Related papers: Error-Correcting Codes for the Sum Channel
Channels with synchronization errors, such as deletion and insertion errors, are crucial in DNA storage, data reconstruction, and other applications. These errors introduce memory to the channel, complicating its capacity analysis. This…
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…
The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as…
In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or…
A (tandem) duplication of length $ k $ is an insertion of an exact copy of a substring of length $ k $ next to its original position. This and related types of impairments are of relevance in modeling communication in the presence of…
In this paper we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a data set is represented by an unordered set of $M$ sequences, each of length $L$. Errors…
In this work, we derive upper bounds on the cardinality of tandem duplication and palindromic deletion correcting codes by deriving the generalized sphere packing bound for these error types. We first prove that an upper bound for tandem…
This paper studies codes that correct bursts of deletions. Namely, a code will be called a $b$-burst-deletion-correcting code if it can correct a deletion of any $b$ consecutive bits. While the lower bound on the redundancy of such codes…
Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai \emph{et al}. to combat errors when a fixed number of noisy channels are available. The central problem on this topic is…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
In this paper, we construct systematic $q$-ary two-deletion correcting codes and burst-deletion correcting codes, where $q\geq 2$ is an even integer. For two-deletion codes, our construction has redundancy $5\log n+O(\log q\log\log n)$ and…
We study the application of polar codes in deletion channels by analyzing the cascade of a binary erasure channel (BEC) and a deletion channel. We show how polar codes can be used effectively on a BEC with a single deletion, and propose a…
Because of its high data density and longevity, DNA is emerging as a promising candidate for satisfying increasing data storage needs. Compared to conventional storage media, however, data stored in DNA is subject to a wider range of errors…
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the…
The persistent storage of big data requires advanced error correction schemes. The classical approach is to use error correcting codes (ECCs). This work studies an alternative approach, which uses the redundancy inherent in data itself for…
Transmit a codeword $x$, that belongs to an $(\ell-1)$-deletion-correcting code of length $n$, over a $t$-deletion channel for some $1\le \ell\le t<n$. Levenshtein, in 2001, proposed the problem of determining $N(n,\ell,t)+1$, the minimum…
Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging…
An insdel refers to a deletion or an insertion, and an edit refers to an insdel or a substitution. In this paper, we consider the segmented single-insdel (resp. single-edit) channel, where the channel's input bit stream is partitioned into…
As sensing and instrumentation play an increasingly important role in systems controlled over wired and wireless networks, the need to better understand delay-sensitive communication becomes a prime issue. Along these lines, this article…