Stochastic unary computing provides low-area circuits. However, the required area consuming stochastic number generators (SNGs) in these circuits can diminish their overall gain in area, particularly if several SNGs are required. We propose area-efficient SNGs by sharing the permuted output of one linear feedback shift register (LFSR) among several SNGs. With no hardware overhead, the proposed architecture generates stochastic bit streams with minimum stochastic computing correlation (SCC). Compared to the circular shifting approach presented in prior work, our approach produces stochastic bit streams with 67% less average SCC when a 10-bit LFSR is shared between two SNGs. To generalize our approach, we propose an algorithm to find a set of $m$ permutations ( $n > m > 2$ ) with a minimum pairwise SCC, for an $n$ -bit LFSR. The search space for finding permutations with an exact minimum SCC grows rapidly when $n$ increases and it is intractable to perform a search algorithm using accurately calculated pairwise SCC values, for $n > 9$ . We propose a similarity function that can be used in the proposed search algorithm to quickly find a set of permutations with SCC values close to the minimum one. We evaluate our approach for several applications. The results show that, compared to prior work, it achieves lower mean-squared error (MSE) with the same (or even lower) area. Additionally, based on simulation results, we show that replacing the comparator component of an SNG circuit with a weighted binary generator can reduce SCC.

中文翻译：

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用于随机计算的低成本随机数生成器

随机一元计算提供低面积电路。然而，这些电路中所需的消耗随机数发生器 (SNG) 的面积会降低它们的总体面积增益，尤其是在需要多个 SNG 的情况下。我们通过在多个 SNG 之间共享一个线性反馈移位寄存器 (LFSR) 的置换输出来提出面积高效的 SNG。在没有硬件开销的情况下，所提出的架构生成具有最小随机计算相关性 (SCC) 的随机比特流。与先前工作中提出的循环移位方法相比，当两个 SNG 之间共享 10 位 LFSR 时，我们的方法产生的随机比特流的平均 SCC 减少了 67%。为了概括我们的方法，我们提出了一种算法来找到一组 百万美元 排列（ $n > m > 2$ ) 具有最小成对 SCC，对于 $n$ 位 LFSR。查找具有精确最小 SCC 的排列的搜索空间在以下情况下迅速增长 $n$ 增加并且难以使用准确计算的成对 SCC 值执行搜索算法，因为 $n > 9$ . 我们提出了一个相似度函数，可以在所提出的搜索算法中使用它来快速找到一组 SCC 值接近最小值的排列。我们针对多种应用评估了我们的方法。结果表明，与之前的工作相比，它在相同（甚至更低）的面积下实现了更低的均方误差 (MSE)。此外，基于仿真结果，我们表明用加权二进制发生器替换 SNG 电路的比较器组件可以降低 SCC。