共查询到20条相似文献,搜索用时 15 毫秒
1.
《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
2.
《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
3.
《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
4.
《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
5.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(3):480-484
Two algorithms are presented for the generation of full-length shift-register cycles, also referred to as de Bruijn sequences. The first algorithm generates2^{k cdot g(n,k) full cycles of length2^{n} , using3n + k cdot g(n, k) bits of storage, wherek is a free parameter in the range1 leq k leq 2^{((n-4)/2)} , andg(n, k) is of the order ofn - 2 log k . The second algorithm generates about2^{n^{2}/4} full cycles of length2^{n} , using aboutn^{2}/2 bits of storage. In both algorithms, the time required to produce the next bit from the lastn bits is close ton . A possible application to the construction of stream ciphers is indicated. 相似文献
6.
《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
7.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1975,21(4):453-458
For a nondecreasing distortion characteristicphi(cdot) and a given signalx(cdot) , the "cross correlation" function defined byR_{phi} (tau) triangleq int_{-infty}^{infty} phi[x(t)]x(t - tau) dt is shown to satisfy the inequalityR_{phi}(tau) leq R_{phi}(0) , for alltau , generalizing an earlier result of Richardson that requiredphi(cdot) to be continuous and strictly increasing. The methods of the paper also show that, under weak conditions, begin{equation} R_{phi,psi}(tau) triangleq int_{-infty}^{infty} phi[x(t)]psi[x(t - tau)] dt leq R_{phi,psi}(0) end{equation} whenpsi is strictly increasing andphi is nondecreasing. In the case of hounded signals (e.g., periodic functions), the appropriate cross correlation function is begin{equation} mathcal{R}_{phi,psi}(tau} triangleq lim_{T rightarrow infty} (2T)^{-l} int_{-T}^T phi[x(t)]psi[x(t - tau)] dt. end{equation} For this case it is shown thatmathcal{R}_{phi,psi} (tau) leq mathcal{R}_{phi,psi}(0) for any nondecreasing (or nonincreasing) distortion functionsphi andpsi . The result is then applied to generalize an inequality on correlation functions for periodic signals due to Prosser. Noise signals are treated and inequalities of a similar nature are obtained for ensemble-average cross correlation functions under suitable hypotheses on the statistical properties of the noise. Inequalities of this type are the basis of a well-known method of estimating the unknown time delay of an observed signal. The extension to nondecreasing discontinuous distortion functions allows the use of hard limiting or quantization to facilitate the cross correlation calculation. 相似文献
8.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1971,17(4):368-371
The following model for the white Gaussian channel with or without feedback is considered: begin{equation} Y(t) = int_o ^{t} phi (s, Y_o ^{s} ,m) ds + W(t) end{equation} wherem denotes the message,Y(t) denotes the channel output at timet ,Y_o ^ {t} denotes the sample pathY(theta), 0 leq theta leq t. W(t) is the Brownian motion representing noise, andphi(s, y_o ^ {s} ,m) is the channel input (modulator output). It is shown that, under some general assumptions, the amount of mutual informationI(Y_o ^{T} ,m) between the messagem and the output pathY_o ^ {T} is directly related to the mean-square causal filtering error of estimatingphi (t, Y_o ^{t} ,m) from the received dataY_o ^{T} , 0 leq t leq T . It follows, as a corollary to the result forI(Y_o ^ {T} ,m) , that feedback can not increase the capacity of the nonband-limited additive white Gaussian noise channel. 相似文献
9.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1974,20(5):598-601
In comparing a signalf(t) with its amplitude-distorted formg(f(t)) , whereg(cdot) is a monotonically increasing function of its argument, one is led to consider the correlation function begin{equation} R(s) triangleq int_{-infty}^{infty} dtg (f(t))f(t-s). end{equation} A rigorous proof is given of the inequalityR(s) leq R(O) . Generalizations are presented for the cases of finite domains and of signals defined in two-dimensional space. 相似文献
10.
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
11.
《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
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》1973,19(6):769-772
In this, the first part of a two-part paper, we establish a theorem concerning the entropy of a certain sequence of binary random variables. In the sequel we will apply this result to the solution of three problems in multi-user communication, two of which have been open for some time. Specifically we show the following. LetX andY be binary randomn -vectors, which are the input and output, respectively, of a binary symmetric channel with "crossover" probabilityp_0 . LetH{X} andH{ Y} be the entropies ofX andY , respectively. Then begin{equation} begin{split} frac{1}{n} H{X} geq h(alpha_0), qquad 0 leq alpha_0 &leq 1, Rightarrow \ qquad qquad &qquad frac{1}{n}H{Y} geq h(alpha_0(1 - p_0) + (1 - alpha_0)p_0) end{split} end{equation} whereh(lambda) = -lambda log lambda - (1 - lambda) log(l - lambda), 0 leq lambda leq 1 . 相似文献
14.
《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
15.
《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
16.
Writing on dirty paper (Corresp.) 总被引:1,自引:0,他引:1
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1983,29(3):439-441
A channel with outputY = X + S + Z is examined, The stateS sim N(0, QI) and the noiseZ sim N(0, NI) are multivariate Gaussian random variables (I is the identity matrix.). The inputX in R^{n} satisfies the power constraint(l/n) sum_{i=1}^{n}X_{i}^{2} leq P . IfS is unknown to both transmitter and receiver then the capacity isfrac{1}{2} ln (1 + P/( N + Q)) nats per channel use. However, if the stateS is known to the encoder, the capacity is shown to beC^{ast} =frac{1}{2} ln (1 + P/N) , independent ofQ . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratioP/N . Therefore, the stateS does not affect the capacity of the channel, even thoughS is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the stateS rather than attempting to cancel it. 相似文献
17.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1972,18(1):20-27
The approach to Gaussianity of the outputy(t) of a narrow-band systemh(t) is investigated. It is assumed that the inputx(t) is ana -dependent process, in the sense that the random variablesx(t) andx(t + u) are independent foru > a . WithF(y) andG(y) the distribution functions ofy(t) and of a suitable normal process, a realistic boundB on the differenceF(y) -- G(y) is determined, and it is shown thatB rightarrow 0 as the bandwidthomega_o of the system tends to zero. In the special case of the shot noise process begin{equation} y(t) = sum_i h(t - t_i) end{equation} it is shown that begin{equation} mid F(y) - G(y) mid < (omega_o/lambda) frac{1}{2} end{equation} wherelambda_i is the average density of the Poisson pointst_i . 相似文献
18.
《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
19.
《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
20.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(4):497-499
It is shown thatsqrt[8]{2} is an element of order2^{n+4} inGF(F_{n}) , whereF_{n}=2^{2^{n}}+1 is a Fermat prime forn=3,4 . Hence it can be used to define a fast Fourier transform (FFT) of as many as2^{n+4} symbols inGF(F_{n}) . Sincesqrt[8]{2} is a root of unity of order2^{n+4} inGF(F_{n}) , this transform requires fewer muitiplications than the conventional FFT algorithm. Moreover, as Justesen points out [1], such an FFT can be used to decode certain Reed-Solomon codes. An example of such a transform decoder for the casen=2 , wheresqrt{2} is inGF(F_{2})=GF(17) , is given. 相似文献