Efficient routing and wavelength assignment for reconfigurable WDM ring networks with wavelength converters

We consider the problem of wavelength assignment in reconfigurable WDM networks with wavelength converters. We show that for N-node P-port bidirectional rings, a minimum number of /spl lceil/PN/4/spl rceil/ wavelengths are required to support all possible connected virtual topologies in a rearrangeably nonblocking fashion, and provide an algorithm that meets this bound using no more than /spl lceil/PN/2/spl rceil/ wavelength converters. This improves over the tight lower bound of /spl lceil/PN/3/spl rceil/ wavelengths required for such rings given in if no wavelength conversion is available. We extend this to the general P-port case where each node i may have a different number of ports P/sub i/, and show that no more than /spl lceil//spl sigma//sub i/P/sub i//4/spl rceil/+1 wavelengths are required. We then provide a second algorithm that uses more wavelengths yet requires significantly fewer converters. We also develop a method that allows the wavelength converters to be arbitrarily located at any node in the ring. This gives significant flexibility in the design of the networks. For example, all /spl lceil/PN/2/spl rceil/ converters can be collocated at a single hub node, or distributed evenly among the N nodes with min{/spl lceil/P/2/spl rceil/+1,P} converters at each node.     

Order statistics from a logistic distribution and applications to survival and reliability analysis

Joint moments involving arbitrary powers of order statistics are the main concern. Consider order statistics u/sub 1/ /spl les/ u/sub 2/ /spl les/ /spl middot//spl middot//spl middot/ /spl les/ u/sub k/ coming from a simple random sample of size n from a real continuous population where u/sub 1/ = x/sub r(1):n/ is order-statistic #r/sub 1/, u/sub 2/ = x/sub r(1)+r(2):n/ is order statistic #(r/sub 1/ + r/sub 2/), et al., and u/sub k/ = x/sub r(1)+/spl middot//spl middot//spl middot/+r(k):n/ is order statistic #(r/sub 1/ +/spl middot//spl middot//spl middot/+ r/sub k/). Product moments are examined of the type E[u/sub 1//sup /spl alpha/(1)/ /spl middot/ u/sub 2//sup /spl alpha/(2)//sub /spl middot/ /spl middot//spl middot//spl middot//spl middot//u/sub k//sup /spl alpha/(k)/] where /spl alpha//sub 1/, ..., /spl alpha//sub k/ are arbitrary quantities that might be complex numbers, and E[/spl middot/] denotes the s-expected value. Some explicit evaluations are considered for a logistic population. Detailed evaluations of all integer moments of u/sub 1/ and recurrence relations, recurring only on the order of the moments, are given. Connections to survival functions in survival analysis, hazard functions in reliability situations, real type-1, type-2 /spl beta/ and Dirichlet distributions are also examined. Arbitrary product moments for the survival functions are evaluated. Very general results are obtained which can be used in many problems in various areas.     

Improving the Gilbert-Varshamov bound for q-ary codes

Given positive integers q,n, and d, denote by A/sub q/(n,d) the maximum size of a q-ary code of length n and minimum distance d. The famous Gilbert-Varshamov bound asserts that A/sub q/(n,d+1)/spl ges/q/sup n//V/sub q/(n,d) where V/sub q/(n,d)=/spl Sigma//sub i=0//sup d/ (/sub i//sup n/)(q-1)/sup i/ is the volume of a q-ary sphere of radius d. Extending a recent work of Jiang and Vardy on binary codes, we show that for any positive constant /spl alpha/ less than (q-1)/q there is a positive constant c such that for d/spl les//spl alpha/n A/sub q/(n,d+1)/spl ges/cq/sup n//V/sub q/(n,d)n. This confirms a conjecture by Jiang and Vardy.     

Asymptotic behavior of the pairwise error probability with applications to transmit beamforming and rake receivers

We derive the precise asymptote of the pairwise error probability for high signal-to-noise ratio (SNR) and apply it to obtain new results concerning transmit beamforming and selective Rake receivers. For downlink beamforming (with N transmit antennas and independently identically distributed (i.i.d.) Rayleigh fading) based on quantized feedback from the mobile, we show that at least /spl lceil/log/sub 2/(N)/spl rceil/ bits of feedback (per coherence time) is required to obtain full diversity, and among all beamforming schemes using /spl lceil/log/sub 2/(N)/spl rceil/ bits of feedback, selection diversity is optimal. We give the exact expression for the SNR loss of selection diversity with respect to ideal beamforming based on perfect knowledge of fading coefficients. Further, we study selective Rake receivers for independent arbitrary fading distribution and arbitrary power delay profile (PDP). In particular, we show that the SNR loss of the SRake receiver with respect to the all-Rake receiver does not depend on the PDP, and we also propose a transformation to adapt the expressions known for the symbol error probability for the case of i.i.d. Rayleigh fading to the general case.     

