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I came across and studies this paper with the title RAPOR privacy enchanced statistics paper. As it mentions the Instantaneous randomized response is calculated from the client as:

Instantaneous randomized response is calculated

Does that mean that it i-th bit will be 1 if the the B'i=1 with propability of q? And in the end in case of implementation how I will take account the propability q?

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    You would get a better answer on implementation part at either programming or Math stack exchange. – Limit Apr 10 '18 at 13:16
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    As for your first question, it means that if Bi' = 1, there is a probability q such that Si = 1 – Limit Apr 10 '18 at 13:16

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