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研究生:蔡尚宏
研究生(外文):CAI,SHANG-HONG
論文名稱:隨機計算的改良應用與硬體實現
論文名稱(外文):Investigation and Hardware Implementation of Stochastic Computing
指導教授:朱紹儀
指導教授(外文):CHU,SHAO-I
口試委員:朱紹儀王鴻猷黃有榕林偉誠
口試委員(外文):CHU,SHAO-IWANG,HUNG-YUHUANG,YU-JUNGLIN,WEI-CHENG
口試日期:2017-07-04
學位類別:碩士
校院名稱:國立高雄應用科技大學
系所名稱:電子工程系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:63
中文關鍵詞:隨機計算完整隨機計算雙曲正切函數指數函數S型函數倒傳遞類神經網路里德-穆勒碼
外文關鍵詞:Stochastic ComputingIntegral Stochastic Computinghyper tangent functionexponential functionsigmoid functionBack Propagation Neural NetworkReed-Muller code
相關次數:
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  • 下載下載:2
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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 stochastic
computing (SC) and its related applications. The advantage of the stochastic
computing lies in the realization of the complicated functions with the simple
logic units. However, the input value of the stochastic computing unit is limited
in 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 expense
of the hardware cost.
The conventional stochastic computing with finite state machine, the integral
stochastic computing with finite state machine and series expansion are
investigated and act as the comparison bases for the implementation of the hyperbolic
tangent and exponential functions. For the hyperbolic tangent function,
the developed architecture by using the symmetric property outperforms
the conventional stochastic computing by 50% in terms of error improvement.
For the exponential function, the proposed scheme is improved by 32% over
the series expansion technique but with more hardware cost.
Finally, the presented new stochastic computing method is applied to the
hardware implementation soft decision decoder of Reed-Muller codes and the
back propagation neural network. The hardware cost of the decoder with stochastic
computing is significantly reduced as compared with the conventional decoder.
中文摘要 i
Abstract ii
致謝 iii
目錄 vi
圖目錄 viii
1 緒論 1
1.1 研究背景 1
1.2 研究動機與目的 2
1.3 研究架構 2
1.4 研究貢獻 2
2 相關文獻 3
2.1 隨機計算介紹(Stochastic Computing) 3
2.1.1 隨機位元流產生與轉換 3
2.1.2 隨機計算簡易邏輯運算 5
2.1.3 隨機計算結合有限狀態機 7
2.2 完整隨機計算介紹(Integral Stochastic Computing) 8
3 隨機計算元件設計與改良 9
3.1 雙曲正切函數tanh(x) 9
3.1.1 隨機計算結合有限狀態機(SCFSM) 9
SCFSM近似推導 9
SCFSM虛擬碼 12
3.1.2 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 14
3.1.3 序列展開法(seq1; 2) 15
序列展開法近似推導 15
3.1.4 以隨機計算改良拼接法(STITCH(SC)) 17
3.1.5 以完整隨機計算改良拼接法(STITCH(ISC)) 19
3.2 指數函數exponential(x) 19
3.2.1 序列展開法(seq) 19
3.2.2 隨機計算結合有限狀態機(SCFSM) 20
SCFSM虛擬碼 22
3.2.3 完整隨機計算結合有限狀態機(ISCFSM) 22
ISCFSM近似推導 23
3.2.4 拼接結合隨機計算與JK正反器(SFJ) 24
3.3 S型函數sigmoid(x) 25
4 軟、硬體模擬結果與討論 26
4.1 軟體模擬誤差比較 26
4.1.1 雙曲正切函數tanh(x) 26
4.1.2 指數函數exponential(x) 31
4.1.3 S型函數sigmoid(x) 36
4.2 硬體合成比較 39
4.2.1 雙曲正切函數tanh(x) 39
4.2.2 指數函數exponential(x) 39
4.2.3 S型函數sigmoid(x) 40
4.3 結果討論 40
5 應用實作 41
5.1 里德-穆勒碼(Reed-Muller code)解碼器設計 41
5.2 倒傳遞類神經網路硬體實現 46
6 結論 50
6.1 研究結論 50
6.2 未來展望 51
參考文獻54
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