Related papers: Sequences with identical autocorrelation functions
Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, with A and B of length m and C and D of length n, such that the sum of their nonperiodic autocorrelation functions is a delta-function. Normal sequences NS(n) are base…
Sequences with good correlation properties have been widely adopted in modern communications, radar and sonar applications. In this paper, we present our new findings on some constructions of single $H$-ary Golay sequence and $4^q$-QAM…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
Sequence classification algorithms, such as SVM, require a definition of distance (similarity) measure between two sequences. A commonly used notion of similarity is the number of matches between $k$-mers ($k$-length subsequences) in the…
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…
Sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. Among the known sequences, cyclotomic families have the optimal autocorrelation property. In this paper, we…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
We describe two families of statistical tests to detect partial correlation in vectorial timeseries. The tests measure whether an observed timeseries Y can be predicted from a second series X, even after accounting for a third series Z…
Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as groundstates of the Bernasconi-model. Computer searches are the main tool to construct such sequences. Due to the…
In the ultraviolet (UV) scattering communication, the received signals exhibit the characteristics of discrete photoelectrons due to path loss. The synchronization is based on maximum Pulse Number-Sequence correlation problem. First of all,…
For any odd positive integer $x$, define $(x_n)_{n\geqslant 0} $ and $(a_n )_{n\geqslant 1} $ by setting $x_{0}=x, \,\, x_n =\cfrac{3x_{n-1} +1}{2^{a_n }}$ such that all $x_n $ are odd. The 3x+1 problem asserts that there is an $x_n =1$ for…
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
In outlier hypothesis testing, one aims to detect outlying sequences among a given set of sequences, where most sequences are generated i.i.d. from a nominal distribution while outlying sequences (outliers) are generated i.i.d. from a…
The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation $t_n=at_{n-1}+t_{n-2}$ if $n$ is even, $t_n=bt_{n-1}+t_{n-2}$ if $n$ is odd, with initial values $t_0=0$ and $t_1=1$, where $a$ and $b$ are…
Nonclassical properties of correlations-- like unpredictability, no-cloning and uncertainty-- are known to follow from two assumptions: nonlocality and no-signaling. For two-input-two-output correlations, we derive these properties from a…
This paper concerns the question to what extent it can be efficiently determined whether an arbitrary program correctly solves a given problem. This question is investigated with programs of a very simple form, namely instruction sequences,…
The de Bruijn graph, its sequences, and their various generalizations, have found many applications in information theory, including many new ones in the last decade. In this paper, motivated by a coding problem for emerging memory…
We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation…
We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing…