Related papers: List Decoding with Double Samplers
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…
In this paper, a derandomized algorithm for sampling decoding is proposed to achieve near-optimal performance in lattice decoding. By setting a probability threshold to sample candidates, the whole sampling procedure becomes deterministic,…
High dimensional expanders simultaneously satisfying spectral and combinatorial (coboundary) expansion have recently played a major role in breakthroughs in PCP and coding theory, but the only known construction of such complexes is…
Folded Reed-Solomon (FRS) and univariate multiplicity codes are prominent polynomial codes over finite fields, renowned for achieving list decoding capacity. These codes have found a wide range of applications beyond the traditional scope…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
The unprecedented performance achieved by deep convolutional neural networks for image classification is linked primarily to their ability of capturing rich structural features at various layers within networks. Here we design a series of…
We present a novel error correcting code and decoding algorithm which have construction similar to expander codes. The code is based on a bipartite graph derived from the subsumption relations of finite projective geometry, and Reed-Solomon…
In this work, we give the first construction of high-rate locally list-recoverable codes. List-recovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In…
We present a novel framework for applying deep neural networks (DNN) to soft decoding of linear codes at arbitrary block lengths. Unlike other approaches, our framework allows unconstrained DNN design, enabling the free application of…
Score-based algorithms that learn the structure of Bayesian networks can be used for both exact and approximate solutions. While approximate learning scales better with the number of variables, it can be computationally expensive in the…
In the last decade there has been a great interest in extending results for codes equipped with the Hamming metric to analogous results for codes endowed with the rank metric. This work follows this thread of research and studies the…
We give an algorithm for solving unique games (UG) instances whenever low-degree sum-of-squares proofs certify good bounds on the small-set-expansion of the underlying constraint graph via a hypercontractive inequality. Our algorithm is in…
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…
In this paper, a robust classification-autoencoder (CAE) is proposed, which has strong ability to recognize outliers and defend adversaries. The main idea is to change the autoencoder from an unsupervised learning model into a classifier,…
An emerging theory of "linear-algebraic pseudorandomness" aims to understand the linear-algebraic analogs of fundamental Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In this work, we study…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low independence. A series of papers, beginning with work by Luby (1988), showed that in many cases…
We present the self-encoder, a neural network trained to guess the identity of each data sample. Despite its simplicity, it learns a very useful representation of data, in a self-supervised way. Specifically, the self-encoder learns to…
This article seeks to advance coded compressed sensing (CCS) as a practical scheme for unsourced random access. The original CCS algorithm features a concatenated structure where an inner code is tasked with support recovery, and an outer…