Optimal Sequence Sets Research Articles

Optimal ternary sequence sets rigorously achieving the Welch bound

Sequences are finite-dimensional discrete signals in the complex domain, which are widely used in communication, radar, sonar, and information security to complete the requirements for synchronization, multiple random access, channel estimation, ranging, anti-interference, and digital watermarking due to their anti-interference, stability, and easy implementation. There are close relations between sequences and mathematical objects such as cyclic Hadamard matrices, difference sets (families), tight frames, unbiased bases, and cyclic codes. Constructing sequences reaching or approximating the theoretical bounds has always been a core topic in sequence design and coding theory. In this paper, based on the Semi-Bent function and difference set, we propose a class of optimal ternary sequence sets (the elements of sequences belong to $\{0,\pm~1\}$), which is the first class of optimal sequence set strictly achieving the Welch bound since this bound was established in 1974. Compared with the binary sequence sets (the elements of sequences take values $\pm~1$), the new sequence set is more suitable for ultra-wideband communication, digital watermarking, and spectrum constrained scenarios. While compared with known ternary sequence sets asymptotically approaching two times the Welch bound, the proposed ternary sequence sets have better correlation properties.

The multilabel naive credal classifier

A credal classifier for multilabel data is presented. This is obtained as an extension of Zaffalon's naive credal classifier to the case of non-exclusive class labels. The dependence relations among the labels are shaped with a tree topology. The classifier, based on a polynomial-time algorithm to compute whether or not a class label is optimal, returns a compact description of the set of optimal sequences of labels. Extensive experiments on real multilabel data show that the classifier gives more robust predictions than its Bayesian counterpart. In practice, when multiple sequences are returned in output, the Bayesian model is more likely to be inaccurate, while the sequences returned by the credal classifier are more likely to include the correct one.

Construction of Optimal or Almost Optimal Sequence Sets with Zero or Low Correlation Zone Based on Interleaving Technique

摘要: 该文提出一种新的移位序列的构造方法，通过给移位序列赋予不同的值，得到一类新的移位序列。基于这种移位序列，利用交织法得到了一类具有灵活相关区长度并且参数接近甚至达到理论界限的低零相关区序列集，扩大了交织法的应用范围，得到了更多的适用于准同步CDMA系统的扩频序列集。 关键词: 准同步CDMA通信系统 / 低零相关区 / 交织法 / 移位序列

Bi-criteria single machine scheduling problem with a learning effect: Aneja–Nair method to obtain the set of optimal sequences

In this paper, we consider the bi-criteria single machine scheduling problem of n jobs with a learning effect. The two objectives considered are the total completion time (TC) and total absolute differences in completion times (TADC). The objective is to find a sequence that performs well with respect to both the objectives: the total completion time and the total absolute differences in completion times. In an earlier study, a method of solving bi-criteria transportation problem is presented. In this paper, we use the methodology of solving bi-criteria transportation problem, to our bi-criteria single machine scheduling problem with a learning effect, and obtain the set of optimal sequences,. Numerical examples are presented for illustrating the applicability and ease of understanding.