Related papers: Error-Correction in Flash Memories via Codes in th…
Answering multi-hop reasoning questions requires retrieving and synthesizing information from diverse sources. Large Language Models (LLMs) struggle to perform such reasoning consistently. Here we propose an approach to pinpoint and rectify…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
Computing-in-memory (CIM) promises to alleviate the Von Neumann bottleneck and accelerate data-intensive applications. Depending on the underlying technology and configuration, CIM enables implementing compute primitives in place, such as…
We propose a novel rank aggregation method based on converting permutations into their corresponding Lehmer codes or other subdiagonal images. Lehmer codes, also known as inversion vectors, are vector representations of permutations in…
We consider a neural network (NN) that may experience memory faults and computational errors. In this paper, we propose a novel real-number-based error correction code (ECC) capable of detecting and correcting both memory errors and…
New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…
We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum…
As memory technologies continue to shrink and memory error rates increase, the demand for stronger reliability becomes increasingly critical. Fine-grain memory replication has emerged as an appealing approach to improving memory fault…
This work deals with error correction for non-volatile memories that are partially defective at some levels. Such memory cells can only store incomplete information since some of their levels cannot be utilized entirely due to, e.g.,…
This paper investigates the design and application of write-once memory (WOM) codes for flash memory storage. Using ideas from Merkx ('84), we present a construction of WOM codes based on finite Euclidean geometries over $\mathbb{F}_2$.…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…
In this paper, we consider modulation codes for practical multilevel flash memory storage systems with cell levels. Instead of maximizing the lifetime of the device [Ajiang-isit07-01, Ajiang-isit07-02, Yaakobi_verdy_siegel_wolf_allerton08,…
Large language models (LLMs) are central to modern natural language processing, delivering exceptional performance in various tasks. However, their substantial computational and memory requirements present challenges, especially for devices…
In-Memory Computing (IMC) introduces a new paradigm of computation that offers high efficiency in terms of latency and power consumption for AI accelerators. However, the non-idealities and defects of emerging technologies used in advanced…
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…
It has been widely observed that there exists a fundamental trade-off between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity achieving code ensembles typically…
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.…
Permutation codes have recently garnered substantial research interest due to their potential in various applications including cloud storage systems, genome resequencing and flash memories. In this paper, we study the theoretical bounds…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…