Coding for Ordered Composite DNA Sequences

Abstract

To increase the information capacity of DNA storage, composite DNA letters were introduced. We propose a novel channel model for composite DNA in which composite sequences are decomposed into ordered standard non-composite sequences. The model is designed to handle any alphabet size and composite resolution parameter. We study the problem of reconstructing composite sequences of arbitrary resolution over the binary alphabet under substitution errors. We define two families of error-correcting codes and provide lower and upper bounds on their cardinality. In addition, we analyze the case in which a single deletion error occurs in the channel and present a systematic code construction for this setting. Finally, we briefly discuss the channel's capacity, which remains an open problem.