A class of 1-generator quasi-cyclic codes

If R = F/sub q/[x/spl rceil/]/(x/sup m/ - 1), S = F/sub qn/[x]/(x/sup m/ - 1), we define the mapping a_(x) /spl rarr/ A(x) =/spl sigma//sub 0//sup n-1/a/sub i/(x)/spl alpha//sub i/ from R/sup n/ onto S, where (/spl alpha//sub 0/, /spl alpha//sub i/,..., /spl alpha//sub n-1/) is a basis for F/sub qn/ over F/sub q/. This carries the q-ray 1-generator quasicyclic (QC) code R a_(x) onto the code RA(x) in S whose parity-check polynomial (p.c.p.) is defined as the monic polynomial h(x) over F/sub q/ of least degree such that h(x)A(x) = 0. In the special case, where gcd(q, m) = 1 and where the prime factorizations of x/sub m/ 1 over F/sub q/ and F/sub qn/ are the same we show that there exists a one-to-one correspondence between the q-ary 1-generator quasis-cyclic codes with p.c.p. h(x) and the elements of the factor group J* /I* where J is the ideal in S with p.c.p. h(x) and I the corresponding quantity in R. We then describe an algorithm for generating the elements of J*/I*. Next, we show that if we choose a normal basis for F/sub qn/ over F/sub q/, then we can modify the aforementioned algorithm to eliminate a certain number of equivalent codes, thereby rending the algorithm more attractive from a computational point of view. Finally in Section IV, we show how to modify the above algorithm in order to generate all the binary self-dual 1-generator QC codes.     

Explicit construction of families of LDPC codes with no 4-cycles

Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which has girth at least 2/spl lceil/m/2/spl rceil/+4. We regard these graphs as Tanner graphs of binary codes LU(m,q). We can determine the dimension and minimum weight of LU(2,q), and show that the weight of its minimum stopping set is at least q+2 for q odd and exactly q+2 for q even. We know that D(2,q) has girth 6 and diameter 4, whereas D(3,q) has girth 8 and diameter 6. We prove that for an odd prime p, LU(3,p) is a [p/sup 3/,k] code with k/spl ges/(p/sup 3/-2p/sup 2/+3p-2)/2. We show that the minimum weight and the weight of the minimum stopping set of LU(3,q) are at least 2q and they are exactly 2q for many LU(3,q) codes. We find some interesting LDPC codes by our partial row construction. We also give simulation results for some of our codes.     

Compression mappings on primitive sequences over Z/(p/sup e/)

Let Z/(p/sup e/) be the integer residue ring with odd prime p/spl ges/5 and integer e/spl ges/2. For a sequence a_ over Z/(p/sup e/), there is a unique p-adic expansion a_=a_/sub 0/+a_/spl middot/p+...+a_/sub e-1//spl middot/p/sup e-1/, where each a_/sub i/ is a sequence over {0,1,...,p-1}, and can be regarded as a sequence over the finite field GF(p) naturally. Let f(x) be a primitive polynomial over Z/(p/sup e/), and G'(f(x),p/sup e/) the set of all primitive sequences generated by f(x) over Z/(p/sup e/). Set /spl phi//sub e-1/ (x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,1/(x/sub 0/, x/sub 1/,...,x/sub e-2/) /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,2/(x/sub 0/,x/sub 1/,...,x/sub e-2/) where /spl eta//sub e-2,1/ and /spl eta//sub e-2,2/ are arbitrary functions of e-1 variables over GF(p) and 2/spl les/k/spl les/p-1. Then the compression mapping /spl phi//sub e-1/:{G'(f(x),p/sup e/) /spl rarr/ GF(p)/sup /spl infin// a_ /spl rarr/ /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) is injective, that is, a_ = b_ if and only if /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl phi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/). Furthermore, if f(x) is a strongly primitive polynomial over Z/(p/sup e/), then /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl psi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) if and only if a_ = b_ and /spl phi//sub e-1/(x/sub 0/,...,x/sub e-1/) = /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/).     

Random properties of the highest level sequences of primitive sequences over Z(2/sup e/)

Using the estimates of the exponential sums over Galois rings, we discuss the random properties of the highest level sequences /spl alpha//sub e-1/ of primitive sequences generated by a primitive polynomial of degree n over Z(2/sup e/). First we obtain an estimate of 0, 1 distribution in one period of /spl alpha//sub e-1/. On the other hand, we give an estimate of the absolute value of the autocorrelation function |C/sub N/(h)| of /spl alpha//sub e-1/, which is less than 2/sup e-1/(2/sup e-1/-1)/spl radic/3(2/sup 2e/-1)2/sup n/2/+2/sup e-1/ for h/spl ne/0. Both results show that the larger n is, the more random /spl alpha//sub e-1/ will be.     

