Related papers: Enhancing simultaneous rational function recovery:…
In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an…
We report our progress in scaling deductive synthesis and repair of recursive functional Scala programs in the Leon tool. We describe new techniques, including a more precise mechanism for encoding the space of meaningful candidate…
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…
There has been a rise in decoding quantum error correction codes with neural network based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger…
This work presents a framework for a-posteriori error-estimating algorithms for differential equations which combines the radii polynomial approach with Haar wavelets. By using Haar wavelets, we obtain recursive structures for the matrix…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
We derive a sphere-packing error exponent for coded transmission over discrete memoryless channels with a fixed decoding metric. By studying the error probability of the code over an auxiliary channel, we find a lower bound to the…
Relax, Compensate and then Recover (RCR) is a paradigm for approximate inference in probabilistic graphical models that has previously provided theoretical and practical insights on iterative belief propagation and some of its…
Decomposition methods have been proposed to approximate solutions to large sequential decision making problems. In contexts where an agent interacts with multiple entities, utility decomposition can be used to separate the global objective…
We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding…
We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients…
We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coefficients. The underlying algorithm is a function-valued…
In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of…
Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes…
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…
In this paper, we study sliding window decoding of braided convolutional codes (BCCs) in the context of a streaming application, where decoder error propagation can be a serious problem. A window extension algorithm and a resynchronization…