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Consider the following two-purty communication problem. Alice and Bob are spatially separated, and their only means of coommunication is through a noisy communication channel. Alice wants to send a randoen bit b to Bob using their sharesd channel. At the end of the protocol, Bob has a bit b'. Our goal is that the probability that 6=b is a high as posible. We consider three different protocols for achieving this task, protocols PA, Pn, and Pe. 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 e = b. 21B. Alice sets e b. 20. Alice sets e =1-6. 3. Alice sends the bit e through the channel. 4. The channel is noisy, and it flips the bit with probability (0.1 if e= 0, and it flips the bit with probability 0.3 if e= 1. Let e denote the output of the channel. 5. Bob reccives the bit e. 6A. Bob sets . 6B. Bob ignores the bit e and he sets -1, regardless of whether d =0 or d=1. 6C. Bob sets =1-e. 7. Bob declares that "I am guesing that Alice sent the bit ." 1. For ench of three protocols, compute the probability Pr = 6. Compute the probability as an irreducible fraction (that is, answer eg. instead of #). Show your caleulations and succinetly explain your work. 2. At the top of your answer, include a table with the three probabilities. Give your probabilities with three significant digits, us in the example below. PA Pe 0.123 0.987

Consider the following two-purty communication problem. Alice and Bob are spatially separated, and their only means of coommunication is through a noisy communication channel. Alice wants to send a randoen bit b to Bob using their sharesd channel. At the end of the protocol, Bob has a bit b'. Our goal is that the probability that 6=b is a high as posible. We consider three different protocols for achieving this task, protocols PA, Pn, and Pe. 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 e = b. 21B. Alice sets e b. 20. Alice sets e =1-6. 3. Alice sends the bit e through the channel. 4. The channel is noisy, and it flips the bit with probability (0.1 if e= 0, and it flips the bit with probability 0.3 if e= 1. Let e denote the output of the channel. 5. Bob reccives the bit e. 6A. Bob sets . 6B. Bob ignores the bit e and he sets -1, regardless of whether d =0 or d=1. 6C. Bob sets =1-e. 7. Bob declares that "I am guesing that Alice sent the bit ." 1. For ench of three protocols, compute the probability Pr = 6. Compute the probability as an irreducible fraction (that is, answer eg. instead of #). Show your caleulations and succinetly explain your work. 2. At the top of your answer, include a table with the three probabilities. Give your probabilities with three significant digits, us in the example below. PA Pe 0.123 0.987

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, tw-purty communication problem. Alice and Bob are spatially separated, and their only means of coommunication is through a noisy communication channel. Alice wants to send a randoen bit b to Bob using their sharesi channel. At the end of the protocol, Bob has a bit b'. Our goal is that the probability that ' =b is as high an posible. We consider three different protocols for achieving this task, protocols PA, Pn, and Pe. 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 scts e. 2B. Alice sets e=b. 20. Alice sets e=1-6. 3. Alice sends the bit e through the channel. 4. The channel is noisy, and it flips the bit with probability 0.1 if e= 0, and it flips the bit with probability 0.3 if e= 1. Let e denote the output of the channel. 5. Bob recciveN the bit e. 6A. Bob sets -d. 6B. Bob ignores the bit e and he sets = 1, regurdless of whether d = 0 or e=1. 6C. Bob sets =1-e. 7. Bob declares that "I am guessing that Alice sent the bit 8." 1. For cach of threxe protocols, compate the probability Pr = 6). Compute the probability as an irreducible fraction (that is, answer e.g. instead of ). Show your caleulations and succinetly explain your work. 2. At the top of your answer, include a table with the three probabilitics. Give your probabilities with three significant digits, as in the example below. PA Pe 0.123 0.987
Transcribed Image Text:Consider the following, tw-purty communication problem. Alice and Bob are spatially separated, and their only means of coommunication is through a noisy communication channel. Alice wants to send a randoen bit b to Bob using their sharesi channel. At the end of the protocol, Bob has a bit b'. Our goal is that the probability that ' =b is as high an posible. We consider three different protocols for achieving this task, protocols PA, Pn, and Pe. 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 scts e. 2B. Alice sets e=b. 20. Alice sets e=1-6. 3. Alice sends the bit e through the channel. 4. The channel is noisy, and it flips the bit with probability 0.1 if e= 0, and it flips the bit with probability 0.3 if e= 1. Let e denote the output of the channel. 5. Bob recciveN the bit e. 6A. Bob sets -d. 6B. Bob ignores the bit e and he sets = 1, regurdless of whether d = 0 or e=1. 6C. Bob sets =1-e. 7. Bob declares that "I am guessing that Alice sent the bit 8." 1. For cach of threxe protocols, compate the probability Pr = 6). Compute the probability as an irreducible fraction (that is, answer e.g. instead of ). Show your caleulations and succinetly explain your work. 2. At the top of your answer, include a table with the three probabilitics. Give your probabilities with three significant digits, as in the example below. PA Pe 0.123 0.987
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