High-rate self-synchronizing codes

Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error-tolerance that generate binary and ternary self-synchronizing codes.Comment: 9 pages, no figure, 2 tables. Final accepted version for publication in the IEEE Transactions on Information Theory. Material presented in part at the International Symposium on Information Theory and its Applications, Honolulu, HI USA, October 201

Design of One-Coincidence Frequency Hopping Sequence Sets for FHMA Systems

Department of Electrical EngineeringIn the thesis, we discuss frequency hopping multiple access (FHMA) systems and construction of optimal frequency hopping sequence and applications. Moreover, FHMA is widely used in modern communication systems such as Bluetooth, ultrawideband (UWB), military, etc. For these systems, it is desirable to employ frequency-hopping sequences (FHSs) having low Hamming correlation in order to reduce the multiple-access interference. In general, optimal FHSs with respect to the Lempel-Greenberger bound do not always exist for all lengths and frequency set sizes. Therefore, it is an important problem to verify whether an optimal FHS with respect to the Lempel-Greenberger bound exists or not for a given length and a given frequency set size. I constructed FHS satisfying optimal with respect to the Lempel-Greenberger bound and Peng-Fan bound for efficiency of available frequency. Parameters of a new OC-FHS set are length p^2-p over Z_(p^2 ) by using a primitive element of Z_p. The new OC-FHS set with H_a (X)=0 and H_c (X)=1 can be applied to several recent applications using ISM band (e.g. IoT) based on BLE and Zigbee. In the construction and theorem, I used these mathematical back grounds in preliminaries (i.e., finite field, primitive element, primitive polynomial, frequency hopping sequence, multiple frequency shift keying, DS/CDMA) in order to prove mathematically. The outline of thesis is as follows. In preliminaries, we explain algorithm for minimal polynomial for sequence, linear complexities, Hamming correlation and bounds for FHSs and some applications are presented. In section ???, algorithm for complexity, correlation and bound for FHSs and some applications are presented. In section ???, using information in section ??? and ???, a new construction of OC-FHS is presented. In order to prove the optimality of FHSs, all cases of Hamming autocorrelation and Hamming cross-correlation are mathematically calculated. Moreover, in order to raise data rate or the number of users, a new method is presented. Using this method, sequences are divided into two times of length and satisfies Lempel-Greenberger bound and Peng-Fan bound.clos

Optimal and near-optimal frequency-hopping sequences based on Gaussian period

Frequency-hopping sequences (FHSs) have a decisive influence on the whole frequency-hopping communication system. The Hamming correlation function plays an important role in evaluating the performance of FHSs. Constructing FHS sets that meet the theoretical bounds is crucial for the research and development of frequency-hopping communication systems. In this paper, three new classes of optimal FHSs based on trace functions are constructed. Two of them are optimal FHSs and the corresponding periodic Hamming autocorrelation value is calculated by using the known Gaussian period. It is shown that the new FHSs are optimal according to the Lempel-Greenberger bound. The third class of FHSs is the near-optimal FHSs

Accurate value-at-risk forecast with the (good) old normal-GARCH model

A resampling method based on the bootstrap and a bias-correction step is developed for improving the Value-at-Risk (VaR) forecasting ability of the normal-GARCH model. Compared to the use of more sophisticated GARCH models, the new method is fast, easy to implement, numerically reliable, and, except for having to choose a window length L for the bias-correction step, fully data driven. The results for several different financial asset returns over a long out-of-sample forecasting period, as well as use of simulated data, strongly support use of the new method, and the performance is not sensitive to the choice of L. Klassifizierung: C22, C53, C63, G12Die Normalverteilung ist, entgegen ihrer hohen Verbreitung in der empirischen Finanzanalyse, im allgemeinen nicht dazu geeignet, die Renditen von Finanzmarkt-Zeitreihen adäquat zu beschreiben. Ein viel beobachtetes PhÄanomen ist insbesondere die über die Zeit variierende Volatilität der Renditen, die eine bedingte Modellierung der Renditen notwendig erscheinen läßt. Der wohl am weitesten verbreitete Ansatz um solche Volatilitätsschwankungen zu modellieren ist das GARCH-Modell. Doch auch bei Berücksichtigung der VolatilitÄatschwankungen, d.h. bei bedingter Modellierung der Renditen mit Hilfe eines GARCH-Modells, ist die Normalverteilung im allgemeinen nicht dazu geeignet, die Verteilung der GARCH-gefilterten Renditen ausreichend genau zu beschreiben. Insbesondere Value-at-Risk (VaR) Prognosen sind mit dem normal-GARCH Modell im allgemeinen verzerrt, da die Normalverteilung die Enden der Rendite-Verteilung nur unzureichend beschreibt. Mögliche Auswege scheinen die Erweiterung und Modifikation der GARCH Dynamik, sowie die Verwendung anderer Verteilungen. Dies führt jedoch im allgemeinen dazu, daß diese Modelle sowohl theoretisch, als auch praktisch schwerer zu beherrschen sind. In der vorliegenden Studie entwickeln wir eine auf dem Bootstrap basierende Methode mit einem Verzerrungs-Korrektur Schritt, um die VaR Prognoseeigenschaften des normal-GARCH Modells zu verbessern. Im Vergleich zur Verwendung von komplexeren GARCH Spezifikationen und/oder Verteilungsannahmen ist diese neue Methode schnell, einfach zu implementieren, numerisch zuverlässig und (abgesehen von einer zu wählenden Fensterlänge L für den Schritt zur Korrektur der VaR-Verzerrung) vollst ndig Daten getrieben. Die vorgeschlagene Methode wird in langen out-of-sample Prognosezeiträumen auf ihre VaR Prognosefähigkeiten geprüft. Sowohl für verschiedene Finanzmarkt-Reihen, als auch für simulierte Daten, erweist sich die neue Methode als sehr gut geeignet, die VaR Prognosen der normal-GARCH Modells entscheidend zu verbessern und liefert auch im Vergleich zu komplexeren Modellen sehr gute Ergebnisse