Related papers: Insertion and Deletion Correction in Polymer-based…
We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the…
In the age of data revolution, a modern storage~or transmission system typically requires different levels of protection. For example, the coding technique used to fortify data in a modern storage system when the device is fresh cannot be…
We introduce synchronization strings as a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to deal with than commonly considered…
Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary $B_2$-sequences. Binary $B_2$-sequences are collections of binary strings of length…
A distributed storage system stores data across multiple nodes, with the primary objective of enabling efficient data recovery even in the event of node failures. The main goal of an exact repair scheme is to recover the data from a failed…
We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
Synchronization strings are recently introduced by Haeupler and Shahrasbi [HS17a] in the study of codes for correcting insertion and deletion errors (insdel codes). A synchronization string is an encoding of the indices of the symbols in a…
In string-bit models, string is described as a polymer of point-like constituents. We attempt to use string-bit ideas to investigate how the size of string is affected by string interactions in a non-perturbative context. Lacking adequate…
Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target…
Data compression is a well-studied (and well-solved) problem in the setup of long coding blocks. But important emerging applications need to compress data to memory words of small fixed widths. This new setup is the subject of this paper.…
We study the combination of two recent coding approaches, in the context of DNA based data storage. Composite DNA alphabets leverage properties of the DNA synthesis and sequencing process. A composite symbol does not represent a single…
We describe an algorithm to find maximal exact matches (MEMs) among HiFi reads with homopolymer errors. The main novelty in our work is that we resort to run-length compression to help deal with errors. Our method receives as input a…
Several recent works have considered the \emph{trace reconstruction problem}, in which an unknown source string $x\in\{0,1\}^n$ is transmitted through a probabilistic channel which may randomly delete coordinates or insert random bits,…
We study the inherent space requirements of shared storage algorithms in asynchronous fault-prone systems. Previous works use codes to achieve a better storage cost than the well-known replication approach. However, a closer look reveals…
In the domain of algorithmic music composition, machine learning-driven systems eliminate the need for carefully hand-crafting rules for composition. In particular, the capability of recurrent neural networks to learn complex temporal…
Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a…
Computing equilibrium concentrations of molecular complexes is generally analytically intractable and requires numerical approaches. In this work we focus on the polymer-monomer level, where indivisible molecules (monomers) combine to form…
This article describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset's unordered structure. Multisets are a generalisation of sets where members are allowed to occur multiple times. A multiset…
Encoding the electronic structure of molecules using 2-electron reduced density matrices (2RDMs) as opposed to many-body wave functions has been a decades-long quest as the 2RDM contains sufficient information to compute the exact molecular…