Related papers: Error-Correction in Flash Memories via Codes in th…
Physical Unclonable Functions (PUFs) exploit variations in the manufacturing process to derive bit sequences from integrated circuits, which can be used as secure cryptographic keys. Instead of storing the keys in an insecure, non-volatile…
Motivated by applications in DNA-based storage, we introduce the new problem of code design in the Damerau metric. The Damerau metric is a generalization of the Levenshtein distance which, in addition to deletions, insertions and…
Position embeddings, encoding the positional relationships among tokens in text sequences, make great contributions to modeling local context features in Transformer-based pre-trained language models. However, in Extractive Question…
Fine-grained sparsity promises higher parametric capacity without proportional per-token compute, but often suffers from training instability, load balancing, and communication overhead. We introduce STEM (Scaling Transformers with…
Error detectable and error correctable coding in Hamming space was researched to discover possible fault tolerant coding constellations, which can implement Boolean logic with fault tolerant property. Basic logic operators of the Boolean…
In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does…
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes,…
Providing timely and personalized guidance for students' programming assignments, offers significant practical value for helping students complete assignments and enhance their learning. In recent years, various automated Fault Localization…
We consider analog error-correcting codes (analog ECCs) that are designed to correct/detect outlying errors arising in analog implementations of vector-matrix multiplication. The error-correction/detection capability of an analog ECC can be…
In this work we continue the study of a new class of codes, called \emph{codes over graphs}. Here we consider storage systems where the information is stored on the edges of a complete directed graph with $n$ nodes. The failure model we…
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the…
Recently, flash memories have become a competitive solution for mass storage. The flash memories have rather different properties compared with the rotary hard drives. That is, the writing of flash memories is constrained, and flash…
The size reduction of transistors in the latest flash memory generation has resulted in programming and data erasure issues within these designs. Consequently, ensuring reliable data storage has become a significant challenge for these…
Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…
We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM…
In this article, we consider the decoding problem of affine Grassmann codes over nonbinary fields. We use matrices of different ranks to construct a large set consisting of parity checks of affine Grassmann codes, which are orthogonal with…
Quantum error correction codes play a central role in the realisation of fault-tolerant quantum computing. Chamon model is a 3D generalization of the toric code. The error correction computation on this model has not been explored so far.…
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…
Generalized Reed-Solomon (RS) codes are a common choice for efficient, reliable error correction in memory and communications systems. These codes add $2t$ extra parity symbols to a block of memory, and can efficiently and reliably correct…
Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…