Related papers: Systematic Error-Correcting Codes for Rank Modulat…
In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…
Selective information transfer in spin ring networks by energy landscape shaping control has the property that the error 1-prob, where prob is the transfer success probability, and the sensitivity of the error to spin coupling uncertainties…
Spinal codes is a new family of capacity-achieving rateless codes that has been shown to achieve better rate performance compared to Raptor codes, Strider codes, and rateless Low-Density Parity-Check (LDPC) codes. This correspondence…
Reducible codes for the rank metric were introduced for cryptographic purposes. They have fast encoding and decoding algorithms, include maximum rank distance (MRD) codes and can correct many rank errors beyond half of their minimum rank…
Recent work by Smagloy et al. (ISIT 2020) shows that the redundancy of a single-deletion $s$-substitution correcting code is asymptotically at least $(s+1)\log n+o(\log n)$, where $n$ is the length of the codes. They also provide a…
Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different…
Function-correcting codes are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we extend function-correcting codes from binary symmetric…
In the era of large language models (LLMs), code benchmarks have become an important research area in software engineering and are widely used by practitioners. These benchmarks evaluate the performance of LLMs on specific code-related…
The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as…
Kendall's tau and conditional Kendall's tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved…
Function-correcting codes are a coding framework designed to minimize redundancy while ensuring that specific functions or computations of encoded data can be reliably recovered, even in the presence of errors. The choice of metric is…
Reed-Solomon (RS) codes are widely used to correct errors in storage systems. Finding the error locator polynomial is one of the key steps in the error correction procedure of RS codes. Modular Approach (MA) is an effective algorithm for…
Insertion and deletion (insdel for short) errors are synchronization errors in communication systems caused by the loss of positional information in the message. Reed-Solomon codes have gained a lot of interest due to its encoding…
Rate-compatible error-correcting codes (ECCs), which consist of a set of extended codes, are of practical interest in both wireless communications and data storage. In this work, we first study the lower bounds for rate-compatible ECCs,…
We present code constructions for masking $u$ partially stuck memory cells with $q$ levels and correcting additional random errors. The results are achieved by combining the methods for masking and error correction for stuck cells in [1]…
The principle of Maximal Coding Rate Reduction (MCR$^2$) has recently been proposed as a training objective for learning discriminative low-dimensional structures intrinsic to high-dimensional data to allow for more robust training than…
This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…
Codes in the Damerau--Levenshtein metric have been extensively studied recently owing to their applications in DNA-based data storage. In particular, Gabrys, Yaakobi, and Milenkovic (2017) designed a length-$n$ code correcting a single…
This paper presents flexible storage codes, a class of error-correcting codes that can recover information from a flexible number of storage nodes. As a result, one can make a better use of the available storage nodes in the presence of…
This paper considers '$\delta$-almost Reed-Muller codes', i.e., linear codes spanned by evaluations of all but a $\delta$ fraction of monomials of degree at most $d$. It is shown that for any $\delta > 0$ and any $\varepsilon>0$, there…