The following equiprobable messages are used to send data over a binary symmetric channel with crossover probability p: M1 = 0000 M2 = 0011 M3 = 0101 M4 = 0110 M5 = 1001 M6 = 1010 M7 = 1100 M8 = 1111 If the sequence Y=0000 is received (a) how much information is provided about M1 by the first digit received? (b) how much additional information about M1 is provided by the second, then the third, and finally the fourth received digit?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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The following equiprobable messages are used to send data over a binary symmetric channel with crossover probability p:
M1 = 0000 M2 = 0011 M3 = 0101 M4 = 0110
M5 = 1001 M6 = 1010 M7 = 1100 M8 = 1111
If the sequence Y=0000 is received
(a) how much information is provided about M1 by the first digit received?
(b) how much additional information about M1 is provided by the second, then the third, and finally the fourth received digit?

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