Related papers: Codes Correcting Two Deletions
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
As a medium for cold data storage, DNA stands out as it promises significant gains in storage capacity and lifetime. However, it comes with its own data processing challenges to overcome. Constrained codes over the DNA alphabet…
Using the idea of interference alignment, Suh and Ramchandran constructed a class of minimum-storage regenerating codes which can repair one systematic or one parity-check node with optimal repair bandwidth. With the same code structure, we…
The performance of Reed--Solomon codes (RS codes, for short) in the presence of insertion and deletion errors has attracted growing attention in recent literature. In this work, we further study this intriguing mathematical problem,…
A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery…
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…
Most memories suffer from both permanent defects and intermittent random errors. The partitioned linear block codes (PLBC) were proposed by Heegard to efficiently mask stuck-at defects and correct random errors. The PLBC have two separate…
We consider the zero-error capacity of deletion channels. Specifically, we consider the setting where we choose a codebook ${\cal C}$ consisting of strings of $n$ bits, and our model of the channel corresponds to an adversary who may delete…
In recent years, several integer programming (IP) approaches were developed for maximum-likelihood decoding and minimum distance computation for binary linear codes. Two aspects in particular have been demonstrated to improve the…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
Cyclic redundancy check (CRC) codes check if a codeword is correctly received. This paper presents an algorithm to design CRC codes that are optimized for the code-specific error behavior of a specified feedforward convolutional code. The…
Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each…
Recently, codes for correcting a burst of errors have attracted significant attention. One of the most important reasons is that bursts of errors occur in certain emerging techniques, such as DNA storage. In this paper, we investigate a…
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…
We generalize Helberg's number-theoretic construction of multiple insertion-deletion correcting binary codes to non-binary alphabets and describe a linear decoding algorithm for correcting multiple deletions.
Consider a linear [n,k,d]_q code C. We say that that i-th coordinate of C has locality r, if the value at this coordinate can be recovered from accessing some other r coordinates of C. Data storage applications require codes with small…
Function-correcting codes, introduced by Lenz, Bitar, Wachter-Zeh, and Yaakobi, protect specific function values of a message rather than the entire message. A central challenge is determining the optimal redundancy -- the minimum…
A single deletion error correcting code (SDECC) is a set of fixed-length sequences consisting of two types of symbols, 0 and 1, such that the original sequence can be recovered for at most one deletion error. The upper bound for the size of…
Reliability is an important requirement for both communication and storage systems. Due to continuous scale down of technology multiple adjacent bits error probability increases. The data may be corrupted due soft errors. Error correction…
In this paper, we consider a synchronization problem between nodes $A$ and $B$ that are connected through a two--way communication channel. {Node $A$} contains a binary file $X$ of length $n$ and {node $B$} contains a binary file $Y$ that…