Balanced nonbinary sequences with good periodic correlationproperties obtained from modified Kumar-Moreno sequences

Kumar and Moreno (see ibid., vol.37, no.3, p.603, 1991) presented a new family of nonbinary sequences which has not only good periodic correlation properties but also the largest family size. First, the unbalanced properties for Kumar-Moreno sequences are pointed out. Second, a new family of balanced nonbinary sequences obtained from modified Kumar-Moreno sequences is proposed, and it is shown that the new family has the same optimal periodic nontrivial correlation as the family of Kumar-Moreno sequences and consists of the balanced nonbinary sequences. It is also shown that the cost of making sequences balanced is a decrease of the family size in addition to the condition that n is an even number. In particular, let the length of Kumar-Moreno sequences and the new sequences be the same and equal to pⁿ-1 with n even, then the family size of the new sequences is p^n/2 which is much smaller than pⁿ, that of Kumar-Moreno sequences     

新的具有大线性复杂度的4值低相关序列集

设正整数n、m和r满足n=4m,r=2m-1 -1,基于Niho序列集和d型函数构造了一类4值低相关序列集S(r).该序列集中序列的数目为2n,相关函数的最大边峰值2(n+2)/2+1,序列的周期为2n-1.通过Key的方法,证明了该序列集中序列线性复杂度的F界为n(2n/2-3+2).该序列集与江文峰等人构造的序列集具有相同的相关函数值和序列数目,但拥有更大的线性复杂度.     

一类具有极低相关性的CDMA序列

 本文利用环Z^p_l上线性递归序列的最高坐标构造了一类序列数目众多的p元序列族,这里p为奇素数且整数l不小于2。对具体可用序列的条数进行了估计。同时利用Galois环上的指数和估计以及Z^p_l的加法群上的谱分析对该序列族的相关性进行了详细分析,得到了其非同步自相关性及互相关性的估计。结果表明,所构造的序列具有极低的相关性,其相关性的模值具有与Welch下界相同的数量级,可以作为CDMA通信系统中的码序列。     

Pseudonoise codes constructed by Legendre sequence

A new family of binary sequences is constructed by Legendre sequence with period P, P = 3 (mod 4). The new signal set includes two subsets consisting of (P - 1)/2 and (P + 1)/2 codes with good balance property. A conjecture about the maximum over all (nontrivial) autocorrelation and crosscorrelation values of sequence contained within the two subsets is proposed     

Preparata codes through lattices

We define an elementary family of lattices, from which we obtain a family of extended cyclic codes with coefficients in the modular integers. The first nontrivial subfamily is the family of quaternary Preparata codes. The family of dual codes coincides with the extended low-correlation sequences introduced by Kumar, Helleseth, and Calderbank (1995)     

4-phase sequences with near-optimum correlation properties

Two families of four-phase sequences are constructed using irreducible polynomials over Z₄. Family A has period L =2^r-1. size L+2. and maximum nontrivial correlation magnitude C_max⩽1+√(L+1), where r is a positive integer. Family B has period L=2(2^r-1). size (L+2)/4. and C_max for complex-valued sequences. Of particular interest, family A has the same size and period as the family of binary Gold sequences. but its maximum nontrivial correlation is smaller by a factor of √2. Since the Gold family for r odd is optimal with respect to the Welch bound restricted to binary sequences, family A is thus superior to the best possible binary design of the same family size. Unlike the Gold design, families A and B are asymptotically optimal whether r is odd or even. Both families are suitable for achieving code-division multiple-access and are easily, implemented using shift registers. The exact distribution of correlation values is given for both families     

Spectral methods for cross correlations of geometric sequences

Families of sequences with low pairwise shifted cross correlations are desirable for applications such as code-division multiple-access (CDMA) communications. Often such sequences must have additional properties for specific applications. Several ad hoc constructions of such families exist in the literature, but there are few systematic approaches to such sequence design. We introduce a general method of constructing new families of sequences with bounded pairwise shifted cross correlations from old families of such sequences. The bounds are obtained in terms of the maximum cross correlation in the old family and the Walsh transform of certain functions.     

