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1.
《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
2.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(6):872-877
Winograd's result concerning Elias' model of computation in the presence of noise can be stated without reference to computation. If a codevarphi: {0,1}^{k} rightarrow {0,1}^{n} is min-preserving(varphi (a wedge b) = varphi (a) wedge varphi (b) fora,b in {0,1}^{k}) andepsilon n -error correcting, then the ratek/n rightarrow 0 ask rightarrow infty . This result is improved and extended in two directions. begin{enumerate} item For min-preserving codes with {em fixed} maximal (and also average) error probability on a binary symmetric channel againk/n rightarrow 0 ask rightarrow infty (strong converses). item Second, codes with lattice properties without reference to computing are studied for their own sake. Already for monotone codes( varphi (a) leq varphi (b) fora leq b) the results in direction 1) hold for maximal errors. end{enumerate} These results provide examples of coding theorems in which entropy plays no role, and they can be reconsidered from the viewpoint of multiuser information theory. 相似文献
3.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1982,28(4):665-668
The modular distance induces a metric if and only if the nonadjacent form of the modulusM has one of the following forms:1) 2^{n}+2^{n-2} pm 2^{i} , wheren-igeq 4; 2) 2^{n} - 2^{j} pm 2^{i} , where2 leq n -j leq 5 andj-igeq 2; 3) 2^{n} pm 2^{j} , wheren -j geq 2; 4) 2^{n} . 相似文献
4.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(3):436-440
Using earlier methods a combinatorial upper bound is derived for|C|. cdot |D| , where(C,D) is adelta -decodable code pair for the noisy two-access binary adder channel. Asymptotically, this bound reduces toR_{1}=R_{2} leq frac{3}{2} + elog_{2} e - (frac{1}{2} + e) log_{2} (1 + 2e) = frac{1}{2} - e + H(frac{1}{2} - e) - frac{1}{2}H(2e), wheree = lfloor (delta - 1)/2 rfloor /n, n rightarrow infty andR_{1} resp.R_{2} is the rate of the codeC resp.D . 相似文献
5.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(3):410-412
For a complex-valued deterministic signal of finite energy band-limited to the normalized frequency band|w| leq pi explicit coefficients{a_{kn}} are found such that for anyT satisfying0 < T leq 1/2 ,left| f(t)-sum^{2n}_{k=1}a_{kn}f(t - kT)right| leq E_{f}cdot beta^{n} whereE_{f} is the signal energy andbeta doteq 0.6863 . Thus the estimate off(t) in terms of2n past samples taken at a rate equal to or in excess of twice the Nyquist rate converges uniformly at a geometric rate tof(t) on(- infty , infty) . The suboptimal coefficients{a_{kn}} have the desirable property of being pure numbers independent of both the particular band-limited signal and of the selected sampling rate1/T . It is also shown that these same coefficients can be used to estimate the value ofx(t) of a wide-sense stationary random process in terms of past samples. 相似文献
6.
《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
7.
The input admittance of a coaxial waveguide fed by a gap of length2d in the center conductor is evaluated using the dyadic Green's function of the guide and a band of equivalent magnetic surface current proportional to the gap's axial electric field via the equivalence principle. The axial electric field is expressed in terms of a rapidly convergent series of ultraspherical polynomials whose weighting function satisfies the edge conditions at each end of the gap. If the inner and outer radii of the coaxial guide area andb , respectively, then the limiting case ofb rightarrow infty is an infinite dipole in free space. Numerical results for the admittance are given as a function ofka (0.01 leq ka leq 0.50) with parameterb/a = 2, 5,10 and 50 for the coaxial guide. For the infinite dipole the admittance is presented as a function ofd/a (10^{-3} leq d/a leq 10) withka as a parameter (0.001 leq ka leq 0.1 ). 相似文献
8.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(3):349-354
An(n, k, d) linear code overF= GF(q) is said to be {em maximum distance separable} (MDS) ifd = n - k + 1 . It is shown that an(n, k, n - k + 1) generalized Reed-Solomon code such that2leq k leq n - lfloor (q - 1)/2 rfloor (k neq 3 {rm if} q is even) can be extended by one digit while preserving the MDS property if and only if the resulting extended code is also a generalized Reed-Solomon code. It follows that a generalized Reed-Solomon code withk in the above range can be {em uniquely} extended to a maximal MDS code of lengthq + 1 , and that generalized Reed-Solomon codes of lengthq + 1 and dimension2leq k leq lfloor q/2 rfloor + 2 (k neq 3 {rm if} q is even) do not have MDS extensions. Hence, in cases where the(q + 1, k) MDS code is essentially unique,(n, k) MDS codes withn > q + 1 do not exist. 相似文献
9.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1970,16(6):745-751
In this paper, we establish the following result. Theorem:A_i , the number of codewords of weighti in the second-order binary Reed-Muller code of length2^m is given byA_i = 0 unlessi = 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} 相似文献
10.
