共查询到20条相似文献,搜索用时 31 毫秒
1.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1981,27(1):132-136
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 ofN Bayesian single-threshold decision rulesphi_{i}^{0}, i = 1,cdots , N having 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 withN pickets 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 allf andphi . 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. 相似文献
2.
An algorithm for maximizing expected log investment return 总被引:3,自引:0,他引:3
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(2):369-373
Let the random (stock market) vectorX geq 0 be drawn according to a known distribution functionF(x), x in R^{m} . A log-optimal portfoliob^{ast} is any portfoliob achieving maximal expectedlog returnW^{ast}=sup_{b} E ln b^{t}X , where the supremum is over the simplexb geq 0, sum_{i=1}^{m} b_{i} = 1 . An algorithm is presented for findingb^{ast} . The algorithm consists of replacing the portfoliob by the expected portfoliob^{'}, b_{i}^{'} = E(b_{i}X_{i}/b^{t}X) , corresponding to the expected proportion of holdings in each stock after one market period. The improvement inW(b) after each iteration is lower-bounded by the Kullback-Leibler information numberD(b^{'}|b) between the current and updated portfolios. Thus the algorithm monotonically improves the returnW . An upper bound onW^{ast} is given in terms of the current portfolio and the gradient, and the convergence of the algorithm is established. 相似文献
3.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1968,14(1):129-134
In a recent series of papers, [2]-[4] Schalkwijk and Kailath have proposed a block coding scheme for transmission over the additive white Gaussian noise channel with one-sided spectral densityN_{0} using a noiseless delayless feedback link. The signals have bandwidthW (W leq infty) and average powerbar{P} . They show how to communicate at ratesR < C = W log (1 + bar{P}/N_{0}W) , the channel capacity, with error probabilityP_{e} = exp {-e^{2(C-R)T+o(T)}} (whereT is the coding delay), a "double exponential" decay. In their scheme the signal energy (in aT -second transmission) is a random variable with only its expectation constrained to bebar{P}T . In this paper we consider the effect of imposing a peak energy constraint on the transmitter such that whenever the Schalkwijk-Kailath scheme requires energy exceeding abar{P}T (wherea > 1 is a fixed parameter) transmission stops and an error is declared. We show that the error probability is degraded to a "single exponential" formP_{e} = e^{-E(a)T+o(T)} and find the exponentE(a) . In the caseW = infty , E(a) = (a - 1)^{2}/4a C . For finiteW, E(a) is given by a more complicated expression. 相似文献
4.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1979,25(4):448-452
A model of an additive non-Gaussian noise channel with generalized average input energy constraint is considered. The asymptotic channel capacityC_{zeta}(S) , for large signal-to-noise ratioS , is found under certain conditions on the entropyH_{ tilde{ zeta}}( zeta) of the measure induced in function space by the noise processzeta , relative to the measure induced bytilde{zeta} , where is a Gaussian process with the same covariance as that ofzeta . IfH_{ tilde{zeta}}( zeta) < infty and the channel input signal is of dimensionM< infty , thenC_{ zeta}(S)= frac{1}{2}M ln(1 + S/M) + Q_{zeta}( M ) + {o}(1) , where0 leq Q_{ zeta}( M ) leq H_{ tilde{ zeta}}( zeta) . If the channel input signal is of infinite dimension andH_{ tilde{ zeta}}( zeta) rightarrow 0 forS rightarrow infty , thenC_{ zeta}(S) = frac{1}{2}S+{o}(1) . 相似文献
5.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1985,31(4):543-545
A "slowly" fluctuating target is assumed to keep its radar cross section constant for the duration of several(M) dwells on target. To resolve multiple range and/or Doppler ambiguities, the received signal, which is presumably coherently processed (i.e., predetection integrated or matched filtered) over each dwell, must often be tested against a threshold, {em independently} of those on other dwells. Such a procedure is referred to as {em multiple detection}. A technique for the evaluation of a tight lower bound on the multiple-detection probabilityP_{M} , under Swerling case I statistics for the cross section, is presented in term of an infinite series and worked out in detail forP_{2} andP_{3} . Estimates on the computation error due to the truncation of the series are derived. Numerical results indicate thatP_{3} comes much closer toP_{1} than top_{1}^{3} or even toP_{1}P_{2} ; at an expected signal-to-noise ratio of13 dB and atP_{1} = 0.51 , it obtains thatP_{3} geq 0.40 , whereasP_{1}P_{2} = 0.23 andp_{1}^{3} = 0.17 . 相似文献
6.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1967,13(3):414-422
This paper considers the performance of a communication system which transmits forT seconds the real part of a sample function of one ofM stationary complex Gaussian processes whose spectral densities are all frequency translations of the functionS_{xi (f) . At the receiver white Gaussian noise of one-sided densityN_{0} is added. The center frequencies of the processes are assumed to be sufficiently separated that theM covariance functions are orthogonal overT . Exponently tight bounds are obtained for the error probability of the maximum likelihood receiver. It is shown that the error probability approaches zero exponentially withT for all ratesR = (ln M)/T up toC= int_{-infty}^{infty} [S_{xi (f)/N_{0}] df - int_{- infty}^{infty} ln [1 + S_{xi}(f)/N_{0}] df which is shown to be the channel capacity. Similar results are obtained for the case of stochastic signals with specular components. 相似文献
7.
