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The most famous error-decoding algorithm for convolutional codes is the Viterbi algorithm. In this paper, we present a new reduced complexity version of this algorithm which can be applied to a class of binary convolutional codes with…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
We analyze the efficiency of available algorithms for the simulation of classical fidelity and show that their computational costs increase exponentially with the number of degrees of freedom for almost all initial states. Then we present…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
We construct a family of (n,k) convolutional codes with degree \delta in {k,n-k} that have a maximum distance profile. The field size required for our construction is of the order n^{2\delta}, which improves upon the known constructions of…
This work proposes algorithms for computing additive and multiplicative free convolutions of two given measures. We consider measures with compact support whose free convolution results in a measure with a density function that exhibits a…
We give an algorithm for determining the distance between two vertices of the complex of curves. While there already exist such algorithms, for example by Leasure, Shackleton, and Webb, our approach is new, simple, and more effective for…
Selectivity estimation aims at estimating the number of database objects that satisfy a selection criterion. Answering this problem accurately and efficiently is essential to many applications, such as density estimation, outlier detection,…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…
We define a new class of Convolutional Codes in terms of fibrations of algebraic varieties generalizaing our previous constructions of Convolutional Goppa Codes. Using this general construction we can give several examples of Maximum…
A new kind of Convolutional Codes generalizing Goppa Codes is proposed. This provides a systematic method for constructing convolutional codes with prefixed properties. In particular, examples of Maximum-Distance Separable (MDS)…
Bosonic codes with rotational symmetry are currently one of the best performing quantum error correcting codes. Little is known about error propagation and code distance for these rotation codes in contrast with qubit codes and Bosonic…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
This article demonstrates how an understanding of the geometry of a family of cost functions can be used to develop efficient numerical algorithms for real-time optimisation. Crucially, it is not the geometry of the individual functions…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
Is perfect error correction always worth the trouble? A framework is presented for the analysis of error detection and correction in multi-level systems of communication that takes into account degrees of freedom attended and ignored by…