Channels with noisy duplications have recently been used to model the nanopore sequencer. This paper extends some foundational information-theoretic results to this new scenario. We prove the asymptotic equipartition property (AEP) for noisy duplication processes based on ergodic Markov processes. A consequence is that the noisy duplication channel is information stable for ergodic Markov sources, and therefore the channel capacity constrained to Markov sources is the Markov-constrained Shannon capacity. We use the AEP to estimate lower bounds on the capacity of the binary symmetric channel with Bernoulli and geometric duplications using Monte Carlo simulations. In addition, we relate the AEP for noisy duplication processes to the AEP for hidden semi-Markov processes.

翻译：带噪声重复信道近期被用于建模纳米孔测序仪。本文将此领域的基础信息论结果拓展至这一新场景。我们基于遍历马尔可夫过程证明了带噪声重复过程的渐近等分性（AEP）。其推论是：对于遍历马尔可夫信源，带噪声重复信道是信息稳定的，因此受限于马尔可夫信源的信道容量即为马尔可夫约束下的香农容量。我们利用AEP通过蒙特卡洛仿真估算了伯努利与几何重复模式下二进制对称信道的容量下界。此外，我们揭示了带噪声重复过程的AEP与隐半马尔可夫过程AEP之间的关联。