Related papers: Ideal-theoretic Explanation of Capacity-achieving …
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic…
In this paper we present a new algorithm for Polynomial Linear System Solving (via evaluation/interpolation) with errors. In this scenario, errors can occur in the black box evaluation step. We improve the bound on the number of errors that…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
In this paper, we establish the list-decoding capacity theorem for sum-rank metric codes. This theorem implies the list-decodability theorem for random general sum-rank metric codes: Any random general sum-rank metric code with a rate not…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most $r$) other symbols. We present a family of LRC codes that attain the maximum possible value of the…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
We construct an explicit family of linear rank-metric codes over any field ${\mathbb F}_h$ that enables efficient list decoding up to a fraction $\rho$ of errors in the rank metric with a rate of $1-\rho-\epsilon$, for any desired $\rho \in…
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter…
This paper deals with the application of list decoding of Reed--Solomon codes to a concatenated code for key reproduction using Physical Unclonable Functions. The resulting codes achieve a higher error-correction performance at the same…
In this paper, we introduce an achievability bound on the frame error rate of random tree code ensembles under a sequential decoding algorithm with a hard computational limit and consider the optimization of the random tree code ensembles…
Coding, which targets compressing and reconstructing data, and intelligence, often regarded at an abstract computational level as being centered around model learning and prediction, interweave recently to give birth to a series of…
International Classification of Diseases (ICD) are the de facto codes used globally for clinical coding. These codes enable healthcare providers to claim reimbursement and facilitate efficient storage and retrieval of diagnostic…
In this work we explore error-correcting codes derived from the "lifting" of "affine-invariant" codes. Affine-invariant codes are simply linear codes whose coordinates are a vector space over a field and which are invariant under…
We consider the problem of coded computing, where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously…
Under polynomial time reduction, the maximum likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is…
We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is…