Related papers: On generic erasure correcting sets and related pro…
This paper introduces the concept of generalized interlacing families of polynomials, which extends the classical interlacing polynomial method to handle polynomials of varying degrees. We establish a fundamental property for these…
For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…
Estimating high-dimensional precision matrices is a fundamental problem in modern statistics, with the graphical lasso and its $\ell_1$-penalty being a standard approach for recovering sparsity patterns. However, many statistical models,…
We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage.…
Recently deep neutral networks have achieved promising performance for filling large missing regions in image inpainting tasks. They usually adopted the standard convolutional architecture over the corrupted image, leading to meaningless…
The analysis of random coding error exponents pertaining to erasure/list decoding, due to Forney, is revisited. Instead of using Jensen's inequality as well as some other inequalities in the derivation, we demonstrate that an exponentially…
We discuss how subspace codes can be used to simultaneously correct errors and erasures when the network performs random linear network coding and the edges are noisy channels. This is done by combining the subspace code with a classical…
Transformer channel decoders, such as the Error Correction Code Transformer (ECCT), have shown strong empirical performance in channel decoding, yet their generalization behavior remains theoretically unclear. This paper studies the…
The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
The length function $\ell_2(r,R)$ is the smallest length of a binary linear code with codimension (redundancy) $r$ and covering radius $R$. We obtain the following new upper bounds on $\ell_2(r,R)$, which yield a decrease $\Delta(r,R)$…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
The length function $\ell_q(r,R)$ is the smallest length of a $ q $-ary linear code of codimension $r$ and covering radius $R$. In this work we obtain new constructive upper bounds on $\ell_q(r,R)$ for all $R\ge4$, $r=tR$, $t\ge2$, and also…
Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as…
We demonstrate a construction of error-correcting codes from graphs by means of $k$-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the $k$-metric dimension of grid graphs…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
The problem of coding for networks experiencing worst-case symbol errors is considered. We argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network…
For an $(n,k,\ell)$ MDS array code over $\mathbb{F}_q$, how small can the repair bandwidth and repair I/O be under linear exact repair? We study this question in the regime where the field size $q$, the redundancy $r=n-k$, and the…
Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to…