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Analysis, Design, and Logic Synthesis of Finite-state Machine-based Stochastic Computing.

机译：基于有限状态机的随机计算的分析，设计和逻辑综合。

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摘要

Most digital systems operate on a positional representation of data, such as binary encoding. An alternative is to operate on random bit streams where the signal value is encoded by the probability of obtaining a one versus a zero. This representation is much less compact than the binary encoding. However, complex operations can be performed with very simple logic. Furthermore, since the representation is uniform, with all bits weighted equally, it is highly tolerant of soft errors (i.e., bit flips).;Complex algorithms, such as artificial neural networks (ANN), low-density parity-check (LPDC) error-correcting coding, and kernel density estimation (KDE)-based image segmentation, can be implemented using stochastic encoding with much lower hardware cost and higher fault-tolerance. For example, the hardware area of the stochastic implementation of the KDE-based image segmentation is only 1.2% of the corresponding deterministic implementation, and it can tolerate more than 30% soft errors. Compared to conventional fault-tolerant techniques, such as triple-module redundance (TMR), the stochastic implementations of the complex algorithms normally consumes equivalent or less energy and have better fault-tolerance. For example, the TMR implementation of the KDE-based implementation can only tolerate up to 10% soft errors, but consumes the same energy as the stochastic implementation. In addition, thanks to the simple construction of the stochastic computing elements, it makes the rounting much easier, which is a big issue for very large scale integrated circuit (VLSI) deterministic implementations of these complex algorithms.;Both combinational and sequential constructs have been proposed for operating on stochastic bit streams. Prior work has shown that combinational logic can implement multiplication and scaled addition effectively while finite-state machines (FSMs) can implement complex functions such as exponentiation and tanh effectively. Although the combinational logic-based stochastic computing elements had been well studied, they are inefficient for complex operations. The FSM-based stochastic computing elements are very efficient for complex operations. However, only three FSM-based stochastic computing elements were proposed by prior work, which limits the applications of stochastic computing. To implement more applications and functions stochastically, this dissertation focuses on the FSM-based stochastic computing.;We first analyze the FSM-based stochastic computing elements proposed by prior work, which had largely been validated empirically. In this dissertation, we provide a rigorous mathematical treatment of the FSM-based stochastic computing elements. This gives us intuition about how to construct arbitrary functions stochastically using the FSM.;Then, based on the existing stochastic computing elements, we implement five digital image processing algorithms as case studies. So far as we know, this is the first time these digital image processing algorithms are implemented stochastically. For all the five algorithms, the stochastic implementation has much less hardware cost and better fault-tolerance than the corresponding deterministic implementation.;Last but not the least, we present a general method to synthesize a given target function stochastically using FSMs. We proposed three FSM topologies and discuss how to use these FSMs to synthesize the given target functions. The trade-offs among these different FSM topologies are introduced. Based on this synthesis method, more applications can be implemented stochastically to achieve lower hardware cost and better fault-tolerance.
机译：大多数数字系统都对数据进行位置表示，例如二进制编码。另一种选择是对随机比特流进行操作，在随机比特流中，信号值通过获得1相对于0的概率进行编码。这种表示比二进制编码的紧凑性要低得多。但是，可以使用非常简单的逻辑执行复杂的操作。此外，由于表示形式是统一的，并且所有比特的权重均等，因此它对软错误（即比特翻转）具有很高的容忍度。；复杂算法，例如人工神经网络（ANN），低密度奇偶校验（LPDC）可以使用随机编码来实现纠错编码和基于核密度估计（KDE）的图像分割，而硬件成本要低得多，而容错能力则要高得多。例如，基于KDE的图像分割的随机实现的硬件面积仅为相应确定性实现的1.2％，并且可以容忍30％以上的软错误。与传统的容错技术（例如三模块冗余（TMR））相比，复杂算法的随机实现通常消耗相同或更少的能量，并且具有更好的容错能力。例如，基于KDE的实现的TMR实现最多只能容忍10％的软错误，但消耗的能量与随机实现相同。另外，由于随机计算元件的简单构造，它使漫游变得容易得多，这对于这些复杂算法的超大规模集成电路（VLSI）确定性实现是一个大问题。建议用于随机比特流。先前的工作表明，组合逻辑可以有效地实现乘法和按比例加法运算，而有限状态机（FSM）可以有效地实现诸如幂运算和tanh等复杂功能。尽管已经对基于组合逻辑的随机计算元素进行了充分的研究，但它们对复杂的操作效率不高。基于FSM的随机计算元素对于复杂的操作非常有效。然而，先前的工作仅提出了三个基于FSM的随机计算元素，这限制了随机计算的应用。为了随机地实现更多的应用程序和功能，本论文着重于基于FSM的随机计算。我们首先分析了先前工作提出的基于FSM的随机计算元素，这些元素在实证上得到了验证。在本文中，我们对基于FSM的随机计算元素进行了严格的数学处理。这使我们对如何使用FSM随机构造任意函数有了直觉。然后，在现有随机计算元素的基础上，我们实现了五种数字图像处理算法作为案例研究。据我们所知，这是第一次随机执行这些数字图像处理算法。对于这五种算法，与相应的确定性实现相比，随机实现的硬件成本低得多，并且容错性更好。最后但并非最不重要的是，我们提出了一种使用FSM随机合成给定目标函数的通用方法。我们提出了三种FSM拓扑，并讨论了如何使用这些FSM来综合给定的目标函数。介绍了这些不同的FSM拓扑之间的权衡。基于这种综合方法，可以随机实现更多应用，以实现更低的硬件成本和更好的容错能力。

著录项

  • 作者

    Li, Peng.;

  • 作者单位

    University of Minnesota.;

  • 授予单位 University of Minnesota.;
  • 学科 Mathematics.;Engineering Computer.;Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 2013
  • 页码 127 p.
  • 总页数 127
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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