In this paper we develop lower and upper bounds on the capacity of an amplitude shift keying (ASK)-based molecular communication (MC) system with feedback. Analyzing the effect of feedback on the performance of MC is motivated by the growing use of feedback in controlling drug delivery. Based on causal knowledge of the number of transmitted and received molecules, the input probability of symbols is adapted so as to maximize directed information in the molecular communication channel. We considered one dimensional channel with drift velocity caused by blood flow. In our system, molecules propagate in a fluid with a drift velocity; the receiver absorbs the molecule unless it is saturated (saturation models a limit on ligand binding). The input is limited by a toxicity constraint of injected molecules. We also study the effects of feedback on the achievable information rates in terms of the time delay in receiving the feedback. We show that, especially for higher values of toxicity constraint and sequence length, feedback, in terms of causal knowledge of the number of delivered molecules, improves performance of ASK-based molecular communication.

在本文中，我们开发了基于带反馈的基于幅度移位键控（ASK）的分子通信（MC）系统的容量的上限和下限。分析反馈对MC性能的影响是由于越来越多地使用反馈来控制药物输送。基于对已发射和已接收分子数量的因果关系知识，可以调整符号的输入概率，以使分子通信通道中的定向信息最大化。我们考虑了一维通道，其具有由血流引起的漂移速度。在我们的系统中，分子在流体中以漂移速度传播。除非分子饱和，否则受体会吸收该分子（饱和模拟了对配体结合的限制）。输入受到注入分子的毒性限制。我们还根据接收反馈的时间延迟研究了反馈对可实现的信息速率的影响。我们表明，特别是对于更高的毒性约束值和序列长度值，就传递的分子数量的因果关系而言，反馈可改善基于ASK的分子通讯的性能。