set is2^{n/2}, and the cross/auto correlation function has three values with magnitudesleq 2^{n/2}+1. The equivalent linear span of the codes is bound above bysum_{i=1}^{n/4}left(stackrel{n}{i} right). These new signal sets have the same size and correlation properties as the small set of Kasami codes, but they have important advantages for use in spread spectrum multiple access communications systems. First, the sequences are "balances," which represents only a slight advantage. Second, the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly "hopped" from sequence to sequence for code division multiple access operation. Most importantly, the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it. This high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing.     

On Parallelepiped-Shaped Passbands for Multidimensional Nonseparable ${bf M}$th-Band Low-Pass Filters

The “shape” of the desired frequency passband is an important consideration in the design of nonseparable multidimensional ($M$ -D) filters in $M$-D multirate systems. For $M$-D ${bf M}$th-band filters, the passband shape should be chosen such that the ${bf M}$th-band constraint is satisfied. The most commonly used shape of the passband for $M$-D ${bf M}$ th-band low-pass filters is the so-called symmetric parallelepiped (SPD) ${rm SPD}(pi {bf M}^{- {rm T}})$ . In this paper, we consider the more general parallelepiped passband ${rm SPD}(pi {bf L} ^{rm T})$, and derive conditions on $ {bf L} $ such that the ${bf M}$ th-band constraint is satisfied. This result gives some flexibility in designing $M$-D ${bf M}$th-band filters with parallelepiped shapes other than the commonly used case of $ {bf L} = {bf M}^{- 1}$. We present design examples of 2-D ${bf M}$th-band filters to illustrate this flexibility in the choice of $ {bf L} $.      

A new class of codes meeting the Griesmer bound

An infinite sequence ofk-dimensional binary linear block codes is constructed with parametersn=2^{k}+2^{k-2}-15,d=2^{k-1}+2^{k-3}-8,k geq 7. Fork geq 8these codes are unique, while there are five nonisomorphic codes fork=7. By shortening these codes in an appropriate way, one finds codes meeting the Griesmer bound for2^{k-1}+2^{k-3}-15 leq d leq 2^{k-1}+2^{k-3}-8; k geq 7.     

Blue-green atomic photodissociation lasers in group IIb: Zn, Cd, and Hg

Four new laser lines, two in atomic Zn at 481.1 and 472.2 nm and two in atomic Cd at 508.6 and 480.0 nm, are reported. The analog laser lines in Hg at 546.1 and 435.8 nm are studied further. These lines correspond to the transitionsn^{3}S_{1} rightarrow (n-1)^{3}P_{2}andn^{3}S_{1} rightarrow (n-1)^{3}P_{1}of the triplet system of the metals. The medium in the three cases is MI2(M= Zn, Cd, or Hg) vapor at about 1 mbar and the pump is a KrF laser at 248 nm. The blue-green superfluorescent pulse power is in the kilowatt range, with a pulse duration of about 1 ns. The pumping process must involve more than one photon. A sequential three-photon pumping process is proposed for the three cases.     

Further classifications of codes meeting the Griesmer bound (Corresp.)

For any(n, k, d)binary linear code, the Griesmer bound says thatn geq sum_{i=0}^{k-1} lceil d/2^{i} rceil, wherelceil x rceildenotes the smallest integergeq x. We consider codes meeting the Griesmer bound with equality. These codes have parametersleft( s(2^{k} - 1) - sum_{i=1}^{p} (2^{u_{i}} - 1), k, s2^{k-1} - sum_{i=1}^{p} 2^{u_{i} -1} right), wherek > u_{1} > cdots > u_{p} geq 1. We characterize all such codes whenp = 2oru_{i-1}-u_{i} geq 2for2 leq i leq p.     

The photoionization cross sections of the Rg*2[3Σ+u] excimer states for Ne*2, Ar*2, and Kr*2

Based on the recently determined Rydberg series of the³Sigma+_{u}excimer states of Ne*2, Ar*2and Kr*2, the photoionization cross sections of these molecules are calculated using a single-channel quantum defect method. These cross sections are found to differ considerably from those of the asymptotic metastable atomic Rg*(ns^{3}P_{2}) states, but are in good agreement with recently reported experiments at isolated wavelengths. The implications of these results for VUV and XUV lasers are discussed.     

Multiple-burst error-correcting cyclic product codes (Corresp.)

LetCbe the cyclic product code ofpsingle parity check codes of relatively prime lengthsn_{1}, n_{2},cdots , n_{p} (n_{1} < n_{2} < cdots < n_{p}). It is proven thatCcan correct2^{P-2}+2^{p-3}-1bursts of lengthn_{1}, andlfloor(max{p+1, min{2^{p-s}+s-1,2^{p-s}+2^{p-s-1}}}-1)/2rfloorbursts of lengthn_{1}n_{2} cdots n_{s} (2leq s leq p-2). Forp=3this means thatCis double-burst-n_{1}-correcting. An efficient decoding algorithm is presented for this code.     

