Related papers: Optimal Codes Detecting Deletions in Concatenated …
In distributed computing systems with stragglers, various forms of redundancy can improve the average delay performance. We study the optimal replication of data in systems where the job execution time is a stochastically decreasing and…
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…
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms…
In steganography, we always hope to maximize the embedding payload subject to an upper-bounded distortion. We need suitable distortion measurement to evaluate the embedding impact. However, different distortion functions exposes different…
We study error-correcting codes in the space $\mathcal{S}_{n,q}$ of length-$n$ multisets over a $q$-ary alphabet, motivated by permutation channels in which ordering is completely lost and errors act solely by deletions of symbols, i.e., by…
Erasure codes are being increasingly used in distributed-storage systems in place of data-replication, since they provide the same level of reliability with much lower storage overhead. We consider the problem of constructing explicit…
We describe properties and constructions of constraint-based codes for DNA-based data storage which account for the maximum repetition length and AT/GC balance. We present algorithms for computing the number of sequences with maximum…
The synthesis of DNA strands remains the most costly part of the DNA storage system. Thus, to make DNA storage system more practical, the time and materials used in the synthesis process have to be optimized. We consider the most common…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
MDS array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with $r$ redundancy nodes can correct any $r$ node erasures by accessing all the remaining information…
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…
The {\em insertion-deletion channel} takes as input a binary string $x \in\{0, 1\}^n$, and outputs a string $\widetilde{x}$ where some of the bits have been deleted and others inserted independently at random. In the {\em trace…
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…
When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…
Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any…
Finding deletion-correcting codes of maximum size has been an open problem for over 70 years, even for a single deletion. In this paper, we propose a novel approach for constructing deletion-correcting codes. A code is a set of sequences…
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire…
Fractional repetition (FR) codes is a family of codes for distributed storage systems that allow for uncoded exact repairs having the minimum repair bandwidth. However, in contrast to minimum bandwidth regenerating (MBR) codes, where a…
The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary…