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QUESTION 3 (a) Consider the code C={010,101} as the input to an extended binary symmetric channel with bit-error probability 0.1. (i) Write out the rows of the channel matrix I3 which corresponds to the two input codewords. (ii) What decision rule should the receiver use if it does not know the input probability distribution [po10 1-po1o]? What is the probability of a mistake with this rule, if 010 is sent? What about 101? (iii) Suppose the probability distribution of the two codewords is [0.02, 0.98]. Alice and Bob each design a decision rule for their receiver. Bob wants to use the decision rule from question (i). Alice, however, thinks she has a decision rule that can reduce the mistake probability even lower. What is Alice's decision rule, and does it work? What is the resulting mistake probability? (b) A number of boxes in a warehouse are labelled using unique IDs, which are converted into 16 bit binary words. What is the maximum amount of unique IDs we can have, if we consider a 1-error correcting code? What about a 2-error correcting code?

QUESTION 3 (a) Consider the code C={010,101} as the input to an extended binary symmetric channel with bit-error probability 0.1. (i) Write out the rows of the channel matrix I3 which corresponds to the two input codewords. (ii) What decision rule should the receiver use if it does not know the input probability distribution [po10 1-po1o]? What is the probability of a mistake with this rule, if 010 is sent? What about 101? (iii) Suppose the probability distribution of the two codewords is [0.02, 0.98]. Alice and Bob each design a decision rule for their receiver. Bob wants to use the decision rule from question (i). Alice, however, thinks she has a decision rule that can reduce the mistake probability even lower. What is Alice's decision rule, and does it work? What is the resulting mistake probability? (b) A number of boxes in a warehouse are labelled using unique IDs, which are converted into 16 bit binary words. What is the maximum amount of unique IDs we can have, if we consider a 1-error correcting code? What about a 2-error correcting code?

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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QUESTION 3 (a) Consider the code C={010,101} as the input to an extended binary symmetric channel with bit-error probability 0.1. Write out the rows of the channel matrix I³which corresponds to the two input codewords. (ii) What decision rule should the receiver use if it does not know the input probability distribution [po10 1-po1o]? What is the probability of a mistake with this rule, if 010 is sent? What about 101? (iii) Suppose the probability distribution of the two codewords is [0.02, 0.98]. Alice and Bob each design a decision rule for their receiver. Bob wants to use the decision rule from question (i). Alice, however, thinks she has a decision rule that can reduce the mistake probability even lower. What is Alice's decision rule, and does it work? What is the resulting mistake probability? (b) A number of boxes in a warehouse are labelled using unique IDs, which are converted into 16 bit binary words. What is the maximum amount of unique IDs we can have, if we consider a 1-error correcting code? What about a 2-error correcting code?
Transcribed Image Text:QUESTION 3 (a) Consider the code C={010,101} as the input to an extended binary symmetric channel with bit-error probability 0.1. Write out the rows of the channel matrix I³which corresponds to the two input codewords. (ii) What decision rule should the receiver use if it does not know the input probability distribution [po10 1-po1o]? What is the probability of a mistake with this rule, if 010 is sent? What about 101? (iii) Suppose the probability distribution of the two codewords is [0.02, 0.98]. Alice and Bob each design a decision rule for their receiver. Bob wants to use the decision rule from question (i). Alice, however, thinks she has a decision rule that can reduce the mistake probability even lower. What is Alice's decision rule, and does it work? What is the resulting mistake probability? (b) A number of boxes in a warehouse are labelled using unique IDs, which are converted into 16 bit binary words. What is the maximum amount of unique IDs we can have, if we consider a 1-error correcting code? What about a 2-error correcting code?
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