New results in binary multiple descriptions 总被引:3,自引:0,他引:3
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1987,33(4):502-521
8.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1974,20(4):517-524
Letxi = {xi(t), 0 leq t leq T} be a process with covariance functionK(s,t) andE int_0^T xi^2(t) dt < infty . It is proved that for everyvarepsilon > 0 thevarepsilon -entropyH_{varepsilon}(xi) satisfies begin{equation} H_{varepsilon}(xi_g) - mathcal{H}_{xi_g} (xi) leq H_{varepsilon}(xi) leq H_{varepsilon}(xi_g) end{equation} wherexi_g is a Gaussian process with the covarianeeK(s,t) andmathcal{H}_{xi_g}(xi) is the entropy of the measure induced byxi (in function space) with respect to that induced byxi_g . It is also shown that ifmathcal{H}_{xi_g}(xi) < infty then, asvarepsilon rightarrow 0 begin{equation} H_{varepsilon}(xi) = H_{varepsilon}(xi_g) - mathcal{H}_{xi_g}(xi) + o(1). end{equation} Furthermore, ff there exists a Gaussian processg = { g(t); 0 leq t leq T } such thatmathcal{H}_g(xi) < infty , then the ratio betweenH_{varepsilon}(xi) andH_{varepsilon}(g) goes to one asvarepsilon goes to zero. Similar results are given for the rate-distortion function, and some particular examples are worked out in detail. Some cases for whichmathcal_{xi_g}(xi) = infty are discussed, and asymptotic bounds onH_{varepsilon}(xi) , expressed in terms ofH_{varepsilon}(xi_g) , are derived. 相似文献
9.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1969,15(4):440-444
Forf(t) a real-valued signal band-limited to- pi r leq omega leq pi r (0 < r < 1) and represented by its Fourier integral, upper bounds are established for the magnitude of the truncation error whenf(t) is approximated at a generic timet by an appropriate selection ofN_{1} + N_{2} + 1 terms from its Shannon sampling series expansion, the latter expansion being associated with the full band[-pi, pi] and thus involving samples off taken at the integer points. Results are presented for two cases: 1) the Fourier transformF(omega) is such that|F(omega)|^{2} is integrable on[-pi, pi r] (finite energy case), and 2)|F(omega)| is integrable on[-pi r, pi r] . In case 1) it is shown that the truncation error magnitude is bounded above byg(r, t) cdot sqrt{E} cdot left( frac{1}{N_{1}} + frac{1}{N_{2}} right) whereE denotes the signal energy andg is independent ofN_{1}, N_{2} and the particular band-limited signal being approximated. Correspondingly, in case 2) the error is bounded above byh(r, t) cdot M cdot left( frac{1}{N_{1}} + frac{1}{N_{2}} right) whereM is the maximum signal amplitude andh is independent ofN_{1}, N_{2} and the signal. These estimates possess the same asymptotic behavior as those exhibited earlier by Yao and Thomas [2], but are derived here using only real variable methods in conjunction with the signal representation. In case 1), the estimate obtained represents a sharpening of the Yao-Thomas bound for values ofr dose to unity. 相似文献
10.
