# 臺灣博碩士論文加值系統

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 本研究主要探討簡稱隨機計算實現、應用與誤差改良，在隨機計算計算中，利用簡易邏輯閘來實現複雜的運算是他的優點，但隨機計算只能實現機率數值介於0到1之間，因此發展出完整隨機計算形式，在完整隨機計算的計算中，實現機率值可以超過1，使完整隨機計算可以計算的範圍更廣闊，且可應用的領域也更寬廣。利用雙曲正切函數、S型函數的輸出具有對稱的特性，我們提出改善誤差與硬體面積的拼接法搭配隨機計算結合有限狀態機。在誤差方面，拼接結合隨機計算比隨機計算結合有限狀態機誤差降低了50%以上。除此之外，實現指數函數方面，我們提出隨機計算結合有限狀態機與JK正反器，在誤差方面我們降低了32%左右。本論文將實現雙曲正切函數、S型函數的四種方法:隨機計算結合有限狀態機、完整隨機計算結合有限狀態機、序列展開法、拼接結合隨機計算，與實現指數函數的四種方法序列展開法、隨機計算結合有限狀態機、完整隨機計算結合有限狀態機與SFJ，作數學推導並用軟體實現比較誤差，與硬體實現面積與時間的比較，且在硬體應用上實現倒傳遞類神經網路以及里德-穆勒碼的解碼器設計誤差比較。
 This thesis mainly focuses on the hardware improvements of stochasticcomputing (SC) and its related applications. The advantage of the stochasticcomputing lies in the realization of the complicated functions with the simplelogic units. However, the input value of the stochastic computing unit is limitedin the range between 0 and 1. The idea of the integral stochastic computing(ISC) is thus proposed with the input value which is more than 1 at the expenseof the hardware cost.The conventional stochastic computing with finite state machine, the integralstochastic computing with finite state machine and series expansion areinvestigated and act as the comparison bases for the implementation of the hyperbolictangent and exponential functions. For the hyperbolic tangent function,the developed architecture by using the symmetric property outperformsthe conventional stochastic computing by 50% in terms of error improvement.For the exponential function, the proposed scheme is improved by 32% overthe series expansion technique but with more hardware cost.Finally, the presented new stochastic computing method is applied to thehardware implementation soft decision decoder of Reed-Muller codes and theback propagation neural network. The hardware cost of the decoder with stochasticcomputing is significantly reduced as compared with the conventional decoder.
 中文摘要 iAbstract ii致謝 iii目錄 vi圖目錄 viii1 緒論 11.1 研究背景 11.2 研究動機與目的 21.3 研究架構 21.4 研究貢獻 22 相關文獻 32.1 隨機計算介紹(Stochastic Computing) 32.1.1 隨機位元流產生與轉換 32.1.2 隨機計算簡易邏輯運算 52.1.3 隨機計算結合有限狀態機 72.2 完整隨機計算介紹(Integral Stochastic Computing) 83 隨機計算元件設計與改良 93.1 雙曲正切函數tanh(x) 93.1.1 隨機計算結合有限狀態機(SCFSM) 9 SCFSM近似推導 9 SCFSM虛擬碼 123.1.2 完整隨機計算結合有限狀態機(ISCFSM) 13 ISCFSM近似推導 13 ISCFSM虛擬碼 143.1.3 序列展開法(seq1; 2) 15 序列展開法近似推導 153.1.4 以隨機計算改良拼接法(STITCH(SC)) 173.1.5 以完整隨機計算改良拼接法(STITCH(ISC)) 193.2 指數函數exponential(x) 193.2.1 序列展開法(seq) 193.2.2 隨機計算結合有限狀態機(SCFSM) 20 SCFSM虛擬碼 223.2.3 完整隨機計算結合有限狀態機(ISCFSM) 22 ISCFSM近似推導 233.2.4 拼接結合隨機計算與JK正反器(SFJ) 243.3 S型函數sigmoid(x) 254 軟、硬體模擬結果與討論 264.1 軟體模擬誤差比較 264.1.1 雙曲正切函數tanh(x) 264.1.2 指數函數exponential(x) 314.1.3 S型函數sigmoid(x) 364.2 硬體合成比較 394.2.1 雙曲正切函數tanh(x) 394.2.2 指數函數exponential(x) 394.2.3 S型函數sigmoid(x) 404.3 結果討論 405 應用實作 415.1 里德-穆勒碼(Reed-Muller code)解碼器設計 415.2 倒傳遞類神經網路硬體實現 466 結論 506.1 研究結論 506.2 未來展望 51參考文獻54
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