Weight enumerator for second-order Reed-Muller codes

In this paper, we establish the following result. Theorem:A_i, the number of codewords of weightiin the second-order binary Reed-Muller code of length2^mis given byA_i = 0unlessi = 2^{m-1}or2^{m-1} pm 2^{m-l-j}, for somej, 0 leq j leq [m/2], A_0 = A_{2^m} = 1, and begin{equation} begin{split} A_{2^{m-1} pm 2^{m-1-j}} = 2^{j(j+1)} &{frac{(2^m - 1) (2^{m-1} - 1 )}{4-1} } \ .&{frac{(2^{m-2} - 1)(2^{m-3} -1)}{4^2 - 1} } cdots \ .&{frac{(2^{m-2j+2} -1)(2^{m-2j+1} -1)}{4^j -1} } , \ & 1 leq j leq [m/2] \ end{split} end{equation} begin{equation} A_{2^{m-1}} = 2 { 2^{m(m+1)/2} - sum_{j=0}^{[m/2]} A_{2^{m-1} - 2^{m-1-j}} }. end{equation}     

Diffraction by a circular aperture in a unidirectionally conducting screen

The diffraction of a normally incident plane electromagnetic wave with wave numberkby a circular aperture of radiusain a unidirectionally conducting plane screen of zero thickness and infinite extent is considered. In the limit of largeka, the ratio of the transmission cross section to the geometrical optics valuepi a^{2}, is found up to the order(ka)^{-3/2}.     

Electromagnetic reflection from an extended turbulent medium: Cumulative forward-scatter single-backscatter approximation

The backscatter cross sectionQfor high-frequency irradiated turbulent dielectric media, many mean free pathsL_{1}wide, is computed. The lengthL_{1}is the distance into the medium over which the mean electric field decreases in amplitude by a factore^{-1}. Previous calculations have always been restricted toL ll L_{1}. It is found thatQincreases from the Born approximationQ = Q_{1}for medium widthL ll L_{1}toQ = 2Q_{1}forL gg L_{1}, and the theory is valid as long asL ll (kL_{0})^{5/3} L_{1}, a significant improvement over the Born approximation, when the macroscaleL_{0}is much larger than the wavelength2_{pi}k^{-1}. The improvement is due to incorporation of the dominant effects of cumulative forward scattering in the local electric field in the medium. A rigorous and a heuristic derivation are given. The transitional behavior is discussed and a simple physical interpretation is given.     

Excitation cross section of some of the states of NE II, Ar II, and KR II by electron collision

The sudden perturbation method has been used to calculate the excitation cross section of some of the states of Ne II, Ar II, and Kr II by high energy electrons. In this method, the ground state of the noble gas atom, after a collision with a fast electron, is considered to lose one of its valence electrons in a time shorter than the relaxation time of the atom. The resulting configuration is then assumed to be a|(p^{5}) ^{2}P_{j}ranglestate withJ = 3/2or 1/2, with the remaining five valence electrons having the same radial coordinates as in the original|(p^{6})^{1}S_{0}ranglestate of the neutral atom. The configuration|(p^{5})^{2}P_{j}rangleis then expanded in terms of the ionic wave functions having the form of|(p^{4})bar{L}bar{S}, nl', LSJrangle, wherebar{L},bar{S}designate the total orbital angular momentum and the total spin angular momentum of the core electrons,l'is the orbital angular momentum of the excited running electron, andLSJdesignates the final orbital, spin, and total angular momenta of the atom. The coefficients of the expansion are calculated in terms of the coefficients of fractional parentage and3-jsymbols. The radial wave functions for the neutral atoms and their excited ionic states for the involved radial integrals are obtained by using a computer program giving the self-consistent Hartree-Fock wave functions in the Slater approximation. Since no experimental measurements for the excitation cross sections with fast electrons are given, the results of the calculations are indirectly compared with the available work reported on the pulsed Ar II laser. Population of various excited ionic states is calculated assuming a uniform energy distribution of electrons having 1.8 times the ionization threshold of argon, and the results are compared with experimental data reported in the literature.     

The Electrical and Interfacial Properties of Metal-High-$kappa$ Oxide-Semiconductor Field-Effect Transistors With $hbox{LaAlO}_{3}$ Gate Dielectric

$hbox{LaAlO}_{3}$ is a promising candidate for gate dielectric of future VLSI devices. In this letter, n-channel metal–oxide–semiconductor field-effect transistors with $hbox{LaAlO}_{3}$ gate dielectric were fabricated, and the electron mobility degradation mechanisms were studied. The leakage current density is $hbox{7.6} times hbox{10}^{-5} hbox{A/cm}^{2}$ at $-!$ 1 V. The dielectric constant is 17.5. The surface-recombination velocity, the minority-carrier lifetime, and the effective capture cross section of surface states were extracted from gated-diode measurement. The rate of threshold voltage change with temperature $(Delta V_{T} / Delta T)$ from 11 K to 400 K is $-!$ 1.51 mV/K, and the electron mobility limited by surface roughness is proportional to $E_{rm eff}^{-0.66}$.      

