Related papers: Noise-Tolerant Codebooks for Semi-Quantitative Gro…
Certain simplicial complexes are used to construct a subset $D$ of $\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over $\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in \mathbb{F}_{2^n}^m$. Here we…
Group-testing refers to the problem of identifying (with high probability) a (small) subset of $D$ defectives from a (large) set of $N$ items via a "small" number of "pooled" tests. For ease of presentation in this work we focus on the…
For a random quasi-abelian code of rate $r$, it is shown that the GV-bound is a threshold point: if $r$ is less than the GV-bound at $\delta$, then the probability of the relative distance of the random code being greater than $\delta$ is…
We consider Bernoulli nonadaptive group testing with $k = \Theta(n^\theta)$ defectives, for $\theta \in (0,1)$. The practical definite defectives (DD) detection algorithm is known to be optimal for $\theta \geq 1/2$. We give a new upper…
This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…
This paper presents an optimal construction of $N$-bit-delay almost instantaneous fixed-to-variable-length (AIFV) codes, the general form of binary codes we can make when finite bits of decoding delay are allowed. The presented method…
In many applications, finding adequate labeled data to train predictive models is a major challenge. In this work, we propose methods to use group-level binary labels as weak supervision to train instance-level binary classification models.…
Score-based generative models (SGMs) aim at estimating a target data distribution by learning score functions using only noise-perturbed samples from the target.Recent literature has focused extensively on assessing the error between the…
Universal variable-to-fixed (V-F) length coding of $d$-dimensional exponential family of distributions is considered. We propose an achievable scheme consisting of a dictionary, used to parse the source output stream, making use of the…
In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algebraic geometry codes. This lemma states that two vector…
It has been shown that good structured codes over non-Abelian groups do exist. Specifically, we construct codes over the smallest non-Abelian group $\mathds{D}_6$ and show that the performance of these codes is superior to the performance…
In this paper, we consider the problem of robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme which achieves the optimal slope of the signal-to-distortion (SDR) curve (unlike the…
Stochastic Gradient Langevin Dynamics (SGLD) is a sampling scheme for Bayesian modeling adapted to large datasets and models. SGLD relies on the injection of Gaussian Noise at each step of a Stochastic Gradient Descent (SGD) update. In this…
We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal…
In this work, we present the first local-decoding algorithm for expander codes. This yields a new family of constant-rate codes that can recover from a constant fraction of errors in the codeword symbols, and where any symbol of the…
We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…
Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…
A family of distance-optimal LRC codes from certain subcodes of $q$-ary Reed-Solomon codes, proposed by I.~Tamo and A.~Barg in 2014, assumes that the code length $n$ is a multiple of $r+1.$ By shortening codes from this family, we show that…
Spatially-coupled (SC) codes are a class of low-density parity-check (LDPC) codes that have excellent performance thanks to the degrees of freedom they offer. An SC code is designed by partitioning a base matrix into components, the number…
This work presents an adaptive group testing framework for the range-based high dimensional near neighbor search problem. Our method efficiently marks each item in a database as neighbor or non-neighbor of a query point, based on a cosine…