Optimal linear identifying codes

Identifying codes can be used to locate malfunctioning processors. We say that a code C of length n is a linear (1,/spl les/l)-identifying code if it is a subspace of F/sub 2//sup n/ and for all X,Y/spl sube/F/sub 2//sup n/ such that |X|, |Y|/spl les/l and X/spl ne/Y, we have /spl cup//sub x/spl isin/X/(B(x)/spl cap/C)/spl ne//spl cup/y/spl isin/Y(B(y)/spl cap/C). Strongly (1,/spl les/l)-identifying codes are a variant of identifying codes. We determine the cardinalities of optimal linear (1,/spl les/l)-identifying and strongly (1,/spl les/l)-identifying codes in Hamming spaces of any dimension for locating any at most l malfunctioning processors.     

Using linear programming to Decode Binary linear codes

A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting "LP decoder" generalizes our previous work on turbo-like codes. A precise combinatorial characterization of when the LP decoder succeeds is provided, based on pseudocodewords associated with the factor graph. Our definition of a pseudocodeword unifies other such notions known for iterative algorithms, including "stopping sets," "irreducible closed walks," "trellis cycles," "deviation sets," and "graph covers." The fractional distance d/sub frac/ of a code is introduced, which is a lower bound on the classical distance. It is shown that the efficient LP decoder will correct up to /spl lceil/d/sub frac//2/spl rceil/-1 errors and that there are codes with d/sub frac/=/spl Omega/(n/sup 1-/spl epsi//). An efficient algorithm to compute the fractional distance is presented. Experimental evidence shows a similar performance on low-density parity-check (LDPC) codes between LP decoding and the min-sum and sum-product algorithms. Methods for tightening the LP relaxation to improve performance are also provided.     

Asymptotic improvement of the Gilbert-Varshamov bound on the size of binary codes

Given positive integers n and d, let A/sub 2/(n,d) denote the maximum size of a binary code of length n and minimum distance d. The well-known Gilbert-Varshamov bound asserts that A/sub 2/(n,d)/spl ges/2/sup n//V(n,d-l), where V(n,d) = /spl sigma//sub i=0//sup d/(/sub i//sup n/) is the volume of a Hamming sphere of radius d. We show that, in fact, there exists a positive constant c such that A/sub 2/(n, d)/spl ges/c2/sup n//V(n,d-1)log/sub 2/V(n, d-1) whenever d/n/spl les/0.499. The result follows by recasting the Gilbert-Varshamov bound into a graph-theoretic framework and using the fact that the corresponding graph is locally sparse. Generalizations and extensions of this result are briefly discussed.     

Dependence of the neodymium random laser threshold on the diameter of the pumped spot

We experimentally studied the dependence of the threshold energy density E/sub th//S in Nd/sub 0.5/La/sub 0.5/Al/sub 3/(BO/sub 3/)/sub 4/ random laser on the diameter of the pumped spot d and found that at d/spl ges/130/spl mu/m, E/sub th//S is proportional to 1/d+const. This functional dependence is different from the one commonly expected in the case of diffusion, /spl prop/1/d/sup 2/+const. However, the obtained experimental dependence does not mean the failure of the diffusion model. Calculating the mean photon's residence time /spl tau//sub res//sup p/ (which photons, making their diffusion-like random walks, spend inside the gain volume) as the function of d and further assuming that E/sub th//S/spl prop/(/spl tau//sup p//sub res/)/sup -1/, we predicted the experimentally obtained functional dependence, /spl prop/1/d+const. The major difference between our model and that of and was in the boundary conditions.     

Frequency hopping sequences with optimal partial autocorrelation properties

We classify some p/sup k/-ary (p prime, k integer) generalized m-sequences and generalized Gordon-Mills-Welch (GMW) sequences of period p/sup 2k/-1 over a residue class ring R=GF(p)[/spl xi/]/(/spl xi//sup k/) having optimal partial Hamming autocorrelation properties. In frequency hopping (FH) spread-spectrum systems, these sequences are useful for synchronizing process. Suppose, for example, that a transmitting p/sup k/-ary FH patterns of period p/sup 2k/-1 are correlated at a receiver. Usually, the length of a correlation window, denoted by L, is shorter than the pattern's overall period. In that case, the maximum value of the out-of-phase Hamming autocorrelation is lower-bounded by /spl lceil/L/p/sup k/+1/spl rceil/ but the classified sequences achieve this bound with equality for any positive integer L.     

