论文标题
信号波动和二进制通信渠道中的信息传输速率
Signal Fluctuations and the Information Transmission Rates in Binary Communication Channels
论文作者
论文摘要
在神经系统中，信息通过一系列动作电位（SPIKES-TRAIN）传达。正如Mackay和McCulloch提出的那样，可以将Spike-Trains表示为来自信息源的位序列。以前，我们研究了通过尖峰，它们的相关性和频率进行的信息传输速率（ITR）之间的关系。在这里，我们专注于峰值波动如何影响ITR的问题。应用香农开发的信息理论方法。信息源被建模为固定随机过程。我们假设马尔可夫流程有两个状态。作为尖峰训练的波动措施，我们考虑了标准偏差SD，实际上，该偏差SD衡量了平均尖峰频率围绕尖峰的平均波动。我们发现ITR和信号波动关系的特征在很大程度上取决于参数s，这是从没有尖峰状态到尖峰状态的过渡概率的总和，反之亦然。事实证明，对于较小的s（s <1），商ITR/SD具有最大值，并且根据过渡概率可能为零。对于s足够大的1 <s，对于每个s，ITR/SD与0分开。当我们通过与多项式的近似值代替了马尔可夫熵公式中的香农熵项时观察到类似的行为。我们还表明，差异的ITR商以一种完全不同的方式行为。我们表明，对于大型过渡参数S，SD的信息传输速率永远不会降至0。具体而言，对于1 <s <1.7，ITR将始终是在构成该s的过渡概率的独立上，即在波动级别上方，即我们有SD <itr。我们得出的结论是，在更加嘈杂的环境中，要获得适当的传输可靠性和效率，从州过渡到较高的趋势的信息来源无尖峰到尖峰状态，反之亦然。
In nervous system information is conveyed by sequence of action potentials (spikes-trains). As MacKay and McCulloch proposed, spike-trains can be represented as bits sequences coming from Information Sources. Previously, we studied relations between Information Transmission Rates (ITR) carried out by the spikes, their correlations, and frequencies. Here, we concentrate on the problem of how spikes fluctuations affect ITR. The Information Theory Method developed by Shannon is applied. Information Sources are modeled as stationary stochastic processes. We assume such sources as two states Markov processes. As a spike-trains' fluctuation measure, we consider the Standard Deviation SD, which, in fact, measures average fluctuation of spikes around the average spike frequency. We found that character of ITR and signal fluctuations relation strongly depends on parameter s which is a sum of transitions probabilities from no spike state to spike state and vice versa. It turned out that for smaller s (s<1) the quotient ITR/SD has a maximum and can tend to zero depending on transition probabilities. While for s large enough 1<s the ITR/SD is separated from 0 for each s. Similar behavior was observed when we replaced Shannon entropy terms in Markov entropy formula by their approximation with polynomials. We also show that the ITR quotient by Variance behaves in a completely different way. We show that for large transition parameter s the Information Transmission Rate by SD will never decrease to 0. Specifically, for 1<s<1.7 the ITR will be always, independently on transition probabilities which form this s, above the level of fluctuations, i.e. we have SD<ITR. We conclude that in a more noisy environment, to get appropriate reliability and efficiency of transmission, Information Sources with higher tendency of transition from the state no spike to spike state and vice versa should be applied.
