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1. Alice picks a bit b at random. She picks b = 0 with probability p = 0.2, and she picks b = 1 with complementary probability p= 0.8. 2A. Alice sets c = b. 2B. Alice sets c= b. 2C. Alice sets c =1 – b. 3. Alice sends the bit e through the channel. 4. The channel is noisy, and it flips the bit with probability 0.1 if c = 0, and it flips the bit with probability 0.3 if c= 1. Let d' denote the output of the channel. 5. Bob receives the bit c'. SA. Bob sets b' = d'. SB. Bob ignores the bit e' and he sets b' = 1, regardless of whether d' = 0 or c' = 1. SC. Bob sets b' = 1 – '. %3D

1. Alice picks a bit b at random. She picks b = 0 with probability p = 0.2, and she picks b = 1 with complementary probability p= 0.8. 2A. Alice sets c = b. 2B. Alice sets c= b. 2C. Alice sets c =1 – b. 3. Alice sends the bit e through the channel. 4. The channel is noisy, and it flips the bit with probability 0.1 if c = 0, and it flips the bit with probability 0.3 if c= 1. Let d' denote the output of the channel. 5. Bob receives the bit c'. SA. Bob sets b' = d'. SB. Bob ignores the bit e' and he sets b' = 1, regardless of whether d' = 0 or c' = 1. SC. Bob sets b' = 1 – '. %3D

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Consider the following two-party communication problem. Alice and Bob are spatially separated, and their only mcans of communication is through a noisy communication channel. Alice wants to send a random bit b to Bob using their shared channel. At the end of the protocol, Bob has a bit b’. Our goal is that the probability that b' = b is as high as possible. We consider three different protocols for achieving this task, protocols PA, PB, and Pc. The three protocols are the same, except for steps 2 and 6. 1. Alice picks a bit b at random. She picks b = 0 with probability p = 0.2, and she picks b = 1 with complementary probability p= 0.8. 2A. Alice sets c= b. 2B. Alice sets c= b. 2C. Alice sets c= 1 – b. 3. Alice sends the bit c through the channel. 4. The channel is noisy, and it flips the bit with probability 0.1 if c= 0, and it flips the bit with probability 0.3 if c= 1. Let c' denote the output of the channel. 5. Bob receives the bit c'. 6A. Bob sets b' = c'. 6B. Bob ignores the bit c' and he sets b' = 1, regardless of whcther d' = 0 or c = 1. 6C. Bob sets b' = 1 – c'. 7. Bob declares that "I am guessing that Alice sent the bit b'." 1. For cach of three protocols, compute the probability Pr[b' = b]. Compute the probability as an irreducible fraction (that is, answer e.g. instead of ). Show your calculations and succinctly explain your work. 2. At the top of your answer, include a table with the three probabilities. Give your probabilities with three significant digits, as in the cexample below. РА 0.123 PB Pc 0.987
Transcribed Image Text:Consider the following two-party communication problem. Alice and Bob are spatially separated, and their only mcans of communication is through a noisy communication channel. Alice wants to send a random bit b to Bob using their shared channel. At the end of the protocol, Bob has a bit b’. Our goal is that the probability that b' = b is as high as possible. We consider three different protocols for achieving this task, protocols PA, PB, and Pc. The three protocols are the same, except for steps 2 and 6. 1. Alice picks a bit b at random. She picks b = 0 with probability p = 0.2, and she picks b = 1 with complementary probability p= 0.8. 2A. Alice sets c= b. 2B. Alice sets c= b. 2C. Alice sets c= 1 – b. 3. Alice sends the bit c through the channel. 4. The channel is noisy, and it flips the bit with probability 0.1 if c= 0, and it flips the bit with probability 0.3 if c= 1. Let c' denote the output of the channel. 5. Bob receives the bit c'. 6A. Bob sets b' = c'. 6B. Bob ignores the bit c' and he sets b' = 1, regardless of whcther d' = 0 or c = 1. 6C. Bob sets b' = 1 – c'. 7. Bob declares that "I am guessing that Alice sent the bit b'." 1. For cach of three protocols, compute the probability Pr[b' = b]. Compute the probability as an irreducible fraction (that is, answer e.g. instead of ). Show your calculations and succinctly explain your work. 2. At the top of your answer, include a table with the three probabilities. Give your probabilities with three significant digits, as in the cexample below. РА 0.123 PB Pc 0.987
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