A new binary sequence family with low correlation and large size

For odd n=2l+1 and an integer /spl rho/ with 1/spl les//spl rho//spl les/l, a new family S/sub o/(/spl rho/) of binary sequences of period 2/sup n/-1 is constructed. For a given /spl rho/, S/sub o/(/spl rho/) has maximum correlation 1+2/sup n+2/spl rho/-1/2/, family size 2/sup n/spl rho//, and maximum linear span n(n+1)/2. Similarly, a new family of S/sub e/(/spl rho/) of binary sequences of period 2/sup n/-1 is also presented for even n=2l and an integer /spl rho/ with 1/spl les//spl rho/相似文献   

Cyclic codes over GR(4/sup m/) which are also cyclic over /spl Zopf//sub 4/

Let GR(4/sup m/) be the Galois ring of characteristic 4 and cardinality 4/sup m/, and /spl alpha/_={/spl alpha//sub 0/,/spl alpha//sub 1/,...,/spl alpha//sub m-1/} be a basis of GR(4/sup m/) over /spl Zopf//sub 4/ when we regard GR(4/sup m/) as a free /spl Zopf//sub 4/-module of rank m. Define the map d/sub /spl alpha/_/ from GR(4/sup m/)[z]/(z/sup n/-1) into /spl Zopf//sub 4/[z]/(z/sup mn/-1) by d/spl alpha/_(a(z))=/spl Sigma//sub i=0//sup m-1//spl Sigma//sub j=0//sup n-1/a/sub ij/z/sup mj+i/ where a(z)=/spl Sigma//sub j=0//sup n-1/a/sub j/z/sup j/ and a/sub j/=/spl Sigma//sub i=0//sup m-1/a/sub ij//spl alpha//sub i/, a/sub ij//spl isin//spl Zopf//sub 4/. Then, for any linear code C of length n over GR(4/sup m/), its image d/sub /spl alpha/_/(C) is a /spl Zopf//sub 4/-linear code of length mn. In this article, for n and m being odd integers, it is determined all pairs (/spl alpha/_,C) such that d/sub /spl alpha/_/(C) is /spl Zopf//sub 4/-cyclic, where /spl alpha/_ is a basis of GR(4/sup m/) over /spl Zopf//sub 4/, and C is a cyclic code of length n over GR(4/sup m/).     

Generalization of the /spl Sigma//sub 0/-rank criteria for space-time codes

Recently, Liu et al., developed the /spl Sigma//sub 0/-rank criteria for space-time codes. It provides a sufficient condition on codeword and generator matrices defined over finite rings /spl Zopf//sub 2k/(j) to ensure full spatial diversity with 2/sup 2k/-QAM modulation. Here, we generalize the /spl Sigma//sub 0/-rank criteria and derive a sufficient condition on the generator matrices defined over finite rings /spl Zopf//sub 2l/(j) to ensure full spatial diversity with 2/sup 2k/-QAM modulation for any positive integer l/spl les/k. We also show that generator matrices defined over GF(2) satisfying the BPSK stacking construction constraint of Mammons and El Gamal achieve full spatial diversity when used with 2/sup 2k/-QAM modulation.     

On /spl Zopf//sub 4/-linear Preparata-like and Kerdock-like codes

We say that a binary code of length n is additive if it is isomorphic to a subgroup of /spl Zopf//sub 2//sup /spl alpha// /spl times/ /spl Zopf//sub 4//sup /spl beta//, where the quaternary coordinates are transformed to binary by means of the usual Gray map and hence /spl alpha/ + 2/spl beta/ = n. In this paper, we prove that any additive extended Preparata (1968) -like code always verifies /spl alpha/ = 0, i.e., it is always a /spl Zopf//sub 4/-linear code. Moreover, we compute the rank and the dimension of the kernel of such Preparata-like codes and also the rank and the kernel of the /spl Zopf//sub 4/-dual of these codes, i.e., the /spl Zopf//sub 4/-linear Kerdock-like codes.     

The rank and kernel of extended 1-perfect /spl Zopf//sub 4/-linear and additive non-/spl Zopf//sub 4/-linear codes

A binary extended 1-perfect code of length n + 1 = 2/sup t/ is additive if it is a subgroup of /spl Zopf//sub 2//sup /spl alpha// /spl times/ /spl Zopf//sub 4//sup /spl beta//. The punctured code by deleting a /spl Zopf//sub 2/ coordinate (if there is one) gives a perfect additive code. 1-perfect additive codes were completely characterized and by using that characterization we compute the possible parameters /spl alpha/, /spl beta/, rank, and dimension of the kernel for extended 1-perfect additive codes. A very special case is that of extended 1-perfect /spl Zopf//sub 4/-linear codes.     