Reduced-state representations for trellis codes using constellation symmetry

This paper presents a symmetry-based technique for trellis-code state-diagram reduction that has more general applicability than the quasi-regularity technique of Rouanne et al. and Zehavi et al. for trellis codes using standard constellations and labelings. For a 2/sup /spl nu/x/-state trellis code, the new technique reduces the 2/sup 2/spl nu/x/ state diagram to 2/sup /spl nu/x+/spl nu/q/-state diagram where 0/spl les//spl nu//sub q//spl les//spl nu//sub x/. The particular value of /spl nu//sub q/ depends on the constellation labeling and the convolutional encoder. For standard rate-k/(k+1) set-partitioned trellis codes, /spl nu//sub q/=0, and the overall number of states is the same with the new technique as with quasi-regularity. For codes that are not quasi-regular (and thus not amenable to the quasi-regularity technique), the new technique often provides some improvement (when /spl nu//sub q/相似文献   

Characterization of accumulation layer capacitance for extracting data on high-/spl kappa/ gate dielectrics

A new parameter extraction technique has been outlined for high-/spl kappa/ gate dielectrics that directly yields values of the dielectric capacitance C/sub di/, the accumulation layer surface potential quotient, /spl beta//sub acc/, the flat-band voltage, the surface potential /spl phi//sub s/, the dielectric voltage, the channel doping density and the interface charge density at flat-band. The parallel capacitance, C/sub p/(=C/sub sc/+C/sub it/), was found to be an exponential function of /spl phi//sub s/ in the strong accumulation regime, for seven different high-/spl kappa/ gate dielectrics. The slope of the experimental lnC/sub p/(/spl phi//sub s/) plot, i.e., |/spl beta//sub acc/|, was found to depend strongly on the physical properties of the high-/spl kappa/ dielectric, i.e., was inversely proportional to [(/spl phi//sub b/m/sup *//m)/sup 1/2/K/C/sub di/], where /spl phi//sub b/ is the band offset, and m/sup */ is the effective tunneling mass. Extraction of /spl beta//sub acc/ represented an experimental carrier confinement index for the accumulation layer and an experimental gate-dielectric direct-tunneling current index. /spl beta//sub acc/ may also be an effective tool for monitoring the effects of post-deposition annealing/processing.     

A low-pass biquad derived filter realization

A biquad derived structure employing two Norton (current differencing) amplifiers is presented which requires the minimum number of components. Transfer characteristics of the form K/SUB 1//D(S) and K/SUB 2/(S+/spl omega//SUB n//Q)/D(S) with D(S)=S/SUP 2/+/spl omega//SUB n/S/Q+/spl omega//SUB n//SUP 2/ are realized. Biasing constraints are of major importance in the detailed realization and a typical circuit design is presented along with a discussion of its performance, which is compared with that of others.     

List decoding of q-ary Reed-Muller codes

The q-ary Reed-Muller (RM) codes RM/sub q/(u,m) of length n=q/sup m/ are a generalization of Reed-Solomon (RS) codes, which use polynomials in m variables to encode messages through functional encoding. Using an idea of reducing the multivariate case to the univariate case, randomized list-decoding algorithms for RM codes were given in and . The algorithm in Sudan et al. (1999) is an improvement of the algorithm in , it is applicable to codes RM/sub q/(u,m) with u相似文献   

Identifying and locating-dominating codes: NP-completeness results for directed graphs

Let G=(V, A) be a directed, asymmetric graph and C a subset of vertices, and let B/sub r//sup -/(v) denote the set of all vertices x such that there exists a directed path from x to v with at most r arcs. If the sets B/sub r//sup -/(v) /spl cap/ C, v /spl isin/ V (respectively, v /spl isin/ V/spl bsol/C), are all nonempty and different, we call C an r-identifying code (respectively, an r-locating-dominating code) of G. In other words, if C is an r-identifying code, then one can uniquely identify a vertex v /spl isin/ V only by knowing which codewords belong to B/sub r//sup -/(v), and if C is r-locating-dominating, the same is true for the vertices v in V/spl bsol/C. We prove that, given a directed, asymmetric graph G and an integer k, the decision problem of the existence of an r-identifying code, or of an r-locating-dominating code, of size at most k in G, is NP-complete for any r/spl ges/1 and remains so even when restricted to strongly connected, directed, asymmetric, bipartite graphs or to directed, asymmetric, bipartite graphs without directed cycles.