Related papers: Systematic Error-Correcting Codes for Rank Modulat…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and…
In recent times, deep neural networks achieved outstanding predictive performance on various classification and pattern recognition tasks. However, many real-world prediction problems have ordinal response variables, and this ordering…
We study two basic problems regarding edit error, i.e. document exchange and error correcting codes for edit errors (insdel codes). For message length $n$ and edit error upper bound $k$, it is known that in both problems the optimal sketch…
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
This work constructs codes that are efficiently decodable from a constant fraction of \emph{worst-case} insertion and deletion errors in three parameter settings: (i) Binary codes with rate approaching 1; (ii) Codes with constant rate for…
We propose $(k,k')$ stabilizing codes, which is a type of delayless error correction codes that are useful for control over networks with erasures. For each input symbol, $k$ output symbols are generated by the stabilizing code. Receiving…
Function-correcting codes are an innovative class of codes that are designed to protect a function evaluation of the data against errors or corruptions. Due to its usefulness in machine learning applications and archival data storage, where…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
For efficient modulation and error control coding, the deliberate flipping approach imposes the run-length-limited(RLL) constraint by bit error before recording. From the read side, a high coding rate limits the correcting capability of RLL…
Token repetition is a typical form of multi-modal problem in fully non-autoregressive translation (NAT). In this work, we revisit the multi-modal problem in recently proposed NAT models. Our study reveals that these advanced models have…
A novel correction algorithm is proposed for multi-class classification problems with corrupted training data. The algorithm is non-intrusive, in the sense that it post-processes a trained classification model by adding a correction…
We investigate two fundamental questions intersecting coding theory and combinatorial geometry, with emphasis on their connections. These are the problem of computing the asymptotic density of MRD codes in the rank metric, and the Critical…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…
In this paper, we give a generalization on the error correcting capability of twisted centralizer codes obtained from a fixed rank 1 matrix. In particular, we fix the combinatorial matrix which is obtained by getting the linear combination…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
In this article, we investigate the decoding of the rank metric Reed--Muller codes introduced by Augot, Couvreur, Lavauzelle and Neri in 2021. These codes are defined from Abelian Galois extensions extending the construction of Gabidulin…
Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The…
In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this…