Unconditional Stability Boundaries of a Three-Port Network

An analytical approach for acquiring the explicit expressions of the boundaries concerning the unconditional stability regions of a three-port network is presented. This approach begins with the expressions for the input reflection coefficients $S_{11}^{prime}$ and $S_{22}^{prime}$ at ports 1 and 2 of a three-port network having port 3 terminated with $Gamma_{3}$ . $vert S_{11}^{prime}vert=1$ and $vert S_{22}^{prime}vert=1$ then give two stability circles in the $Gamma_{3}$-plane. One can graphically determine that the tangent point of these two stability circles is on the boundary of the unconditional stability region for the terminating port. The explicit expressions of the boundary for port 3 are then acquired. This procedure may be followed for the other two ports in order to fully characterize the unconditional stability boundaries of a three-port network. In addition, issues pertaining to uniqueness and continuity in the plotting of unconditional stability boundaries are addressed. Using the Agilent Advanced Design System software tool, the derived expressions of the unconditional stability boundary for the terminating port and related extreme phase values of reflection coefficients of the other two ports are implemented. These derived expressions can then enhance the computer-aided capability on the stability analysis of a three-port network and provide useful information for the microwave circuit designer.      

On certain projective geometry codes (Corresp.)

LetVbe an(n, k, d)binary projective geometry code withn = (q^{m}-1)/(q - 1), q = 2^{s}, andd geq [(q^{m-r}-1)/(q - 1)] + 1. This code isr-step majority-logic decodable. With reference to the GF(q^{m}) = {0, 1, alpha , alpha^{2} , cdots , alpha^{n(q-1)-1} }, the generator polynomialg(X), ofV, hasalpha^{nu}as a root if and only ifnuhas the formnu = i(q - 1)andmax_{0 leq l < s} W_{q}(2^{l} nu) leq (m - r - 1)(q - 1), whereW_{q}(x)indicates the weight of the radix-qrepresentation of the numberx. LetSbe the set of nonzero numbersnu, such thatalpha^{nu}is a root ofg(X). LetC_{1}, C_{2}, cdots, C_{nu}be the cyclotomic cosets such thatSis the union of these cosets. It is clear that the process of findingg(X)becomes simpler if we can find a representative from eachC_{i}, since we can then refer to a table, of irreducible factors, as given by, say, Peterson and Weldon. In this correspondence it was determined that the coset representatives for the cases ofm-r = 2, withs = 2, 3, andm-r=3, withs=2.     

On the survival of sequence information in filters (Corresp.)

Given a binary data streamA = {a_i}_{i=o}^inftyand a filterFwhose output at timenisf_n = sum_{i=0}^{n} a_i beta^{n-i}for some complexbeta neq 0, there are at most2^{n +1)distinct values off_n. These values are the sums of the subsets of{1,beta,beta^2,cdots,beta^n}. It is shown that all2^{n+1}sums are distinct unlessbetais a unit in the ring of algebraic integers that satisfies a polynomial equation with coefficients restricted to +1, -1, and 0. Thus the size of the state space{f_n}is2^{n+1}ifbetais transcendental, ifbeta neq pm 1is rational, and ifbetais irrational algebraic but not a unit of the type mentioned. For the exceptional values ofbeta, it appears that the size of the state space{f_n}grows only as a polynomial innifmidbetamid = 1, but as an exponentialalpha^nwith1 < alpha < 2ifmidbetamid neq 1.     

Cooperative Quantum Cutting in Yb $^{3+}$–Tb $^{3+}$ Codoped Borosilicate Glasses

Quantum cutting down-conversion (DC) with the emission of two near-infrared photons for each blue photon absorbed is realized in $hbox{Yb}^{3+}hbox{–}hbox{Tb}^{3+}$ codoped borosilicate glasses. With the excitation of $hbox{Tb}^{3+}$ ion by a 484-nm monochromatic light, emission from the $^{2} hbox{F} _{5/2}rightarrow ^{2} hbox{F} _{7/2}$ transition of $hbox{Yb}^{3+}$ ions is observed and this emission is proved to originate from the DC between $hbox{Tb}^{3+}$ ions and $hbox{Yb}^{3+}$ ions. Results shows that maximum quantum efficiency reach as high as 153%, which is comparable with that in oxyfluoride glass ceramics in this system. With the advantages of excellent transparence, easy shaping, good stability, and low cost, $hbox{Yb}^{3+}hbox{–}hbox{Tb}^{3+}$ codoped borosilicate glasses are potentially used as down-converter layer in silicon-based solar cells.