List decoding from erasures: bounds and code constructions

We consider the problem of list decoding from erasures. We establish lower and upper bounds on the rate of a (binary linear) code that can be list decoded with list size L when up to a fraction p of its symbols are adversarially erased. Such bounds already exist in the literature, albeit under the label of generalized Hamming weights, and we make their connection to list decoding from erasures explicit. Our bounds show that in the limit of large L, the rate of such a code approaches the "capacity" (1 - p) of the erasure channel. Such nicely list decodable codes are then used as inner codes in a suitable concatenation scheme to give a uniformly constructive family of asymptotically good binary linear codes of rate /spl Omega/(/spl epsiv//sup 2//log(1//spl epsiv/)) that can be efficiently list-decoded using lists of size O(1//spl epsiv/) when an adversarially chosen (1 - /spl epsiv/) fraction of symbols are erased, for arbitrary /spl epsiv/ > 0. This improves previous results in this vein, which achieved a rate of /spl Omega/(/spl epsiv//sup 3/log(1//spl epsiv/)).     

On The General Relation Between /spl alpha/ and Q (Correspondence)

The relation between the quality factor Q and the attenuation constant /spl alpha/ of a transmission line has been known as follows: /spl alpha/ = /spl beta/ / /2Q where /spl beta/ is the phase constant. Recently from the following relation of propagation constant at resonance /spl Gamma/(/spl omega//sub 0/) + /spl part//spl Gamma/ / /spl part//spl omega/ /spl Delta//spl omega//spl cong/ i/spl beta/(/spl omega//sub 0/), where /spl Gamma/(/spl omega//sub 0/) = /spl alpha/(/spl omega//sub 0/) + i/spl beta/(/spl omega//sub 0/). Yeh derived a general relation between Q and /spl alpha/, namely, /spl alpha/ = /spl upsi//sub p/ / /spl upsi//sub g/ /spl beta/ / /2Q where /spl upsi//sub p/, and /spl upsi//sub g/ are the phase velocity and group velocity of the wave respectively. This general relation can be derived very simply from the generally accepted definition of /spl alpha/ and Q.     

Lee metric decoding of alternant codes over /spl Zopf//sub q/

A multi-stage Lee metric list decoding approach for alternant codes over /spl Zopf/(p/sup l/ )where p is prime and l/spl ges/2 is proposed. It is demonstrated that the error-correcting capability of such a decoding scheme increasingly surpasses that of a single-stage decoding approach as the length of the code and l increases.     

The inequalities of quantum information theory

Let /spl rho/ denote the density matrix of a quantum state having n parts 1, ..., n. For I/spl sube/N={1, ..., n}, let /spl rho//sub I/=Tr/sub N/spl bsol/I/(/spl rho/) denote the density matrix of the state comprising those parts i such that i/spl isin/I, and let S(/spl rho//sub I/) denote the von Neumann (1927) entropy of the state /spl rho//sub I/. The collection of /spl nu/=2/sup n/ numbers {S(/spl rho//sub I/)}/sub I/spl sube/N/ may be regarded as a point, called the allocation of entropy for /spl rho/, in the vector space R/sup /spl nu//. Let A/sub n/ denote the set of points in R/sup /spl nu// that are allocations of entropy for n-part quantum states. We show that A~/sub n/~ (the topological closure of A/sub n/) is a closed convex cone in R/sup /spl nu//. This implies that the approximate achievability of a point as an allocation of entropy is determined by the linear inequalities that it satisfies. Lieb and Ruskai (1973) have established a number of inequalities for multipartite quantum states (strong subadditivity and weak monotonicity). We give a finite set of instances of these inequalities that is complete (in the sense that any valid linear inequality for allocations of entropy can be deduced from them by taking positive linear combinations) and independent (in the sense that none of them can be deduced from the others by taking positive linear combinations). Let B/sub n/ denote the polyhedral cone in R/sup /spl nu// determined by these inequalities. We show that A~/sub n/~=B/sub n/ for n/spl les/3. The status of this equality is open for n/spl ges/4. We also consider a symmetric version of this situation, in which S(/spl rho//sub I/) depends on I only through the number i=/spl ne/I of indexes in I and can thus be denoted S(/spl rho//sub i/). In this case, we give for each n a finite complete and independent set of inequalities governing the symmetric allocations of entropy {S(/spl rho//sub i/)}/sub 0/spl les/i/spl les/n/ in R/sup n+1/.     

