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1.
《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
2.
《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
3.
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
4.
《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
5.
《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
6.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(2):395-403
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 rceil denotes 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 = 2 oru_{i-1}-u_{i} geq 2 for2 leq i leq p . 相似文献
7.
《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
8.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1983,29(3):345-348
Ifm is odd andsigma /in Aut GF(2^{m}) is such thatx rightarrow x^{sigma^{2}-1} is1-1 , there is a[2^{m+1}-1,2^{m+l}-2m-2] nonlinear binary codeP(sigma) having minimum distance 5. All the codesP(sigma) have the same distance and weight enumerators as the usual Preparata codes (which rise asP(sigma) whenx^{sigma}=x^{2}) . It is shown thatP(sigma) andP(tau) are equivalent if and only iftau=sigma^{pm 1} , andAut P(sigma) is determined. 相似文献
9.
《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
10.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1975,21(4):460-462
Skew-symmetric sequences of(2n + 1) terms,a_0,a_1,cdots,a_{2n} , are described for which the "merit factor" begin{equation} F_h = frac{biggl[sum_{i=0}^{2n} mid a_i mid biggr] ^2}{ 2 sum_{k=1}^{2n} biggl[ sum_{i=0}^{2n-k} text{sign} (a_i) cdot a_{i+k} biggl] ^2} end{equation} is unusually high. 相似文献
11.
《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
12.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1972,18(3):409-414
The weight enumerator of a code is the polynomial begin{equation} W(x,y)= sum_{r=0}^n A_r x^{n-r} y^r, end{equation} wheren denotes the block length andA_r , denotes the number of codewords of weightr . LetC be a self-dual code overGF(q) in which every weight is divisible byc . Then Gleason's theorem states that 1) ifq = 2 andc = 2, the weight enumerator ofC is a sum of products of the polynomialsx^2 + y^2 andx^2y^2 (x^2 - y^2 )^2 ifq = 2 andc = 4, the weight enumerator is a sum of products ofx^8 + 14x^4 y^4 + y^8 andx^4 y^4 (x^4 - y^4)^4 ; and 3) ifq = 3 andc = 3, the weight enumerator is a sum of products ofx^4 + 8xy^3 andy^3(x^3 - y^3)^3 . In this paper we give several proofs of Gleason's theorem. 相似文献
13.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1987,33(5):744-747
Letalpha_{n} denote the number of cosets with minimum weightn of the(2^{m}, m + 1) Reed-Muller code. Thealpha_{n} for2^{m-2} leq n < 2^{m-2} + 2^{m - 4} is determined. 相似文献
14.
《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
15.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1975,21(1):95-96
Some integrals are presented that can be expressed in terms of theQ_M function, which is defined as begin{equation} Q_M(a,b) = int_b^{infty} dx x(x/a)^{M-1} exp (- frac{x^2 + a^2}{2}) I_{M-1}(ax), end{equation} whereI_{M-1} is the modified Bessel function of orderM-1 . Some integrals of theQ_M function are also evaluated. 相似文献
16.
《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
17.
《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
18.
Higher dimensional orthogonal designs and applications 总被引:2,自引:0,他引:2
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1981,27(6):772-779
The concept of orthogonal design is extended to higher dimensions. A properg -dimensional design[d_{ijk cdots upsilon}] is defined as one in which all parallel(g-1) -dimensional layers, in any orientation parallel to a hyper plane, are uncorrelated. This is equivalent to the requirement thatd_{ijk cdots upsilon} in {0, pm x_{1}, cdots , pm x_{t} } , wherex_{1}, cdots , x_{t} are commuting variables, and thatsum_{p} sum_{q} sum_{r} cdots sum_{y} d_{pqr cdots ya} d_{pqr cdots yb} = left( sum_{t} s_{i}x_{i}^{2} right)^{g-1} delta ab, where(s{1}, cdots , s{t}) are integers giving the occurrences ofpm x_{1}, cdots , pm x_{t} in each row and column (this is called the type(s_{1}, cdot ,s_{t})^{g-1}) and(pqr cdots yz) represents all permutations of(ijk cdots upsilon) . This extends an idea of Paul J. Shlichta, whose higher dimensional Hadamard matrices are special cases withx_{1}, cdots , x_{t} in {1,- 1}, (s_{1}, cdots, s_{t})=(g) , and(sum_{t}s_{i}x_{i}^{2})=g . Another special case is higher dimensional weighing matrices of type(k)^{g} , which havex_{1}, cdots , x_{t} in {0,1,- 1}, (s_{1}, cdots, s_{t})=(k) , and(sum_{t}s_{i}x_{i}^{2})=k . Shlichta found properg -dimensional Hadamard matrices of size(2^{t})^{g} . Proper orthogonal designs of type 相似文献
19.
《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
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