The DNA storage channel is considered, in which the MM Deoxyribonucleic acid (DNA) molecules comprising each codeword are stored without order, sampled NN times with replacement, and then sequenced over a discrete memoryless channel. For a constant coverage depth M/NM/N and molecule length scaling Θ(logM)\Theta (\log M) , lower (achievability) and upper (converse) bounds on the capacity of the channel, as well as a lower (achievability) bound on the reliability function of the channel are provided. Both the lower and upper bounds on the capacity generalize a bound which was previously known to hold only for the binary symmetric sequencing channel, and only under certain restrictions on the molecule length scaling and the crossover probability parameters. When specified to binary symmetric sequencing channel, these restrictions are completely removed for the lower bound and are significantly relaxed for the upper bound in the high-noise regime. The lower bound on the reliability function is achieved under a universal decoder, and reveals that the dominant error event is that of outage – the event in which the capacity of the channel induced by the DNA molecule sampling operation does not support the target rate.

中文翻译：

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DNA 存储通道：容量和错误概率界限


考虑 DNA 存储通道，其中组成每个码字的 MM 脱氧核糖核酸 (DNA) 分子无序存储，替换采样 NN 次，然后通过离散的无记忆通道进行测序。对于恒定的覆盖深度 M/NM/N 和分子长度缩放 θ(logM)\Theta (\log M) ，通道容量的下限（可实现性）和上限（逆），以及下限（可实现性） ）提供了对信道可靠性函数的约束。容量的下限和上限都概括了一个界限，该界限以前已知仅适用于二元对称测序通道，并且仅在分子长度缩放和交叉概率参数的某些限制下成立。当指定为二元对称测序通道时，这些限制对于下限被完全消除，并且对于高噪声区域的上限显着放宽。可靠性函数的下界是在通用解码器下实现的，并揭示了主要错误事件是中断——在该事件中，由 DNA 分子采样操作引起的通道容量不支持目标速率。