Fast transform for decoding both errors and erasures of Reed-Solomon codes over GF(2/sup m/) for 8/spl les/m/spl les/10

In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2/sup m/-1 points over GF(2/sup m/), where 8/spl les/m/spl les/10. Using these transforms, together with the Berlekamp-Massey algorithm, the complexity of the transform-domain decoder for correcting both errors and erasures of the Reed-Solomon codes of block length 2/sup m/-1 over GF(2/sup m/) for 8/spl les/m/spl les/10 is reduced substantially from the previous time-domain decoder. A computer simulation verifies these new results.     

A highly reliable 3-D integrated SBT ferroelectric capacitor enabling FeRAM scaling

Ferroelectric random access memories (FeRAMs) combine very attractive properties such as low-voltage operation, fast write and nonvolatility. However, unlike Flash memories, FeRAMs are difficult to scale along with the CMOS technology roadmap, mainly because of the decrease of available signal with decreasing cell area. One solution for further scaling is to integrate three-dimensional (3-D) FeCAPs. In this paper, we have integrated a 3-D FeCAP structure in a 0.35-/spl mu/m CMOS technology whereby the effective area of <1 /spl mu/m/sup 2/ single FeCAPs is increased by a factor of almost two. We show that, after optimization of the metal-organic chemical vapor deposition (MOCVD) deposition and post-anneal steps of the Sr/sub 0.8/Bi/sub 2.2/Ta/sub 2/O/sub 9/ (SBT) layer, the sidewall SBT contributes to the polarization Pr, resulting in higher Pr values for 0.81-/spl mu/m/sup 2/ three-dimensional (3-D) capacitors (2Pr/spl ap/15 /spl mu/C/cm/sup 2/) than for 1000 /spl mu/m/sup 2/ 2-D capacitors (2Pr/spl ap/10 /spl mu/C/cm/sup 2/). Moreover, these 3-D capacitors are observed to be fatigue-free and imprint-free up to 10/sup 11/ cycles (5-V square pulses), and extrapolations of retention tests indicate less than 10% Pr loss after ten years at 85/spl deg/C, which shows that sidewall SBT retains the same excellent reliability properties as 2-D capacitors. We demonstrate in this paper that the negative signal-scaling trend can be halted using 3-D FeCAPs. To our knowledge, this paper is the first report on electrical and reliability properties of integrated 3-D FeCAPs, and is a starting point for future development work on densely scaled FeRAMs.     

Monomial and quadratic bent functions over the finite fields of odd characteristic

Considered are p-ary bent functions having the form f(x)=Tr/sub n/(/spl sigma//sub i=0//sup s/a/sub i/x/sup di/). A new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value -1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. The (weak) regularity of the new as well as of known monomial bent functions is discussed and the first example of a not weakly regular bent function is given. Finally, some criteria for an arbitrary quadratic function to be bent are proven.     

Maximum minimal distance partitioning of the /spl Zopf//sup 2/ lattice

We study the problem of dividing the /spl Zopf//sup 2/ lattice into partitions so that minimal intra-partition distance between the points is maximized. We show that this problem is analogous to the problem of sphere packing. An upper bound on the achievable intra-partition distances for a given number of partitions follows naturally from this observation, since the optimal sphere packing in two dimensions is achieved by the hexagonal lattice. Specific instances of this problem, when the number of partitions is 2/sup m/, were treated in trellis-coded modulation (TCM) code design by Ungerboeck (1982) and others. It is seen that methods previously used for set partitioning in TCM code design are asymptotically suboptimal as the number of partitions increases. We propose an algorithm for solving the /spl Zopf//sup 2/ lattice partitioning problem for an arbitrary number of partitions.     

