Related papers: Improved Lower Bounds for Constant GC-Content DNA …
A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence,we…
Constant-dimension codes (CDCs) have been investigated for noncoherent error correction in random network coding. The maximum cardinality of CDCs with given minimum distance and how to construct optimal CDCs are both open problems, although…
A genetic algorithm is suitable for exploring large search spaces as it finds an approximate solution. Because of this advantage, genetic algorithm is effective in exploring vast and unknown space such as molecular search space. Though the…
The massive interest in deep neural networks (DNNs) for both computer vision and natural language processing has been sparked by the growth in computational power. However, this led to an increase in the memory footprint, to a point where…
DNA is an attractive candidate for data storage. Its millennial durability and nanometer scale offer exceptional data density and longevity. Its relevance to medical applications also drives advances in DNA-related biotechnology. To protect…
Distributed optimization algorithms are frequently faced with solving sub-problems on disjoint connected parts of a network. Unfortunately, the diameter of these parts can be significantly larger than the diameter of the underlying network,…
Most DNA sequencing technologies are based on the shotgun paradigm: many short reads are obtained from random unknown locations in the DNA sequence. A fundamental question, studied in arXiv:1203.6233, is what read length and coverage depth…
The exponential growth of DNA sequencing data has outpaced traditional heuristic-based methods, which struggle to scale effectively. Efficient computational approaches are urgently needed to support large-scale similarity search, a…
Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, the size of the search space and consequently the decoding complexity grows exponentially, making it impractical to be…
We investigate the fundamental limits of the recently proposed random access coverage depth problem for DNA data storage. Under this paradigm, it is assumed that the user information consists of $k$ information strands, which are encoded…
The study of large Condorcet domains (CD) has been a significant area of interest in voting theory. In this paper, our goal is to search for large CDs that are hitherto unknown. With a straightforward combinatorial definition, searching for…
Designing short DNA words is a problem of constructing a set (i.e., code) of n DNA strings (i.e., words) with the minimum length such that the Hamming distance between each pair of words is at least k and the n words satisfy a set of…
We explore the potential of continuous local search (CLS) in SAT solving by proposing a novel approach for finding a solution of a hybrid system of Boolean constraints. The algorithm is based on CLS combined with belief propagation on…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…
Motivated by applications in DNA-based data storage, constrained codes have attracted a considerable amount of attention from both academia and industry. We study the maximum cardinality of constrained codes for which the constraints can be…
In real life, it is always an urge to reach our goal in minimum effort i.e., it should have a minimum constrained path. The path may be shortest route in practical life, either physical or electronic medium. The scenario is to represents…
DNA is a promising storage medium, but its stability and occurrence of Indel errors pose a significant challenge. The relative occurrence of Guanine(G) and Cytosine(C) in DNA is crucial for its longevity, and reverse complementary base…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…