The Maximum Run-Length Constrained Balanced Codes for Random-Access DNA Storage

DeoxyriboNucleic Acid (DNA) is a molecule composed of two polynucleotide chains that form a double helix, and each DNA strand contains generic information. DNAs are getting a huge amount of attention these days as new data storage media with ultra high density and long lifespan.When data is stored in DNA strands, some constraints on DNA strands (e.g. the ratio of Cytosine and Guanine within a strand should be 50%, the run-length of each nucleotide is limited up to 5 or the prefix cannot appear within the main data sequence) should be considered for reliability. To examine effectiveness of coding schemes satisfying these constraints, it is important to observe the capacity (the maximum code rate) of such codes. Therefore, in this paper, we present the explicit capacities of codes when certain constraints are given, based on the study of constrained systems. We also observe a coding scheme that focuses on further conditions on the addresses, prefixes of DNA strands appended to identify their positions in the original DNA string, for executing random access in DNA storage.