Scanning and prediction in multidimensional data arrays

The problem of sequentially scanning and predicting data arranged in a multidimensional array is considered. We introduce the notion of a scandictor, which is any scheme for the sequential scanning and prediction of such multidimensional data. The scandictability of any finite (probabilistic) data array is defined as the best achievable expected "scandiction" performance on that array. The scandictability of any (spatially) stationary random field on /spl Zopf//sup m/ is defined as the limit of its scandictability on finite "boxes" (subsets of /spl Zopf//sup m/), as their edges become large. The limit is shown to exist for any stationary field, and essentially be independent of the ratios between the box dimensions. Fundamental limitations on scandiction performance in both the probabilistic and the deterministic settings are characterized for the family of difference loss functions. We find that any stochastic process or random field that can be generated autoregressively with a maximum-entropy innovation process is optimally "scandicted" the way it was generated. These results are specialized for cases of particular interest. The scandictability of any stationary Gaussian field under the squared-error loss function is given a single-letter expression in terms of its spectral measure and is shown to be attained by the raster scan. For a family of binary Markov random fields (MRFs), the scandictability under the Hamming distortion measure is fully characterized.     

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.     

Near-ellipsoidal Voronoi coding

We consider a special case of Voronoi coding, where a lattice /spl Lambda/ in /spl Ropf//sup n/ is shaped (or truncated) using a lattice /spl Lambda/'={(m/sub 1/x/sub 1/,...,m/sub n/x/sub n/)|(x/sub 1/,...,x/sub n/)/spl isin//spl Lambda/} for a fixed m_=(m/sub 1/,...,m/sub n/)/spl isin/(/spl Nopf//spl bsol/{0,1})/sup n/. Using this technique, the shaping boundary is near-ellipsoidal. It is shown that the resulting codes can be indexed by standard Voronoi indexing algorithms plus a conditional modification step, as far as /spl Lambda/' is a sublattice of /spl Lambda/. We derive the underlying conditions on m_ and present generic near-ellipsoidal Voronoi indexing algorithms. Examples of constraints on m_ and conditional modification are provided for the lattices A/sub 2/, D/sub n/ (n/spl ges/2) and 2D/sub n//sup +/ (n even /spl ges/4).     

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.     

Fully depleted dual-gated thin-film SOI P-MOSFETs fabricated in SOI islands with an isolated buried polysilicon backgate

P-channel dual-gated thin-film silicon-on-insulator (DG-TFSOI) MOSFETs have been fabricated with an isolated buried polysilicon backgate in an SOI island formed by epitaxial lateral overgrowth (ELO) of silicon. This structure allows individual operation of both the top and back gates rather than the conventional common backgate structure. When fully-depleted, the buried gate is used to individually shift the top gate threshold voltage (V/sub T/). A linear shift of /spl Delta/V/sub T,top///spl Delta/V/sub G,back/ of 0.5 V/V was achieved with a thin buried oxide. The effective density of interface traps (D/sub it/) for the backgate polysilicon-oxide SOI interface was measured to be 1.8/spl times/10/sup 11/ #/cm/sup 2//spl middot/eV as compared to the substrate-oxide of 1.1/spl times/10/sup 11/ #/cm/sup 2//spl middot/eV.     

Analysis of cross-flow jet-type singlet oxygen generator

A cross-flow jet-type singlet oxygen generator has been developed, tested and analyzed in order to characterize the dependence of output performance on major input parameters. A thermal-balance model, which can predict O/sub 2/(/sup 1//spl Delta/) yield, gas temperature, and gas residence time, is proposed, and the resultant theoretical results are compared to the experimental data. Combined with computational fluid dynamics-based gas residence-time analysis, the model provides good agreement with the measured value of the O/sub 2/(/sup 1//spl Delta/) yield and the gas temperature. The surface chemistry model was applied to the measured Cl/sub 2/ utilization data, and was found to be inconsistent in the regime of high Cl/sub 2/ loading on the basic hydrogen peroxide jet, indicating that depletion of HO/sub 2//sup -/ is taking place.     

High-power P-i-N diode with local lifetime control using palladium diffusion controlled by radiation defects

We demonstrate for the first time a high-power P-i-N diode with local lifetime control using palladium (Pd) diffusion. Low-temperature (600/spl deg/C-700/spl deg/C) diffusion of Pd is stimulated by radiation defects resulting from alpha-particle irradiation (/sup 4/He/sup 2+/: 10 MeV, 10/sup 12/ cm/sup -2/). The region of maximal radiation damage of Gaussian shape is decorated by substitutional Pd after diffusion from a palladium silicide surface layer through the P/sup +/--P region into the N-base close to the anode junction. Significantly lower leakage current compared to that of standard /sup 4/He/sup 2+/ irradiation and very good ruggedness under fast recovery (di/dt/spl ap/500 A//spl mu/s, V/sub R//spl ap/2 kV) is demonstrated for Pd diffusion at 600/spl deg/C.