A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span

A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound expression on the linear span of sequences in the family is given. With suitable choices of parameters, it is proved that the family has exponentially larger linear spans than both No sequences and TN sequences. A class of ideal autocorrelation sequences is also constructed and proved to have large linear span.Comment: 21 page

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

A linear construction for certain Kerdock and Preparata codes

The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over \ZZ_4, the integers $\bmod~4$. The Kerdock and Preparata codes are duals over \ZZ_4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over \ZZ_4. This provides a simple definition for these codes and explains why their Hamming weight distributions are dual to each other. First- and second-order Reed-Muller codes are also linear codes over \ZZ_4, but Hamming codes in general are not, nor is the Golay code.Comment: 5 page

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

Positive Definite Kernels in Machine Learning

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set of functions $\{k(x,\cdot),x\in\mathcal{X}\}$ associated with a kernel $k$ defined on a space $\mathcal{X}$. We discuss at length the construction of kernel functions that take advantage of well-known statistical models. We provide an overview of numerous data-analysis methods which take advantage of reproducing kernel Hilbert spaces and discuss the idea of combining several kernels to improve the performance on certain tasks. We also provide a short cookbook of different kernels which are particularly useful for certain data-types such as images, graphs or speech segments.Comment: draft. corrected a typo in figure