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As mobile robots and autonomous vehicles become increasingly prevalent in human-centred environments, there is a need to control the risk of collision. Perceptual modules, for example machine vision, provide uncertain estimates of object…
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…
Raptor code ensembles with linear random outer codes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight…
Classical dependence measures such as Pearson correlation, Spearman's $\rho$, and Kendall's $\tau$ can detect only monotonic or linear dependence. To overcome these limitations, Szekely et al.(2007) proposed distance covariance as a…
Codes considered as structures within unit schemes greatly extends the availability of linear block and convolutional codes and allows the construction of these codes to required length, rate, distance and type. Properties of a code emanate…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
In this work we examine recently proposed distance-based classification method designed for near-term quantum processing units with limited resources. We further study possibilities to reduce the quantum resources without any efficiency…
The field of computational complexity is concerned both with the intrinsic hardness of computational problems and with the efficiency of algorithms to solve them. Given such a problem, normally one designs an algorithm to solve it and sets…
In this paper we will discuss isometries and strong isometries for convolutional codes. Isometries are weight-preserving module isomorphisms whereas strong isometries are, in addition, degree-preserving. Special cases of these maps are…
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…
Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
In this paper numerical methods of computing distances between two Radon measures on R are discussed. Efficient algorithms for Wasserstein-type metrics are provided. In particular, we propose a novel algorithm to compute the flat metric…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…
In this paper, we provide a new approach to the analytical estimation of the bit-error rate (BER) for convolutional codes for Viterbi decoding in the binary symmetric channel (BSC). The expressions we obtained for lower and upper BER bounds…
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with…
This paper investigates the use of different transformations for improving the randomness of sequences. In particular, convolutional codes are used for increasing the size of a given sequence and then a random mapping function is used for…
Convolutional neural networks (CNN) exhibit unmatched performance in a multitude of computer vision tasks. However, the advantage of using convolutional networks over fully-connected networks is not understood from a theoretical…