Related papers: Decoding Balanced Linear Codes With Preprocessing
Quantum processors are often affected by biased noise and noisy readout, which reduce reliability and reproducibility. This work combines two complementary strategies to address these challenges. The first is bias tailoring, which aligns…
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…
The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
Guessing random additive noise decoding (GRAND) is a universal maximum-likelihood decoder that recovers code-words by guessing rank-ordered putative noise sequences and inverting their effect until one or more valid code-words are obtained.…
We improve the runtime of the linear compression scheme for hidden Markov sources presented in a 2018 paper of Guruswami, Nakkiran, and Sudan. Under the previous scheme, compressing a message of length $n$ takes $O(n \log n)$ runtime, and…
High quality data is essential in deep learning to train a robust model. While in other fields data is sparse and costly to collect, in error decoding it is free to query and label thus allowing potential data exploitation. Utilizing this…
Pauli Correlation Encoding (PCE) compresses $m$ binary variables onto $n=O(m^{1/k})$ qubits by mapping them to commuting Pauli correlators, but its continuous expectation values must be decoded into feasible binary solutions, a challenge…
Parity check matrices (PCMs) are used to define linear error correcting codes and ensure reliable information transmission over noisy channels. The set of codewords of such a code is the null space of this binary matrix. We consider the…
Network coding is a highly efficient data dissemination mechanism for wireless networks. Since network coded information can only be recovered after delivering a sufficient number of coded packets, the resulting decoding delay can become…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
Information set decoding (ISD) algorithms are the best known procedures to solve the decoding problem for general linear codes. These algorithms are hence used for codes without a visible structure, or for which efficient decoders…
In this paper, we discuss two-stage encoding algorithms capable of correcting a fraction of asymmetric errors. Suppose that the encoder transmits $n$ binary symbols $(x_1,\ldots,x_n)$ one-by-one over the Z-channel, in which a 1 is received…
A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates. We show that any {\em zero-error} $2$-query locally correctable code…
Accurate decoding of quantum error-correcting codes is a crucial ingredient in protecting quantum information from decoherence. It requires characterizing the error channels corrupting the logical quantum state and providing this…
Learning with Errors (LWE) is a hard math problem underpinning many proposed post-quantum cryptographic (PQC) systems. The only PQC Key Exchange Mechanism (KEM) standardized by NIST is based on module~LWE, and current publicly available PQ…
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…
Lossy compression algorithms are typically designed to achieve the lowest possible distortion at a given bit rate. However, recent studies show that pursuing high perceptual quality would lead to increase of the lowest achievable distortion…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…