Prime-phase sequences with periodic correlation properties better than binary sequences

For the case where p is an odd prime, n>or=2 is an integer, and omega is a complex primitive pth root of unity, a construction is presented for a family of p/sup n/ p-phase sequences (symbols of the form omega /sup i/), where each sequence has length p/sup n/-1, and where the maximum nontrivial correlation value C/sub max/ does not exceed 1+ square root p/sup n/. A complete distribution of correlation values is provided. As a special case of this construction, a previous construction due to Sidelnikov (1971) is obtained. The family of sequences is asymptotically optimum with respect to its correlation properties, and, in comparison with many previous nonbinary designs, the present design has the additional advantage of not requiring an alphabet of size larger than three. The new sequences are suitable for achieving code-division multiple access and are easily implemented using shift registers. They wee discovered through an application of Deligne's bound (1974) on exponential sums of the Weil type in, several variables. The sequences are also shown to have strong identification with certain bent functions.<>     

A new family of binary pseudorandom sequences having optimalperiodic correlation properties and larger linear span

A collection of families of binary {0,1} pseudorandom sequences is introduced. Each sequence within a family has period N=2"-1, where n=2m is an even integer. There are 2^m sequences within a family, and the maximum overall (nontrivial) auto- and cross-correlation values equals 2^m+1. Thus, these sequences are optimal with respect to the Welch bound on the maximum correlation value. Each family contains a Gordon-Mills-Welch (GMW) sequence, and the collection of families includes as a special case the small set of Kasami sequences. The linear span of these sequences varies within a family but is always greater than or equal to the linear span of the GMW sequence contained within the family. Exact closed-form expressions for the linear span of each sequence are given. The balance properties of such families are evaluated, and a count of the number of distinct families of given period N that can be constructed is provided     

Large families of quaternary sequences with low correlation

A family of quaternary (Z₄-alphabet) sequences of length L=2^r-1, size M⩾L²+3L+2, and maximum nontrivial correlation parameter C_max⩽2√(L+1)+1 is presented. The sequence family always contains the four-phase family 𝒜. When r is odd, it includes the family of binary Gold sequences. The sequence family is easily generated using two shift registers, one binary, the other quaternary. The distribution of correlation values is provided. The construction can be extended to produce a chain of sequence families, with each family in the chain containing the preceding family. This gives the design flexibility with respect to the number of intermittent users that can be supported, in a code-division multiple-access cellular radio system. When r is odd, the sequence families in the chain correspond to shortened Z₄-linear versions of the Delsarte-Goethals codes     

Optimal phases for a family of quadriphase CDMA sequences

Signature sequences with good even even and odd (or polyphase) correlations are crucial for asynchronous code-division multiple access (CDMA). When the data sequence is random, the even and odd (or polyphase) correlations are equally important. However, for most known signature sequences, only their even correlations were analyzed. It appears that determining the odd (or the polyphase) correlations is generally a very hard problem since the odd (or the polyphase) correlations depend on the phases of the signature sequences. Sole (1989), Boztas, Hammons, and Kumar (1992) found a family of quadriphase sequences that are asymptotically optimal. These sequences gain a factor √2 in terms of their maximum periodic even correlations when compared with the best possible binary phase-shift keying (BPSK) sequences. We find the optimal phases of these sequences. The optimality is in the sense that at these phases, the mean square values of the even, odd, and the polyphase correlations are minimal, and achieve the Welch (1974) bound-equality simultaneously. Furthermore, we show that at these phases, the average user interference of these sequences is always smaller than that of the ideal random signature sequences. Comprehensive analytical and numerical results show that good phase sequences can offer a nonnegligible amount of gain over bad phase sequences at modest and high signal-to-noise ratios     

New family of bipolar sequences and its correlation spectrum

Based on a class of bipolar sequences with two-values autocorrelation functions, a new family of bipolar sequences is constructed and its correlation spectrum is calculated. It is shown that the new family is optimal with respect to Welch‘s bound and is different from the small set of Kasami sequences, while both of them have the same correlation properties.     

