Related papers: Codes Correcting a Burst of Deletions or Insertion…
Function-correcting codes are an innovative class of codes that are designed to protect a function evaluation of the data against errors or corruptions. Due to its usefulness in machine learning applications and archival data storage, where…
Recovery of data packets from packet erasures in a timely manner is critical for many streaming applications. An early paper by Martinian and Sundberg introduced a framework for streaming codes and designed rate-optimal codes that permit…
Recent efforts in coding theory have focused on building codes for insertions and deletions, called insdel codes, with optimal trade-offs between their redundancy and their error-correction capabilities, as well as efficient encoding and…
Streaming codes (SCs) are packet-level codes that recover erased packets within a strict decoding-delay deadline. Streaming codes for various packet erasure channel models such as sliding-window (SW) channel models that admit random or…
We consider the problem of correcting insertion and deletion errors in the $d$-dimensional space. This problem is well understood for vectors (one-dimensional space) and was recently studied for arrays (two-dimensional space). For vectors…
Insdel errors occur in communication systems caused by the loss of positional information of the message. Since the work by Guruswami and Wang, there have been some further investigations on the list decoding of insertion codes, deletion…
Motivated by modern network communication applications which require low latency, we study codes that correct erasures with low decoding delay. We provide a simple explicit construction that yields convolutional codes that can correct both…
We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued…
Emerging applications in manufacturing, wireless communication, and molecular data storage require robust coding schemes that remain effective under physical distortions where codewords may be arbitrarily fragmented and partially missing.…
The deletion distance between two binary words $u,v \in \{0,1\}^n$ is the smallest $k$ such that $u$ and $v$ share a common subsequence of length $n-k$. A set $C$ of binary words of length $n$ is called a $k$-deletion code if every pair of…
We introduce the sum channel, a new channel model motivated by applications in distributed storage and DNA data storage. In the error-free case, it takes as input an $\ell$-row binary matrix and outputs an $(\ell+1)$-row matrix whose first…
We analyse the prequential plug-in codes relative to one-parameter exponential families M. We show that if data are sampled i.i.d. from some distribution outside M, then the redundancy of any plug-in prequential code grows at rate larger…
This paper investigates the use of redundancy and self repairing against node failures in distributed storage systems, using various strategies. In replication method, access to one replication node is sufficient to reconstruct a lost node,…
Large-scale distributed storage systems typically use erasure codes to provide durability of data in the face of failures. A set of $k$ blocks to be stored is encoded using an $[n, k]$ code to generate $n$ blocks that are then stored on…
In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…
Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are…
We prove that certain classical cyclic redundancy check codes can be used for classical error correction and not just classical error detection. We extend the idea of classical cyclic redundancy check codes to quantum cyclic redundancy…
Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the…
Erasure coding is a storage-efficient alternative to replication for achieving reliable data backup in distributed storage systems. During the storage process, traditional erasure codes require a unique source node to create and upload all…
We study low-delay error correction codes for streaming recovery over a class of packet-erasure channels that introduce both burst-erasures and isolated erasures. We propose a simple, yet effective class of codes whose parameters can be…