Related papers: Mutually Uncorrelated Codes for DNA Storage
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study…
The performance and the decoding complexity of a novel coding scheme based on the concatenation of maximum distance separable (MDS) codes and linear random fountain codes are investigated. Differently from Raptor codes (which are based on a…
In recent years, distinctive-dictionary construction has gained importance due to his usefulness in data processing. Usually, one or more dictionaries are constructed from a training data and then they are used to classify signals that did…
Domain adaptation has received a lot of attention in recent years, and many algorithms have been proposed with impressive progress. However, it is still not fully explored concerning the joint probability distribution (P(X, Y)) distance for…
The monotone minimal perfect hash function (MMPHF) problem is the following indexing problem. Given a set $S= \{s_1,\ldots,s_n\}$ of $n$ distinct keys from a universe $U$ of size $u$, create a data structure $DS$ that answers the following…
The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This…
Non-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes…
DNA strands serve as a storage medium for $4$-ary data over the alphabet $\{A,T,G,C\}$. DNA data storage promises formidable information density, long-term durability, and ease of replicability. However, information in this intriguing…
We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing…
Motivated by applications to the theory of rank-metric codes, we study the problem of estimating the number of common complements of a family of subspaces over a finite field in terms of the cardinality of the family and its intersection…
Decompressing a file made by the gzip program at an arbitrary location is in principle impossible, due to the nature of the DEFLATE compression algorithm. Consequently, no existing program can take advantage of parallelism to rapidly…
The construction of uniform designs (UDs) has received much attention in computer experiments over the past decades, but most of the previous works obtain uniform designs over a U-type by lattice domain. Due to increasing demands for…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…
We derive theoretical upper and lower bounds on the maximum size of DNA codes of length n with constant GC-content w and minimum Hamming distance d, both with and without the additional constraint that the minimum Hamming distance between…
In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given…
Maximum distance separable (MDS) array codes are XOR-based optimal erasure codes that are particularly suitable for use in disk arrays. This paper develops an innovative method to build MDS array codes from an elegant class of nested…
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in this domain are typically large, with rows and columns…
We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA…
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…
In this paper, we study how often unique decoding from $t$ insertions or $t$ deletions occurs for error correcting codes. Insertions and deletions frequently occur in synchronization problems and DNA, a medium which is beginning to be used…