Related papers: Parity Check Matrix Recognition from Noisy Codewor…
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples.…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their…
We study the problem of interactively learning a binary classifier using noisy labeling and pairwise comparison oracles, where the comparison oracle answers which one in the given two instances is more likely to be positive. Learning from…
In this paper, we investigate the problem of recovering source information from an incomplete set of network coded data. We first study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and derive the…
We study the Closest Pair Problem in Hamming metric, which asks to find the pair with the smallest Hamming distance in a collection of binary vectors. We give a new randomized algorithm for the problem on uniformly random input…
We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations…
In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
Pairwise comparisons based on human judgements are an effective method for determining rankings of items or individuals. However, as human biases perpetuate from pairwise comparisons to recovered rankings, they affect algorithmic decision…
In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the…
This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…
Consider transmission over a binary additive white gaussian noise channel using a fixed low-density parity check code. We consider the posterior measure over the code bits and the corresponding correlation between two codebits, averaged…
Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only…
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm…
Life relies on the efficient performance of molecular codes, which relate symbols and meanings via error-prone molecular recognition. We describe how optimizing a code to withstand the impact of molecular recognition noise may be…
Nonlinear optimization methods are typically iterative and make use of gradient information to determine a direction of improvement and function information to effectively check for progress. When this information is corrupted by noise,…