Related papers: Optimal codes for correcting a single (wrap-around…
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…
In this paper, we present an efficiently encodable and decodable code construction that is capable of correction a burst of deletions of length at most $k$. The redundancy of this code is $\log n + k(k+1)/2\log \log n+c_k$ for some constant…
The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at most $t$ deletions in…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
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…
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of…
In this paper, we investigate codes designed to correct two bursts of deletions, where each burst has a length of exactly $b$, where $b>1$. The previous best construction, achieved through the syndrome compression technique, had a…
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…
Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error…
The $(n,k,d)$ regenerating code is a class of $(n,k)$ erasure codes with the capability to recover a lost code fragment from other $d$ existing code fragments. This paper concentrates on the design of exact regenerating codes at Minimum…
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable…
This paper constructs a non-binary code correcting a single $b$-burst of insertions or deletions with a large cardinality. This paper also proposes a decoding algorithm of this code and evaluates a lower bound of the cardinality of this…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
Motivated by applications in DNA-based storage and communication systems, we study deletion and insertion errors simultaneously in a burst. In particular, we study a type of error named $t$-deletion-$s$-insertion-burst ($(t,s)$-burst for…
In this paper we study codes for correcting deletable errors in binary words, where each bit is either retained, substituted, erased or deleted and the total number of errors is much smaller compared to the length of the codeword. We…
We study optimal reconstruction codes over the multiple-burst substitution channel. Our main contribution is establishing a trade-off between the error-correction capability of the code, the number of reads used in the reconstruction…
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…
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.…
This paper considers the transmission of an infinite sequence of messages (a streaming source) over a packet erasure channel, where every source message must be recovered perfectly at the destination subject to a fixed decoding delay. While…
This paper presents a new construction of error correcting codes which achieves optimal recovery of a streaming source over a packet erasure channel. The channel model considered is the sliding window erasure model, with burst and arbitrary…