Constrained Channel Capacity for DNA-Based Data Storage Systems

Deoxyribonucleic acid (DNA)-based data storage has grown rapidly due to its advantages with the increase in infrequently large amounts of data. However, when the maximum homopolymer runlength (RLL) of the DNA strand is large and the GC-content is either too high or too low, the DNA synthesis and sequencing processes are prone to substitution, deletion and insertion errors. To reduce errors in DNA synthesis and sequencing, we require that the DNA storage channel satisfies both k-RLL and strong-(l,d)-locally-GC-balanced constraints, where the former refers to the maximum homopolymer runlength in each sequence is at most k, and the latter refers to the number of G and C of every length-(l' >= l) subsequence is bounded between [ (2)/(l') - delta,(2)/(l') + delta]. This constrained channel allows DNA data storage system to be less prone to errors during synthesis and sequencing and improves the success rate of Polymerase Chain Reaction (PCR) amplification. We propose a method to calculate the channel capacity. In particular, we provide a relationship between the 4-ary constrained channel capacity and the 2-ary constrained channel capacity, which makes it simpler to calculate the 4-ary constrained channel capacity.