New Constructions of Zero-Correlation Zone Sequences

In this paper, we propose three classes of systematic approaches for constructing zero correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on the family size ($K$) and the ZCZ width ($T$) for a given sequence period ($N$). Our approaches can produce various binary and polyphase ZCZ families with desired parameters $(N,K,T)$ and alphabet size. They also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size. Furthermore, the constructed families have nested-like property that can be either decomposed or combined to constitute smaller or larger ZCZ sequence sets. We make detailed comparisons with related works and present some extended properties. For each approach, we provide examples to numerically illustrate the proposed construction procedure.Comment: 37 pages, submitted to IEEE Transactions on Information Theor

Design of sequences with good correlation properties

This thesis is dedicated to exploring sequences with good correlation properties. Periodic sequences with desirable correlation properties have numerous applications in communications. Ideally, one would like to have a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. However, theoretical bounds show that the maximum magnitudes of auto-correlation and cross-correlation of a sequence set are mutually constrained, i.e., if a set of sequences possesses good auto-correlation properties, then the cross-correlation properties are not good and vice versa. The design of sequence sets that achieve those theoretical bounds is therefore of great interest. In addition, instead of pursuing the least possible correlation values within an entire period, it is also interesting to investigate families of sequences with ideal correlation in a smaller zone around the origin. Such sequences are referred to as sequences with zero correlation zone or ZCZ sequences, which have been extensively studied due to their applications in 4G LTE and 5G NR systems, as well as quasi-synchronous code-division multiple-access communication systems. Paper I and a part of Paper II aim to construct sequence sets with low correlation within a whole period. Paper I presents a construction of sequence sets that meets the Sarwate bound. The construction builds a connection between generalised Frank sequences and combinatorial objects, circular Florentine arrays. The size of the sequence sets is determined by the existence of circular Florentine arrays of some order. Paper II further connects circular Florentine arrays to a unified construction of perfect polyphase sequences, which include generalised Frank sequences as a special case. The size of a sequence set that meets the Sarwate bound, depends on a divisor of the period of the employed sequences, as well as the existence of circular Florentine arrays. Paper III-VI and a part of Paper II are devoted to ZCZ sequences. Papers II and III propose infinite families of optimal ZCZ sequence sets with respect to some bound, which are used to eliminate interference within a single cell in a cellular network. Papers V, VI and a part of Paper II focus on constructions of multiple optimal ZCZ sequence sets with favorable inter-set cross-correlation, which can be used in multi-user communication environments to minimize inter-cell interference. In particular, Paper~II employs circular Florentine arrays and improves the number of the optimal ZCZ sequence sets with optimal inter-set cross-correlation property in some cases.Doktorgradsavhandlin

A Direct Construction of Prime-Power-Length Zero-Correlation Zone Sequences for QS-CDMA System

In recent years, zero-correlation zone (ZCZ) sequences are being studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, the lengths of most existing ZCZ sequences are limited, and their parameters are not flexible, which are leading to practical limitations in their use in QS-CDMA and other communication systems. The current study proposes a direct construction of ZCZ sequences of prime-power length with flexible parameters by using multivariable functions. In the proposed construction, we first present a multivariable function to generate a vector with specific properties; this is further used to generate another class of multivariable functions to generate the desired $(p^t,(p-1)p^n,p^{n+t+1})$-ZCZ sequence set, where $p$ is a prime number, $t,n$ are positive integers, and $t\leq n$. The constructed ZCZ sequence set is optimal for the binary case and asymptotically optimal for the non-binary case by the \emph{Tang-Fan-Matsufuji} bound. Moreover, a relation between the second-order cosets of first-order generalized Reed-Muller code and the proposed ZCZ sequences is also established. The proposed construction of ZCZ sequences is compared with existing constructions, and it is observed that the parameters of this ZCZ sequence set are a generalization of that of in some existing works. Finally, the performance of the proposed ZCZ-based QS-CDMA system is compared with the Walsh-Hadamard and Gold code-based QS-CDMA system

The Human version of Moore-Shannon's Theorem: The Design of Reliable Economic Systems

Moore & Shannon's theorem is the cornerstone in reliability theory, but cannot be applied to human systems in its original form. A generalization to human systems would therefore be of considerable interest because the choice of organization structure can remedy reliability problems that notoriously plaque business operations, financial institutions, military intelligence and other human activities. Our main result is a proof that provides answers to the following three questions. Is it possible to design a reliable social organization from fallible human individuals? How many fallible human agents are required to build an economic system of a certain level of reliability? What is the best way to design an organization of two or more agents in order to minimize error? On the basis of constructive proofs, this paper provides answers to these questions and thus offers a method to analyze any form of decision making structure with respect to its reliability.Organizational design; reliability theory; decision making; project selection

The Construction and Performance of a Novel Intergroup Complementary Code

 On the basis of the analyses for intergroup complementary (IGC) code and zero correlation zone complementary code, a novel IGC code has been proposed to adapt M-ary orthogonal code spreading spectrum system or quasi-synchronous CDMA system. The definition and construction methods of the new IGC codes are presented and an applied example is given in this paper. Theoretical research and simulation results show that the main advantages of the novel IGC code are as following: The code sets of the novel IGC code is more than IGC code under the same code length. The zero correlation zone length is longer than the intergroup IGC code, but shorter than the intergroup IGC code. Under the same code length, the auto-correlation performance of the novel IGC code is better than that of the IGC code, and both are of similar cross-correlation performance

Unity and Plurality of the European Cycle

We apply uni- and multivariate unobserved components models to the study of European growth cycles. The multivariate dimension enables to search similar or, more strongly, common components among national GDP series (quarterly data from 1960 to 1999). Three successive ways to exhibit the European cycle satisfactorily converge: the direct decomposition of the aggregate European GDP; the aggregation of the member countries' national cycles; the search for common components between these national cycles. The European aggregate fluctuations reveal two distinct cyclical components, assimilated to the classical Juglar (decennial, related to investment) and Kitchin (triennial, related to inventories) cycles. The European Juglar cycle cannot be reduced to a single common component of the national cycles. It has at least a dimension of "three": it can be understood as the interference of three elementary and independent sequences of stochastic shocks, that correspond to the European geographical division. The euro-zone is not yet an optimal currency area, as the shocks generating the European cycles are not completely symmetrical. Studying the sequences of innovations extracted from the models shows that euro-zone vulnerability to strong shocks and asymmetry of these shocks tend to decrease during the last decades, but this trend is neither regular, nor irreversible.(A)symmetrical shocks, Common factors, European integration, Growth cycles, Stochastic trends, Structural time series model.