Related papers: Function-Correcting Codes With Data Protection
The growing demand for highly reliable communication systems drives the research and development of algorithms that identify and correct errors during data transmission and storage. This need becomes even more critical in hard-to-access or…
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…
In this paper, we present error-correcting codes which are the results of our research on the sub-exceeding functions. For a short and medium distance data transmission (wifi network, bluetooth, cable, ...), we see that these codes…
We consider the \emph{functional index coding problem} over an error-free broadcast network in which a source generates a set of messages and there are multiple receivers, each holding a set of functions of source messages in its cache,…
In coding theory, handling errors that occur when symbols are inserted or deleted from a transmitted message is a long-standing challenge. Optimising redundancy for insertion and deletion channels remains a key open problem with significant…
In this paper, we further extend the study of function-correcting codes in the homogeneous metric over a chain ring $\mathbb{Z}_{2^s}$ for broader classes of functions, namely, locally bounded functions and linear functions, and for weight…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
We present a precise characterization of linear functional-repair storage codes in terms of {\em admissible states/}, with each state made up from a collection of vector spaces over some fixed finite field. To illustrate the usefulness of…
We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS honeycomb code, is geometrically similar to…
Physical Unclonable Functions evaluate manufacturing variations to generate secure cryptographic keys for embedded systems without secure key storage. It is explained how methods from coding theory are applied in order to ensure reliable…
Given an array with defective elements, failure correction (FC) aims at finding a new set of weights for the working elements so that the properties of the original pattern can be recovered. Unlike several FC techniques available in the…
In this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance $\delta$ is a family $C$ of graphs on a common vertex set of size $n$, such that if we start with any graph in $C$, we would have to modify…
Methodology is proposed to uncover structural breaks in functional data that is "fully functional" in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break…
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,…
Data shaping is a coding technique that has been proposed to increase the lifetime of flash memory devices. Several data shaping codes have been described in recent work, including endurance codes and direct shaping codes for structured…
Conventional database architectures often secure local consistency by discarding information, entangling correctness with loss. We introduce the Functorial-Categorical Database (FCDb), which models data operations as morphisms in a layered…
Error correction is an indispensable component when Physical Unclonable Functions (PUFs) are used in cryptographic applications. So far, there exist schemes that obtain helper data, which they need within the error correction process. We…
The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
In response to the increasing volume and sensitivity of data, traditional centralized computing models face challenges, such as data security breaches and regulatory hurdles. Federated Computing (FC) addresses these concerns by enabling…