《Electron Devices, IEEE Transactions on》1974,21(1):89-93
Assuming the conventional divisions of the semiconductor into depleted and neutral regions, it is shown that for an abrupt p-n junction with nondegenerate carriers a relation exists between the open circuit photovoltage and the PN product at the junction(PN)_{0} , which is valid for all signal levels. In the small-signal case this leads to the standard result. At intermediate levels a new relationV = KT/q (1 pm m) log_{e} ([(PN)_{0}]^{1/2}/n_{i}) holds, the upper sign for p+-n junctions, the lower for n+-p junctions;m = (micro_{e}-micro_{h})/(micro_{e}+micro_{h}) . At very high levels the photovoltage saturates toV = kT/q[log_{e}(M_{p}M_{n}/n_{i^{2}}) + m log_{e}(micro_{h}M_{p}/micro_{e}M_{N})] . Since Mp and MN are the doping levels in the p and n regions, the first term is the diffusion potential and the second term will be positive for p+-n junctions and negative for n+-p junctions. These results compare satisfactorily with the available experimental data. 相似文献
11.
An optimum predetection Gaussian bandpass filter for differential detection of MSK is derived theoretically with numerical techniques. The optimum product of bandwidth(B) and bit duration(T) , compromising the noise reduction effect with the intersymbol interference effect, is calculated at a given bit error rate (BER). It is shown that the optimumBT product is 1.21 with 4.02 dB degradation at 10-6BER where the degradation is defined as the increase inE_{b}/N_{0} relative to ideal coherent detection of MSK. 相似文献
12.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1987,33(3):443-448
For a joint distribution{rm dist}(X,Y) , the functionT(t)=min { H(Y|U): I(U wedge Y|X)=O, H(X|U)geq t} is an important characteristic. It equals the asymptotic minimum of(1/n)H(Y^{n}) for random pairs of sequences(X^{n}, Y^{n}) , wherefrac{1}{n} sum ^{n}_{i=1}{rm dist} X_{i} sim {rm dist} X, {rm dist} Y^{n}|X^{n} = ({rm dist} Y|X)^{n}, frac{1}{n}H(X^{n})geq t. We show that if, for(X^{n}, Y^{n}) as given, the rate pair[(1/n)H(X^{n}) ,(1/n)H(Y^{n})] approaches the nonlinear part of the curve(t,T(t)) , then the sequenceX^{n} is virtually memoryless. Using this, we determine some extremal sections of the rate region of entropy characterization problems and find a nontrivial invariant for weak asymptotic isomorphy of discrete memoryless correlated sources. 相似文献
13.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1966,12(2):183-189
In Part I of this paper, we presented a scheme for effectively exploiting a noiseless feedback link associated with an additive white Gaussian noise channel with {em no} signal bandwidth constraints. We now extend the scheme for this channel, which we shall call the wideband (WB) scheme, to a band-limited (BL) channel with signal bandwidth restricted to(- W, W) . Our feedback scheme achieves the well-known channel capacity,C = W ln (1 +P_{u,v}/N_{0} W) , for this system and, in fact, is apparently the first deterministic procedure for doing this. We evaluate the fairly simple exact error probability for our scheme and find that it provides considerable improvements over the best-known results (which are lower bounds on the performance of sphere-packed codes) for the one-way channel. We also study the degradation in performance of our scheme when there is noise in the feedback link. 相似文献
14.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1967,13(1):91-94
The probability of a set of binaryn -tuples is defined to be the sum of the probabilities of the individualn -tuples when each digit is chosen independently with the same probabilityp of being a "one." It is shown that, under such a definition, the ratio between the probability of a subgroup of order2^{k} and any of its proper cosets is always greater than or equal to a functionF_{k}(p) , whereF_{k}(p) geq 1 forp leq frac{1}{2} with equality when and only whenp = frac{1}{2} . It is further shown thatF_{k}(p) is the greatest lower bound on this ratio, since a subgroup and proper coset of order2^{k} can always be found such that the ratio between their probabilities is exactlyF_{k}(p) . It is then demonstrated that for a linear code on a binary symmetric channel the "tall-zero" syndrome is more probable than any other syndrome. This result is applied to the problem of error propagation in convolutional codes. 相似文献
15.
