We study the amount of reliable information that can be stored in a DNA-based storage system with noisy sequencing, where each codeword is composed of short DNA molecules. We analyze a concatenated coding scheme, where the outer code is designed to handle the random sampling, while the inner code is designed to handle the random sequencing noise. We assume that the sequencing channel is symmetric and choose the inner coding scheme to be composed by a linear block code and a zero-undetected-error decoder. As a byproduct, the resulting optimal maximum-likelihood decoder land itself for an amenable analysis, and we are able to derive an achievability bound for the scaling of the number of information bits that can be reliably stored. As a result of independent interest, we prove that the average error probability of random linear block codes under zero-undetected-error decoding converges to zero exponentially fast with the block length, as long as its coding rate does not exceed some critical value, which is known to serve as a lower bound to the zero-undetected-error capacity.

翻译：本研究探讨了在存在噪声测序的DNA存储系统中可存储的可靠信息量，其中每个码字由短DNA分子构成。我们分析了一种级联编码方案：外码用于处理随机采样，内码用于处理随机测序噪声。假设测序通道具有对称性，我们选择由线性分组码和零未检测错误解码器构成的内码方案。作为副产品，所得的最优最大似然解码器便于分析，使我们能够推导出可可靠存储信息比特数规模的可达性界。作为具有独立意义的结果，我们证明了在零未检测错误解码下，随机线性分组码的平均错误概率随码长呈指数级收敛至零，只要其编码率不超过某个临界值——该值已知为零未检测错误容量的下界。