《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
11.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1970,16(2):226-230
The problem of estimating a probability density functionp(x) over[0, infty) when several low-order moments are known is considered. A computational procedure, based on information theory, is used to obtain the maximum entropy estimates ofp(x) in a number of cases. The situation when the first two moments only are known is considered in some detail. A table is included for estimatingp(x) when givenmu_1 ^{prime} , mu_2 ^{prime} withmu_2 ^{prime} leq 2(mu_1 ^{prime}) ^ 2 . 相似文献
12.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1970,16(3):353-355
An interleaved fading channel whose state is known to the receiver is analyzed. The reliability functionE(R) is obtained for ratesR in the rangeR_c leq R leq C . The capacity is shown to beC = E_A { frac{1}{2} ln (1 + A^2 n)} whereA is a factor describing the fading mechanism andu is the signal-to-noise ratio per dimension. 相似文献
13.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1974,20(2):278-279
Asymptotic properties of expected distortion are studied for the delay-time-weighted probability of error distortion measured_n(x,tilde{x}) = n^{-1} sum_{t=0}^{n-1} f(t + n)[l - delta(x_t,tilde{x}_t)] ,, wherex = (x_0,x_1,cdots,x_{n-1}) andtilde{x} = (tilde{x}_0,tilde{x}_1,cdots,tilde{x}_{n-1}) are source and reproducing vectors, respectively, anddelta (cdot, cdot) is the Kronecker delta. With reasonable block coding and transmission constraintsx_t is reproduced astilde{x}_t with a delay oft + n time units. It is shown that if the channel capacity is greater than the source entropyC > H(X) , then there exists a sequence of block lengthn codes such thatE[d_n(X,tilde{X})] rigjhtarrow 0 asn rightarrow infty even iff(t) rightarrow infty at an exponential rate. However, iff(t) grows at too fast an exponential rate, thenE[d_n(X,tilde{X})] rightarrow infty asn rightarrow infty . Also, ifC < H(X) andf(t) rightarrow infty thenE[d_n(X,tilde{X})] rightarrow infty asn rightarrow infty no matter how slowlyf(t) grows. 相似文献
14.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1976,22(3):357-359
For a given finite set of messages and their assigned probabilities, Huffman's procedure gives a method of computing a length set (a set of codeword lengths) that is optimal in the sense that the average word length is minimized. Corresponding to a particular length set, however, there may be more than one code. LetL(n) consist of all length sets with largest termn , and, for anyell in L(n) , let{cal S}( ell) be the smallest number of states in any finite-state acceptor which accepts a set of codewords with length setell . It is shown that, for alln > 1 ,n^{2}/(16 log_{2} n) leq max {cal S}(ell) leq 0(n^{2}). ell in L(n) 相似文献
15.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(5):706-709
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} - 1 withm geq 8 and designed distance2t + 1 with4 leq t leq 5 is 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 + 1 andm geq 16 ; (2)t = 4, j geq 2t + 3 and10 leq m leq 15 ; (3)t=4, j geq 2t+5 and8 leq m leq 9 ; (4)t=5,j geq 2t+ 1 andm geq 20 ; (5)t=5, j geq 2t+ 3 and12 leq m leq 19 ; (6)t=5, j geq 2t+ 5 and10 leq m leq 11 ; (7)t=5, j geq 2t + 7 andm=9 ; (8)t= 5, j geq 2t+ 9 andm = 8 . 相似文献
16.
《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
17.
《Electron Devices, IEEE Transactions on》1977,24(11):1285-1287
The normalized nonlinear equation(dI/dtau) pm [alpha + beta|I|^{1/2}] + intmin{0}max{tau}I dbar{tau}= 1 describing current evolution in a single mesh flashlamp driving circuit has been solved using numerical methods for the case of a critically damped pulse (alpha simeq 0.84) and beta = r/Z_{0} neq 0 . Normalized current, power, and energy waveforms for values of β in the range0 leq beta leq 0.5 are obtained. The energy efficiency ηE , which is numerically equal to the flashlamp dissipated energy di-Vided by the energy stored in the driving circuit, is also shown as a function of β. Increased numerical accuracy has improved the previously used value of α for critical damping and leads to a slightly different form for the curve representing the locus of values (α β) to obtain critically damped pulses in the presence of restrictive losses. 相似文献
18.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(6):760-767
LetC be a code of lengthn and rateR over the alphabetA(Q)={ exp (2pi ir/Q): r=O,1, cdots ,Q-1} , and letd(C) be the minimum Euclidean distance ofC . For largen , the lower and upper bounds are obtained in parametric form on the achievable pairs(R, delta) , wheredelta = d^{2}(C)/n holds. To obtain these bounds, the arguments leading to the Gilbert bound and the Elias bound, respectively, are applied to the alphabetA(Q) . ForQ rightarrow infty , they are shown to be expressible in terms of the modified Bessel function of the first kind. The Elias type bound is compared with the Kabatyanskii-Levenshtein (K-L) bound that holds for less restrictive alphabets. It turns out that our upper bound improves the K-L bound fordelta leq 0.93 . 相似文献
19.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1981,27(1):131-132
The system modeldx_{t}=m(x_{t})dt+sigma_{o}dw_{t} and the observationdy_{t}=h(x_{t})dt+rho dv_{t} are considered, and a lower bound on the error for the least-square estimate of a function ofx_{t} , sayz(x_{t}) , is derived. This bound is then applied to derive a lower bound on the error in estimatingx_{t} in the case where the constantsigma_{o} in the equation for the system dynamics is replaced bysigma (x_{t}) . 相似文献
20.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1964,10(1):72-74
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 anytau and the lower bound fortau < pi / omega_{c} . These estimates are applied to the mean-square variation of the envelope of a quasi-monochromatic process. 相似文献