A New Class of p-Ary Sequence Families with Low Correlation Prop erty via m-Sequence

For an odd prime p which is congruent to 3 module 4 and an odd integer k, we investigate the upper bound on the magnitude of cross correlation values of a p-ary m-sequence s(t) and its decimated sequences s(dt+l) for a decimation value d. Using the above upper bound of the magnitude of cross correlation values of p-ary m-sequence and its decimated sequences, we construct a new class of p-ary sequence families with low correlation property via m-sequence.     

Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications

In this paper we present a unified way to determine the values and their multiplicities of the exponential sums Sigma_xisinF(q)zeta_p ^Tr(af(x)+bx)(a,bisinF_q,q=p^m,pges3) for all perfect nonlinear functions f which is a Dembowski-Ostrom polynomial or p = 3,f=^x(3(k)+1)/2 where k is odd and (k,m)=1. As applications, we determine (1) the correlation distribution of the m-sequence {a_lambda=Tr(gamma^lambda)}(lambda=0,1,...) and the sequence {b_lambda=Tr(f(gamma^lambda))}(lambda=0,1,...) over F_p where gamma is a primitive element of F_q and (2) the weight distributions of the linear codes over F_p defined by f.     

Rate k/(k+1) punctured convolutional encoders

G.D. Forney (1970, 1975) defined a minimal encoder as a polynomial matrix G such that G generates the code and G has the least constraint length among all generators for the code. Any convolutional code can be generated by a minimal encoder. High-rate k(k+1) punctured convolutional codes were introduced to simplify Viterbi decoding. An ordinary convolutional encoder G can be obtained from any punctured encoder. A punctured encoder is minimal if the corresponding ordinary encoder G is minimal and the punctured and ordinary encoders have the same constraint length. It is shown that any rate k/(k+1), noncatastrophic, antipodal punctured encoder is a minimal encoder.<>     

Motion-compensated DCT temporal filters for efficient spatio-temporal scalable video coding

Although most of the proposals for implementing motion-compensated temporal filtering (MCTF) schemes are based on the wavelet transform, in this paper, we propose an MCTF framework based on the discrete cosine transform (DCT). Using DCT decimation and interpolation, several temporal decomposition structures named motion-compensated DCT temporal filters (MCDCT-TF) are introduced. These structures are able to employ filters of any length with particular emphasis on 5/3 DCT and 7/4 DCT. The proposed MCDCT-TF and the two-dimensional (2D) DCT decimation technique are incorporated into H.264/AVC to provide spatio-temporal scalability. Compared with the current MCTF-based lifting schemes such as Haar, and 5/3 wavelet filters, simulation results show that the proposed MCDCT-TF utilizing longer tap DCT filters achieves a significant improvement in coding gain. The impact of odd/even group of frames, the decimation/interpolation ratios, and motion-compensated connectivity on the MCDCT-TF performance are also analyzed. Moreover, simulation results show that the performance of the presented scalable video coding is close to the single layer H.264/AVC and is slightly inferior to the temporal scalability supported in JSVM, the state-of-the-art scalable video coding standard, that gets its gain from Hierarchical B-pictures. However, our spatio-temporal coding scheme outperforms the spatio-temporal supported in JSVM even if it uses hierarchical B-pictures to improve its gain.     

On MDS extensions of generalized Reed- Solomon codes

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} qis 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 withkin the above range can be {em uniquely} extended to a maximal MDS code of lengthq + 1, and that generalized Reed-Solomon codes of lengthq + 1and dimension2leq k leq lfloor q/2 rfloor + 2 (k neq 3 {rm if} qis 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 + 1do not exist.     

The L(2,1)-labeling and operations of graphs

Motivated by a variation of the channel assignment problem, a graph labeling analogous to the graph vertex coloring has been presented and is called an L(2,1)-labeling. More precisely, an L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)-f(y)| /spl ges/ 2 if d(x,y)=1 and |f(x)-f(y)| /spl ges/ 1 if d(x,y) = 2. The L(2,1)-labeling number /spl lambda/(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v):v/spl isin/V(G)}=k. A conjecture states that /spl lambda/(G) /spl les/ /spl Delta//sup 2/ for any simple graph with the maximum degree /spl Delta//spl ges/2. This paper considers the graphs formed by the Cartesian product and the composition of two graphs. The new graph satisfies the conjecture above in both cases(with minor exceptions).     

