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

Full-length non-linear binary sequences with Zero Correlation Zone for multiuser communications

none3noThe research on new sets of sequences that can be applied as spreading codes in multiple user communications is still an active area, even if this topic has been extensively investigated since long time. In fact, new communication paradigms like dense and decentralized wireless networks, where there is no central controller to assign the resources to the nodes, are revamping the interest on finding large sets of sequences providing adequate correlation properties to support a big number of nodes, in potentially hostile channels. This paper focuses on the Zero Correlation Zone (ZCZ) property exhibited by a family of nonlinear binary sequences featuring a great cardinality of their set, and good security-related features, and provides evidence of their suitability to multiuser communications, in channels affected by multipath.Sarayloo, M.; Gambi, E.; Spinsante, S.Sarayloo, Mahdiyar; Gambi, Ennio; Spinsante, Susann

Full-length non-linear binary sequences with Zero Correlation Zone for multiuser communications

The research on new sets of sequences to be used asspreading codes in multiple user communications is still an activearea, despite the great amount of literature available since manyyears on this topic. In fact, new paradigms like dense anddecentralized wireless networks, where there is no centralcontroller to assign the resources to the nodes, are revamping theinterest on large sets of sequences providing adequate correlationproperties to support a big number of nodes, in potentially hostilechannels. This paper focuses on the Zero Correlation Zone (ZCZ)property exhibited by a family of non-linear binary sequencesfeaturing a great cardinality of their set and good securityrelatedfeatures, and provides evidence of their suitability tomultiuser communications, in channels affected by multipath

Recursion Polynomials of Unfolded Sequences

Watermarking digital media is one of the important chal- lenges for information hiding. Not only the watermark must be resistant to noise and against attempts of modification, legitimate users should not be aware that it is embedded in the media. One of the techniques for watermarking is using an special variant of spread-spectrum tech- nique, called frequency hopping. It requires ensembles of periodic binary sequences with low off-peak autocorrelation and cross-correlation. Un- fortunately, they are quite rare and difficult to find. The small Kasami, Kamaletdinov, and Extended Rational Cycle constructions are versatile, because they can also be converted into Costas-like arrays for frequency hopping. We study the implementation of such ensembles using linear feedback shift registers. This permits an efficient generation of sequences and arrays in real time in FPGAs. Such an implementation requires minimal memory usage and permits dynamic updating of sequences or arrays. The aim of our work was to broaden current knowledge of sets of se- quences with low correlation studying their implementation using linear feedback shift registers. A remarkable feature of these families is their similarities in terms of implementation and it may open new way to characterize sequences with low correlation, making it easier to gener- ate them. It also validates some conjectures made by Moreno and Tirkel about arrays constructed using the method of composition.Supported by Consejería de Universidades e Investigación, Medio Ambiente y Política Social, Gobierno de Cantabria (ref. VP34