Weakly Mutually Uncorrelated Codes
S. M. Hossein Tabatabaei Yazdi, Han Mao Kiah, Olgica Milenkovic
TL;DR
This paper introduces weakly mutually uncorrelated (WMU) sequences with applications in DNA storage, providing constructions that ensure balance, error correction, and synchronization properties for reliable data encoding.
Contribution
The paper defines WMU sequences and develops new constructions that incorporate balancing, error correction, and synchronization for DNA-based storage systems.
Findings
Constructed balanced, error-correcting WMU codes using Dyck paths.
Developed methods based on Knuth's balancing principle and cyclic codes.
Demonstrated applicability to DNA storage and synchronization protocols.
Abstract
We introduce the notion of weakly mutually uncorrelated (WMU) sequences, motivated by applications in DNA-based storage systems and synchronization protocols. WMU sequences are characterized by the property that no sufficiently long suffix of one sequence is the prefix of the same or another sequence. In addition, WMU sequences used in DNA-based storage systems are required to have balanced compositions of symbols and to be at large mutual Hamming distance from each other. We present a number of constructions for balanced, error-correcting WMU codes using Dyck paths, Knuth's balancing principle, prefix synchronized and cyclic codes.
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Taxonomy
TopicsDNA and Biological Computing · Cellular Automata and Applications · Algorithms and Data Compression