非对称多模量子叠加态光场的等幂高次和压缩

根据量子力学中的态叠加原理,构造了由多模复共轭相干态|{zj(a)*}>q和多模复共轭相干态|{zj(b)*}>q的相反态|{-zj(b)*}>q的线性叠加所组成的非对称两态叠加多模量子叠加态光场|ψ(2)>q,利用多模压缩态理论研究了态|ψ1f(2)>q的等幂高次和压缩特性,结果表明: 1)当Rj(a)=Rj(b)和ψj(a)-ψj(b)=±(2k 1)π(k=0,1,2,3……),态|ψ1f(2)>q的两个正交相位分量均处于N-H最小测不准态的结果;2)当Rj(a)=Rj(b)=Rj和ψj(a)=ψj(b)=ψj,ψ态|1f(2)>q的等幂高次和压缩与文献3的结果相似; 3)当Rj(a)≠Rj(b)=Rj和ψj(a)=ψj(b)=ψj,且和满足一定条件时,无论qN为奇数还是偶数,态|ψ1f(2)>q的两个正交相位分量均可分别呈现周期性变化的等幂高次和压缩效应,但qN为奇数时的压缩深度大于qN为偶数时的压缩深度。     

A new construction for n-track (d, k) codes with redundancy

A new construction for n-track (d, k) codes with redundancy r, referred to as (d, k; n, r) codes, is presented. This construction applies single-track (d, k+Δk) codes (with certain extra constraints and appropriate amounts of delay) on each of the n tracks. This construction achieves a large part of the capacity increases possible when using (d, k; n, r) codes, has simple encoders and decoders, and exhibits considerable robustness to faulty tracks. It is shown that under this construction, (d, k; n, r) codes can achieve at least (n-r-1:)/n*100% of the gap in capacity between conventional (d, k) and (d, ∞) codes. Several practical examples of (d, k; n, r) codes under this construction are presented     

A New Family of Ternary Almost Perfect Nonlinear Mappings

A mapping f(x) from GF(pⁿ) to GF(pⁿ) is differentially k-uniform if k is the maximum number of solutions x isin GF(pⁿ) of f(x+a) - f(x) = b, where a, b isin GF(pⁿ) and a ne 0. A 2-uniform mapping is called almost perfect nonlinear (APN). This correspondence describes new families of ternary APN mappings over GF(3ⁿ), n>3 odd, of the form f(x) = ux^d + x^{d 2} where d₁ = (3^n-1)/2 - 1 and d₂ = 3ⁿ - 2.     

A method of generalized projections (MGP) ghost correction algorithm for interleaved EPI

Investigations into the method of generalized projections (MGP) as a ghost correction method for interleaved EPI are described. The technique is image-based and does not require additional reference scans. The algorithm was found to be more effective if a priori knowledge was incorporated to reduce the degrees of freedom, by modeling the ghosting as arising from a small number of phase offsets. In simulations with phase variation between consecutive shots for n-interleaved echo planar imaging (EPI), ghost reduction was achieved for n = 2 only. With no phase variation between shots, ghost reduction was obtained with n up to 16. Incorporating a relaxation parameter was found to improve convergence. Dependence of convergence on the region of support was also investigated. A fully automatic version of the method was developed, using results from the simulations. When tested on in vivo 2-, 16-, and 32-interleaved spin-echo EPI data, the method achieved deghosting and image restoration close to that obtained by both reference scan and odd/even filter correction, although some residual artifacts remained.     

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.     

基于相位差分方法的BPSK引信信号m序列识别

该文根据二相移相键控(BPSK)引信信号脉冲相位差分和m序列的一一对应关系,通过求解脉冲相位差分方程组来得到m序列。首先,通过FFT求得脉冲相位,然后分别采用了一阶相位差分方法和二阶相位差分方法来对m序列进行识别。经计算机仿真验证,该方法是完全正确的。最后对该方法进行了可靠性分析,分析表明,即使某一个码元由于对应的脉冲相位测量误差很大而被错误识别,也不会对后续的PN码识别产生影响,说明该方法具有很高的可靠性。     

Generalized Kasami Sequences: The Large Set

In this correspondence, new binary sequence families F^k of period 2ⁿ-1 are constructed for even n and any k with gcd(k,n)=2 if n/2 is odd or gcd(k,n)=1 if n/2 is even. The distribution of their correlation values is completely determined. These families have maximum correlation 2^n/2+1 and family size 2^3n/2 + 2^n/2 for odd n/2 or 2^3n/2+2^n/2-1 for even n/2. The proposed families include the large set of Kasami sequences, where the k is taken as k=n/2+1.     