A convenient method of evaluating theQ function over the parameter space quarter plane is presented. TheQ function is first expressed as an infinite series. TheN term truncated seriesQ_{N}(a, b) is used to approximateQ(a, b) fora^{2} + b^{2} leq R where the choice ofN depends on the accuracy desired andR is determined by considerations such as computer bit capacity, computational time, and accuracy. Fora^{2} + b^{2} > R , alternate expressions are used. Whenb - a geq d , we approximateQ by 0, and whenb - a leq d , we approximateQ by 1. The accuracy is dependent on the choice of the constantd . In the reniainder of the quarter plane,a^{2} + b^{2} > R and| b - a < d , and an efficient expression is used, but it is of limited accuracy (from 10-5to 10-9) near the linea = b . 相似文献
16.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(2):254-256
An upper bound is derived for the mean-square error involved when a non-band-limited, wide-sense stationary random processx(t) (possessing an integrable power spectral density) is approximated by a cardinal series expansion of the formsum^{infty}_{-infty}x(n/2W) sinc2W(t-n/2W) , a sampling expansion based on the choice of some nominal bandwidthW > 0 . It is proved thatlim_{N rightarrow infty} E {|x(t) - x_{N}(t)|^{2}} leq frac{2}{pi}int_{| omega | > 2 pi W}S_{x}( omega) d omega, wherex_{N}(t) = sum_{-N}^{N}x(n/2W) sinc2W(t-n/2W) , andS_{x}(omega) is the power spectral density forx(t) . Further, the constant2/ pi is shown to be the best possible one if a bound of this type (involving the power contained in the frequency region lying outside the arbitrarily chosen band) is to hold uniformly int . Possible reductions of the multiplicative constant as a function oft are also discussed, and a formula is given for the optimal value of this constant. 相似文献
17.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(4):422-432
In 1964 the author proposed as an explication of {em a priori} probability the probability measure induced on output strings by a universal Turing machine with unidirectional output tape and a randomly coded unidirectional input tape. Levin has shown that iftilde{P}'_{M}(x) is an unnormalized form of this measure, andP(x) is any computable probability measure on strings,x , thentilde{P}'_{M}geqCP(x) whereC is a constant independent ofx . The corresponding result for the normalized form of this measure,P'_{M} , is directly derivable from Willis' probability measures on nonuniversal machines. If the conditional probabilities ofP'_{M} are used to approximate those ofP , then the expected value of the total squared error in these conditional probabilities is bounded by-(1/2) ln C . With this error criterion, and when used as the basis of a universal gambling scheme,P'_{M} is superior to Cover's measurebast . WhenHastequiv -log_{2} P'_{M} is used to define the entropy of a rmite sequence, the equationHast(x,y)= Hast(x)+H^{ast}_{x}(y) holds exactly, in contrast to Chaitin's entropy definition, which has a nonvanishing error term in this equation. 相似文献
18.
In the past, smoothly varying turbulence has been studied by changing the structure constant to the functionC_{n}^{2}(bar{r} ). The purpose of this paper is to show that this approach is insufficient, and that a random process developed by Silverman can be used to describe the wave fluctuations in localized smoothly varying turbulence. The localized turbulence is characterized by a correlation function which is a product of a function of the average coordinate and a function of the difference coordinate. The corresponding spectrum is also given by a product of a function of the difference wavenumber and a function of the average wavenumber. They are related to each other through two Fourier transform pairs. Making use of the preceding representations, the fluctuations of a wave propagating through such a turbulence can be given either by the integrals with respect to the two wavenumbers or by a convolution integral of the structure constantC_{n}^{2}(bar{r} ) and a function involving the outer scale of the turbulenceL_{0} . It is shown that for a plane wave case, if the distanceL is within (L_{0}^{2}/lambda ), then the usual formula given by Tatarski is valid. But if the distance is betweenL_{0}^{2}/lambda and(bL_{0})/lambda whereb is the total transverse size of the turbulence, the variance of the wave is nearly constant, and ifL gg (bL_{0})/lambda , the variance decays asL^{-2} . Similar conclusions are shown for a spherical wave case. Some examples are shown illustrating the effectiveness of this method. 相似文献
19.
We measured the energy extraction for 60-ns pulses and compared our experimental and theoretical results. The theoretical curve is in agreement with the experimental results. We plotted the theoretical evolution ofalpha, N_{001}/N_{A}, N_{100}/N_{A} , andT in an amplifying stage. We finally compared the different energy extraction versus the pulse duration. 相似文献
20.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(2):385-388
LetV be 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 ifnu has 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-q representation of the numberx . LetS be 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 thatS is 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 . 相似文献