REAL SEQUENCES WITH GOOD AUTO-CORRELATION AND CROSS-CORRELATION

New classes of real sequences with good auto-correlation and cross-correlation areconstructed by using sinusoidal functions. The new sequences are better than the FZC and Alltopsequences in two aspects: (1) lower correlations and (2) taking real values. The new sequencescan be used in many areas.     

具有二值自相关特性的p元伪随机序列族的构造

具有二值自相关特性的伪随机序列在扩频通信、流密码、雷达和声纳等领域中具有重要的应用。本文首先基于d-型序列的思想，给出了具有二值自相关特性的p元伪随机序列的构造表达式。此外，基于已有的具有二值自相关函数序列，本文提出了构造具有同样自相关特性的伪随机序列的方法。可以用来构造具有最佳Hamming相关特性的跳频序列族。     

具有良好相关特性的实序列

本文利用正(余)弦函数的特性构造出了几类新型的具有良好相关特性的实序列。与已知的FZC序列和A、B型的Alltop序列相比较,文中新序列的相关特性更好,容量更大。此外新序列在实数中取直,因此更加实用。FZC序列和Alltop序列的广泛应用保证了新序列具有很大的实用价值。     

信任网络中多维信任序列模式挖掘方法研究

现有信任网络研究大多侧重于信任的推理及聚合计算,缺乏对实体重要性及其关联性分析,为此该文提出一种多维信任序列模式(Multi-dimensional Trust Sequential Patterns, MTSP)挖掘算法。该算法包括频繁信任序列挖掘和多维模式筛选两个处理过程,综合考虑信任强度、路径长度和实体可信度等多维度因素,有效地挖掘出信任网络中的频繁多维信任序列所包含的重要实体及其关联结构。仿真实验表明该文所提MTSP算法的挖掘结果全面、准确地反映了信任网络中重要信任实体关联性及其序列结构特征。     

Complex spreading sequences with a wide range of correlationproperties

This paper presents a new family of complex valued pseudo-random sequences for use in coded multiple access communication systems. The family offers a very wide range of values for both auto-correlation (AC) and cross-correlation (CC) functions, allowing great flexibility in the selection of characteristics of sequence sets. Based on the measure described in this paper for the mean-square aperiodic AC and CC values of a set of sequences, the correlation properties of sets of these sequences are compared to well-known sequence sets, and it is shown that sets from the new family of sequences have superior qualities. Tables of parameters for various sequence sets are presented to enable the construction and comparison of sets from this new family     

On ternary complementary sequences

A pair of real-valued sequences A=(a₁,a₂,...,a_N) and B=(b₁,b ₂,...,b_N) is called complementary if the sum R(·) of their autocorrelation functions R_A(·) and R_B(·) satisfies R(τ)=R_A(τ)+R _B(τ)=Σ_i=1^N$ -^τa_ia_i+τ+Σ_j=1 ^N-τb_jb_j+τ=0, ∀τ≠0. In this paper we introduce a new family of complementary pairs of sequences over the alphabet α₃=+{1,-1,0}. The inclusion of zero in the alphabet, which may correspond to a pause in transmission, leads both to a better understanding of the conventional binary case, where the alphabet is α₂={+1,-1}, and to new nontrivial constructions over the ternary alphabet α₃. For every length N, we derive restrictions on the location of the zero elements and on the form of the member sequences of the pair. We also derive a bound on the minimum number of zeros necessary for the existence of a complementary pair of length N over α₃. The bound is tight, as it is met by some of the proposed constructions, for infinitely many lengths     

New families of p-ary sequences with low correlation and large linear span

This article presents a new family of p-ary sequences. The proposed sequences are proved to have not only low correlation property, but also large linear span and large family size. Furthermore, it shows that the new family of sequences contains Tang's construction as a subset if m-sequences are excluded from both constructions.     

Auto-Cross-and Triple-Correlations of Sequences

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