有限域上m序列与其采样序列的互相关性

本文研究了有限域GF(p)上的m序列与其采样序列之间的互相关函数C_d(t),得到以下结论:(1)当采样因子d= pⁿ+1 p+1 + pⁿ-1 2 ,n为奇数且p≡3(mod 4)时,|1+C_d(t)| 1+p 2 pⁿ ,从而解决了Muller在文献 中提出的一个公开问题,并将文献[1]中的p=3时的结论推广为一般情形;(2)当d= pⁿ+1 p+1 ,n为奇数且p≡3(mod 4)时,C_d(t)∈{-1,-1+ p n+1 -1- pⁿ⁺¹ };(3)在以上两种情况下,对|1+C_d(t)|关于t的分布进行了研究,结果表明,当p很大时,|1+C_d(t)|取最大值的概率很小.     

Ternary m-sequences with three-valued cross-correlation function:new decimations of Welch and Niho type

We show that the cross correlation between two ternary m-sequences of period 3ⁿ-1 that differ by the decimation d=2·3^m+1, where n=2m+1, takes on three different values. We conjecture the same result for the decimation d=2·3 ^r+1, where n is odd and r is defined by the condition 4r+1≡0 mod n. These two new cases form in a sense ternary counterparts of two previously confirmed binary cases, the conjectures of Welch and Niho (1972)     

Electrical properties of Ge metal–oxide–semiconductor capacitors with high-k La2O3 gate dielectric incorporated by N or/and Ti

LaON, LaTiO and LaTiON films are deposited as gate dielectrics by incorporating N or/and Ti into La2O3 using the sputtering method to fabricate Ge MOS capacitors, and the electrical properties of the devices are carefully examined. LaON/Ge capacitors exhibit the best interface quality, gate leakage property and device reliability, but a smaller k value (14.9). LaTiO/Ge capacitors exhibit a higher k value (22.7), but a deteriorated interface quality, gate leakage property and device reliability. LaTiON/Ge capacitors exhibit the highest k value (24.6), and a relatively better interface quality (3.1E11 eV^-1cm^-2), gate leakage property (3.6E3 A/cm^2 at Vg = 1 V + Vfb) and device reliability. Therefore, LaTiON is more suitable for high performance Ge MOS devices as a gate dielectric than LaON and LaTiO materials.     

An improved random walk model for PCS networks

We propose an improvement to a random walk model for personal communications services networks with hexagonal configuration. The number of states required is reduced from n(n + 1)/2 to (n/sup 2/ + 2n + 4)/4 if n is even, and to (n/sup 2/ + 2n + 5) /4 if n is odd, where n is the layers of a cluster.     

An extension of the channel-assignment problem: L(2, 1)-labelings of generalized Petersen graphs

The channel-assignment problem involves assigning frequencies represented by nonnegative integers to radio transmitters such that transmitters in close proximity receive frequencies that are sufficiently far apart to avoid interference. In one of its variations, the problem is commonly quantified as follows: transmitters separated by the smallest unit distance must be assigned frequencies that are at least two apart and transmitters separated by twice the smallest unit distance must be assigned frequencies that are at least one apart. Naturally, this channel-assignment problem can be modeled with vertex labelings of graphs. An L(2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the nonnegative integers such that |f(x)-f(y)|/spl ges/2 if d(x,y)=1 and |f(x)-f(y)|/spl ges/1 if d(x,y)=2. The /spl lambda/-number of G, denoted /spl lambda/(G), is the smallest number k such that G has an L(2, 1)-labeling using integers from {0,1,...,k}. A long-standing conjecture by Griggs and Yeh stating that /spl lambda/(G) can not exceed the square of the maximum degree of vertices in G has motivated the study of the /spl lambda/-numbers of particular classes of graphs. This paper provides upper bounds for the /spl lambda/-numbers of generalized Petersen graphs of orders 6, 7, and 8. The results for orders 7 and 8 establish two cases in a conjecture by Georges and Mauro, while the result for order 6 improves the best known upper bound. Furthermore, this paper provides exact values for the /spl lambda/-numbers of all generalized Petersen graphs of order 6.     

A Grounded-Resistor Current Conveyor-Based Active-R Multiphase Sinusoidal Oscillator

A multiphase active-R sinusoidal oscillator circuit is presented.The oscillator can produce M signals (M being even or odd) equally spaced inphase. The circuit has low component count, uses grounded resistors andenjoys low active and passive sensitivities. The feasibility of convertingthe circuit into a voltage controlled multiphase oscillator is studied.Simulation results are included.     

L(j, k)-Labelings of Kronecker Products of Complete Graphs

For positive integers j ges k, an L(j, k)-labeling of a graph G is an integer labeling of its vertices such that adjacent vertices receive labels that differ by at least j and vertices that are distance two apart receive labels that differ by at least k. We determine lambda^j _k(G) for the case when G is a Kronecker product of finitely many complete graphs, where there are certain conditions on j and k. Areas of application include frequency allocation to radio transmitters.