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》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
2.
《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
3.
《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
4.
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
5.
《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
6.
Construction of de Bruijn sequences of minimal complexity 总被引:1,自引:0,他引:1
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(5):705-709
It is well known that the linear complexity of a de Bruijn sequenceS of length2^{n} is bounded below by2^{n- 1} + n forn geq 3 . It is shown that this lower bound is attainable for alln . 相似文献
7.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1976,22(5):568-573
Modern communication theory and practice are heavily dependent on the representation of continuous parameter signals by linear combinations, involving a denumerable set of random variables. Among the best known and most useful is the cardinal seriesf_{n} (t) = sum^{+n}_{-n} f(k) frac{sin pi (t - k)}{ pi ( t - k )} for deterministic functions and wide-sense stationary stochastic processes bandlimited to(-pi, pi) . When, as invariably occurs in applications, samplesf(k) are available only over a finite period, the resulting finite approximation is subject to a truncation error. For functions which areL_{1} Fourier transforms supported on[-pi + delta, + pi - delta] , uniform trunction error bounds of the formO(n^{-1}) are known. We prove that analogousO(n^{-1}) bounds remain valid without the guard banddelta and for Fourier-Stieltjes transforms; we require only a bounded variation condition in the vicinity of the endpoints- pi and+ pi of the basic interval. Our methods depend on a Dirichlet kernel representation forf_{n}(t) and on properties of functions of bounded variation; this contrasts with earlier approaches involving series or complex variable theory. Other integral kernels (such as the Fejer kernel) yield certain weighted truncated cardinal series whose errors can also be bounded. A mean-square trunction error bound is obtained for bandlimited wide-sense stationary stochastic processes. This error estimate requires a guard band, and leads to a uniformO(n^{-2}) bound. The approach again employs the Dirichlet kernel and draws heavily on the arguments applied to deterministic functions. 相似文献
8.
《Electron Devices, IEEE Transactions on》1977,24(10):1245-1248
A knowledge of the MOSFET operating in weak inversion is important for circuits with low leakage specifications. This paper discusses the effect of temperature on the MOSFET in weak inversion. The reciprocal slopen of the log IDS versus VGS relationship between source-drain current IDS and gate bias VGS may be given byfrac{1}{(n - 1 - gamma)^{2}} = frac{2Cmin{ox}max{2}}{qepsilon_{s}N_{B}} [frac{3}{4} frac{E_{g^{0}}{q} - (frac{3}{2}alpha + frac{k}{q})T] withalpha equiv (k/q)(38.2 - ln N_{B} + (3/2) ln T) and γ ≡C_{ss}/C_{ox} , where Cox is the oxide capacitance per unit area, Css the surface states capacitance per unit area,q the electronic charge, εs the permittivity of silicon, NB the bulk doping concentration,k the Boltzmann's constant,T the absolute temperature, andE_{g0} the extrapolated value of the energy gap of lightly doped silicon atT = 0 K. This theoretical formula was in good agreement with experimental results in a temperature range of interest. 相似文献
9.
《Quantum Electronics, IEEE Journal of》1981,17(8):1324-1325
Classically, the thermal noise in electricalRC circuits andLCR series circuits is governed by the equipartition lawfrac{1}{2}overline{CV^{2}} = frac{1}{2}kT , whereV(t) is the noise voltage developed acrossC . When quantum effects are taken into account, the equipartition law no longer holds forRC circuits, although an equipartition law can be deemed for the measured mean square noise voltage under certain conditions. InLCR series circuits the equipartition lawfrac{1}{2}overline{CV^{2}} = frac{1}{2}kT , changes intofrac{1}{2}overline{CV^{2}} = frac{1}{2}bar{E}(f_{0}) for high-Q tuned circuits, wherebar{E}(f_{0}) is the average energy of a harmonic oscillator tuned at the tuning frequency of the tuned circuit. 相似文献
10.
《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
11.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1970,16(3):352-353
An upper bound on the minimum probability of error for an equal-strength diversity channel is simply derived that improves a previously known bound by the factor[4(1 - p)]^(-1) ,0 leq p leq frac{1}{2} . 相似文献
12.
《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
13.
A first-order Markov process is used to model the sequence of quantization noise samples in delta modulation. An autocorrelation parameterC in the Markov model controls the shape of the noise spectrum, and asC decreases from 1 to 0 and then to -1, the spectrum changes from a low-pass to a flat, and then to a high-pass characteristic. One can also use the Markov model to predict the so-called out-of-band noise rejection that is obtained when delta modulation is performed with an oversampled input, and the resulting quantization noise is lowpass filtered to the input band. The noise rejectionG is a function ofC as well as an oversampling factorF and an interesting asymptotic result is thatG=frac{1-C}{1+C} dot F ifF gg frac{1+C}{1-C} dot frac{pi}{2} . Delta modulation literature has noted the importance of the specialG values,F and2F . These correspond to autocorrelation values of 0 and -1/3. 相似文献
14.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(4):592-594
For a discreteN -valued random variable (N possibly denumerably infinite) Leung-Yan-Cheong and Cover have given bounds for the minimal expected length of a one-to-one (not necessarily uniquely decodable) codeL_{1:1}=sum_{i=1}^{N} p_{i} log left( frac{1}{2} + 1 right). It is shown that the best possible case occurs for certain denumerably infinite sets of nonzero probabilities. This absolute bound is related to the Shannon entropyH of the distribution by(h (cdot) is the binary entropy function). 相似文献
15.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1973,19(3):371-372
This paper gives a tabulation of binary convolutional codes with maximum free distance for ratesfrac{1}{2}, frac{1}{3} , andfrac{1}{4} for all constraint lengths (measured in information digits)nu up to and includingnu = 14 . These codes should be of practical interest in connection with Viterbi decoders. 相似文献
16.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1968,14(5):752-755
A Gilbert bound for periodic binary convolutional (PBC) codes is established. This bound shows that regardless of previous decoding decisions any fraction of errors less thanalpha/2 can be corrected in a constraint length by some PBC code if the constraint length is sufficiently large andR , the code rate, is less than[1 - H(alpha)]/2, 0 leq alpha < frac{1}{2} . 相似文献
17.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1974,20(3):311-316
Upper bounds to the capacity of band-limited Gaussianm th-order autoregressive channels with feedback and average energy constraintE are derived. These are the only known hounds on one- and two-way autoregressive channels of order greater than one. They are the tightest known for the first-order case. In this case letalpha_1 be the regression coefficient,sigma^2 the innovation variance,N the number of channel iterations per source symbol, ande = E/N ; then the first-order capacityC^1 is bounded by begin{equation} C^1 leq begin{cases} frac{1}{2} ln [frac{e}{sigma^2}(1+ mid alpha_1 mid ) ^ 2 +1], & frac{e}{sigma^2} leq frac{1}{1- alpha_1^2} \ frac{1}{2} ln [frac{e}{sigma^2} + frac{2mid alpha_1 mid}{sqrt{1-alpha_1^2}} sqrt{frac{e}{simga^2}} + frac{1}{1-alpha_1^2}], & text{elsewhere}.\ end{cases} end{equation} This is equal to capacity without feedback for very low and very highe/sigma^2 and is less than twice this one-way capacity everywhere. 相似文献
18.
《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
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》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