Related papers: Construction of Error-Correcting Codes for Random …
It has been observed that particular rate-1/2 partially systematic parallel concatenated convolutional codes (PCCCs) can achieve a lower error floor than that of their rate-1/3 parent codes. Nevertheless, good puncturing patterns can only…
This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number…
In this paper, we investigate an artificial-intelligence (AI) driven approach to design error correction codes (ECC). Classic error correction code was designed upon coding theory that typically defines code properties (e.g., hamming…
A method for improving the performance of sparse-matrix based parity check codes is proposed, based on insight gained from methods of statistical physics. The advantages of the new approach are demonstrated on an existing encoding/decoding…
We construct Gray codes over permutations for the rank-modulation scheme, which are also capable of correcting errors under the infinity-metric. These errors model limited-magnitude or spike errors, for which only single-error-detecting…
Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a…
We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-elimination corresponds to error correction.
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecting codes in the Hamming metric. A rank-metric code is said…
Batched network coding is a low-complexity network coding solution to feedbackless multi-hop wireless packet network transmission with packet loss. The data to be transmitted is encoded into batches where each of which consists of a few…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the symbols received at their incoming edges on their…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
Permutation codes were extensively studied in order to correct different types of errors for the applications on power line communication and rank modulation for flash memory. In this paper, we introduce the neural network decoders for…
To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times…
Large language models (LLMs) have demonstrated an impressive ability to generate code for various programming tasks. In many instances, LLMs can generate a correct program for a task when given numerous trials. Consequently, a recent trend…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
Quantitative research relies heavily on coding, and coding errors are relatively common even in published research. In this paper, we examine whether individuals are more or less likely to check their code depending on the results they…
In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…