IEICE TRANSACTIONS on Fundamentals
Stochastic Number Generation with the Minimum Inputs
Summary :
For some applications, it has been known that stochastic computing (SC) has many potential advantages compared with conventional computation on binary radix encoding. Thus, there has been proposed many design methodologies to realize SCs. Recently, a general design method to realize SC operations by designing Boolean circuits (functions) has been proposed. As a central part of the method, we need to design a logic circuit such that its output becomes 1 with a certain desired probability with respect to random inputs. Also, to realize an SC arithmetic operation with a constant value, in some situations we need to prepare a random bit-stream that becomes 1 with a desired probability from a set of predetermined physical random sources. We call such a bit-stream as a stochastic number (SN). We can utilize the above-mentioned previous method to prepare stochastic numbers by designing Boolean circuits. The method assumes all the random sources become 1 with the same probability 1/2. In this paper, we investigate a different framework where we can prepare different probabilities of each stochastic number in the physical random sources. Then, this paper presents the necessary and sufficient condition of given random inputs in order to produce a stochastic number with a given specified precision. Based on the condition, we can propose a method to generate a stochastic number by using the minimum number of random inputs. Indeed our method uses much less number of inputs than the previous method, and our preliminary experiment shows that the generated circuits by our method also tend to be smaller than the ones by the previous method.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.8 pp.1661-1671
- Publication Date
- 2017/08/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E100.A.1661
- Type of Manuscript
- PAPER
- Category
- VLSI Design Technology and CAD
Authors
Ritsuko MUGURUMA
Ritsumeikan University
Shigeru YAMASHITA
Ritsumeikan University
Keyword
Latest Issue
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Ritsuko MUGURUMA, Shigeru YAMASHITA, "Stochastic Number Generation with the Minimum Inputs" in IEICE TRANSACTIONS on Fundamentals,
vol. E100-A, no. 8, pp. 1661-1671, August 2017, doi: 10.1587/transfun.E100.A.1661.
Abstract: For some applications, it has been known that stochastic computing (SC) has many potential advantages compared with conventional computation on binary radix encoding. Thus, there has been proposed many design methodologies to realize SCs. Recently, a general design method to realize SC operations by designing Boolean circuits (functions) has been proposed. As a central part of the method, we need to design a logic circuit such that its output becomes 1 with a certain desired probability with respect to random inputs. Also, to realize an SC arithmetic operation with a constant value, in some situations we need to prepare a random bit-stream that becomes 1 with a desired probability from a set of predetermined physical random sources. We call such a bit-stream as a stochastic number (SN). We can utilize the above-mentioned previous method to prepare stochastic numbers by designing Boolean circuits. The method assumes all the random sources become 1 with the same probability 1/2. In this paper, we investigate a different framework where we can prepare different probabilities of each stochastic number in the physical random sources. Then, this paper presents the necessary and sufficient condition of given random inputs in order to produce a stochastic number with a given specified precision. Based on the condition, we can propose a method to generate a stochastic number by using the minimum number of random inputs. Indeed our method uses much less number of inputs than the previous method, and our preliminary experiment shows that the generated circuits by our method also tend to be smaller than the ones by the previous method.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.1661/_p
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@ARTICLE{e100-a_8_1661,
author={Ritsuko MUGURUMA, Shigeru YAMASHITA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Stochastic Number Generation with the Minimum Inputs},
year={2017},
volume={E100-A},
number={8},
pages={1661-1671},
abstract={For some applications, it has been known that stochastic computing (SC) has many potential advantages compared with conventional computation on binary radix encoding. Thus, there has been proposed many design methodologies to realize SCs. Recently, a general design method to realize SC operations by designing Boolean circuits (functions) has been proposed. As a central part of the method, we need to design a logic circuit such that its output becomes 1 with a certain desired probability with respect to random inputs. Also, to realize an SC arithmetic operation with a constant value, in some situations we need to prepare a random bit-stream that becomes 1 with a desired probability from a set of predetermined physical random sources. We call such a bit-stream as a stochastic number (SN). We can utilize the above-mentioned previous method to prepare stochastic numbers by designing Boolean circuits. The method assumes all the random sources become 1 with the same probability 1/2. In this paper, we investigate a different framework where we can prepare different probabilities of each stochastic number in the physical random sources. Then, this paper presents the necessary and sufficient condition of given random inputs in order to produce a stochastic number with a given specified precision. Based on the condition, we can propose a method to generate a stochastic number by using the minimum number of random inputs. Indeed our method uses much less number of inputs than the previous method, and our preliminary experiment shows that the generated circuits by our method also tend to be smaller than the ones by the previous method.},
keywords={},
doi={10.1587/transfun.E100.A.1661},
ISSN={1745-1337},
month={August},}
Copy
TY - JOUR
TI - Stochastic Number Generation with the Minimum Inputs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1661
EP - 1671
AU - Ritsuko MUGURUMA
AU - Shigeru YAMASHITA
PY - 2017
DO - 10.1587/transfun.E100.A.1661
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2017
AB - For some applications, it has been known that stochastic computing (SC) has many potential advantages compared with conventional computation on binary radix encoding. Thus, there has been proposed many design methodologies to realize SCs. Recently, a general design method to realize SC operations by designing Boolean circuits (functions) has been proposed. As a central part of the method, we need to design a logic circuit such that its output becomes 1 with a certain desired probability with respect to random inputs. Also, to realize an SC arithmetic operation with a constant value, in some situations we need to prepare a random bit-stream that becomes 1 with a desired probability from a set of predetermined physical random sources. We call such a bit-stream as a stochastic number (SN). We can utilize the above-mentioned previous method to prepare stochastic numbers by designing Boolean circuits. The method assumes all the random sources become 1 with the same probability 1/2. In this paper, we investigate a different framework where we can prepare different probabilities of each stochastic number in the physical random sources. Then, this paper presents the necessary and sufficient condition of given random inputs in order to produce a stochastic number with a given specified precision. Based on the condition, we can propose a method to generate a stochastic number by using the minimum number of random inputs. Indeed our method uses much less number of inputs than the previous method, and our preliminary experiment shows that the generated circuits by our method also tend to be smaller than the ones by the previous method.
ER -
English
