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arXiv 1602.07757cs.ITmath.IT
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基于扩散的分子定时信道的容量极限

Capacity Limits of Diffusion-Based Molecular Timing Channels

Nariman Farsad, Yonathan Murin, Andrew Eckford, Andrea Goldsmith

摘要:

这项工作介绍了分子定时(MT)通道的容量限制,其中信息被调制在小信息粒子的释放时间,并从到达接收器的时间解码。它示出的随机到达时间可以表示为一个加性噪声信道,和基于扩散的MT(DBMT)信道的噪声分布根据Lévy分布。DBMT信道的容量的上下限推导的情况下,与信道中的信息粒子的传播的延迟是有限的,即,当信息粒子消散后,一个有限的时间间隔。对于每个通道使用释放单个粒子的情况,这些边界显示为紧密的。当发射器同时释放大量粒子时,接收器处的检测器可能无法精确检测所有粒子的到达时间。因此,考虑两种替代模型:基于首先到达的颗粒的检测,或基于平均到达时间的检测。紧的下限和上限推导出这两个模型。结果表明,通过控制信息粒子的最大延迟,系统容量可以随释放粒子数的增加而成倍增加。由于每个粒子采用随机独立路径,因此这种路径分集类似于接收器分集,并且可以用于显著增加可实现的数据率。

英文摘要:

This work introduces capacity limits for molecular timing (MT) channels, where information is modulated in the release timing of small information particles, and decoded from the time of arrivals at the receiver. It is shown that the random time of arrival can be represented as an additive noise channel, and for the diffusion-based MT (DBMT) channel this noise is distributed according to the Lévy distribution. Lower and upper bounds on the capacity of the DBMT channel are derived for the case where the delay associated with the propagation of the information particles in the channel is finite, namely, when the information particles dissipate after a finite time interval. For the case where a single particle is released per channel use, these bounds are shown to be tight. When the transmitter simultaneously releases a large number of particles, the detector at the receiver may not be able to precisely detect the arrival time of all the particles. Therefore, two alternative models are considered: detection based on the particle that arrives first, or detection based on the average arrival times. Tight lower and upper bounds are derived for these two models. It is shown that by controlling the maximal delay of the information particles, the capacity can increase poly-logarithmically with the number of released particles. As each particle takes a random independent path, this diversity of paths is analogous to receiver diversity and can be used to considerably increase the achievable data rates.

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