  DNA Data storage has recently attracted much attention due to its durable
preservation and extremely high information density (bits per gram) properties.
In this work, we propose a hybrid coding strategy comprising of generalized
constrained codes to tackle homopolymer (run-length) limit and a protograph
based low-density parity-check (LDPC) code to correct asymmetric nucleotide
level (i.e., A/T/C/G) substitution errors that may occur in the process of DNA
sequencing. Two sequencing techniques namely, Nanopore sequencer and Illumina
sequencer with their equivalent channel models and capacities are analyzed. A
coding architecture is proposed to potentially eliminate the catastrophic
errors caused by the error-propagation in the constrained decoding while
enabling high coding potential. We also show the log likelihood ratio (LLR)
calculation method for the belief propagation decoding with this coding
architecture. The simulation results and the theoretical analysis show that the
proposed coding scheme exhibits good bit-error rate (BER) performance and high
coding potential ($\sim1.98$ bits per nucleotide).
