In large-scale array-based DNA synthesis, optical and chemical coupling between nearby sites can limit simultaneous activations. Motivated by this constraint, we study strands synthesized according to a fixed global synthesis sequence, with at most one strand per row advancing in each cycle. We focus on the fundamental case of two strands in a single row and analyze the expected completion time of row-constrained synthesis. We introduce the laggard-first (LF) policy, a simple rule that always advances the strand with fewer synthesized symbols when a conflict arises, and establish that it is asymptotically optimal among online policies without look-ahead. In the binary case, one-symbol look-ahead strictly improves on the no-look-ahead bound. We further show that even complete advance knowledge does not eliminate the scheduling loss, as even a globally optimal schedule incurs an unavoidable expected overhead that grows linearly with the strand length. Finally, we complement these scheduling results with a dynamic programming algorithm for computing an optimal offline synthesis order and a constant-redundancy binary coding scheme that yields a deterministic worst-case synthesis time guarantee.

DNA-based storage systems face a primary bottleneck in their parallel strand synthesis processes, affecting both economic viability and operational efficiency. Current methodologies predominantly employ either enzymatic DNA synthesis, permitting the addition of any nucleotide to individual strands per cycle, or photolithographic synthesis, facilitating the selective addition of a single nucleotide across multiple strands simultaneously. This research studies a theoretical hybrid framework combining both approaches, enabling the selection of a fixed number of nucleotides within each synthesis cycle. We introduce the term complex synthesis sequence to describe the nucleotide addition pattern and extend the concepts of subsequence and supersequence to enable standard sequences to be subsequences of complex synthesis sequences. We extend Lenz et al.'s definition of information rate and use an analog of the deletion ball to derive expressions for the maximal information rate obtainable in this model. We develop an algorithm to determine the optimal synthesis sequence in this model for known strands, show that the solution is analogous to finding an SCS, and derive the required dynamic programming algorithm to solve it.

The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as a collection of two-dimensional arrays. Motivated by error patterns observed in recent prototype architectures, our study focuses on correcting erasures in the last few symbols of each row, and also correcting arbitrary deletions across rows. We present code constructions and explicit encoders and decoders that are shown to be nearly optimal in many scenarios. We show that the new coding schemes are capable of effectively mitigating these errors, making these emerging storage platforms potentially promising solutions.