Related papers: Simultaneous Rational Function Codes: Improved Ana…
We present two algorithms for constructing orthonormal bases of rational function vectors with respect to a discrete inner product, and discuss how to use them for a rational approximation problem. Building on the pencil-based formulation…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
A new score function is proposed for stack decoding of polar codes, which enables one to accurately compare paths of different lengths. The proposed score function includes bias, which reflects the average behaviour of the correct path.…
As improved versions of successive cancellation (SC) decoding algorithm, successive cancellation list (SCL) decoding and successive cancellation stack (SCS) decoding are used to improve the finite-length performance of polar codes. Unified…
We introduce an error resilient distributed computing method based on an extension of the channel polarization phenomenon to distributed algorithms. The method leverages an algorithmic split operation that transforms two identical compute…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then,…
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…
We present Polaris, a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs…
It is well known that to fulfill their full potential, the design of polar codes must be tailored to their intended decoding algorithm. While for successive cancellation (SC) decoding, information theoretically optimal constructions are…
Polar codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming 5G standard. As such, a lot of attention has been devoted to the development of…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
The use of non-orthogonal signals has several benefits over orthogonal signals in multi-coded communications. We provide a novel, theoretical study of non-orthogonal signaling to expand the applicability of these schemes. Motivated by a…
We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are…
We investigate the sparse functional identification of complex cells and the decoding of visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm of both temporal and spatio-temporal stimuli is formulated as a…
We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a…