1) Consider a 128-bit binary message being transmitted over a noisy channel that
ID: 3044914 • Letter: 1
Question
1) Consider a 128-bit binary message being transmitted over a noisy channel that has a probability of error equal to 10^-9. If your system has the capability to correct for only one bit error within every code word (a code word is 8-bits). If you were told that the received message had 16 bit errors. What is the probability that the message will be received accurately (using the error correction process). Assume that bits are independent of each other.2) How many ways can you put 10 indistinguishable desks into 3 grad students offices (assuming each office can hold up to 10 desks)? 1) Consider a 128-bit binary message being transmitted over a noisy channel that has a probability of error equal to 10^-9. If your system has the capability to correct for only one bit error within every code word (a code word is 8-bits). If you were told that the received message had 16 bit errors. What is the probability that the message will be received accurately (using the error correction process). Assume that bits are independent of each other.
2) How many ways can you put 10 indistinguishable desks into 3 grad students offices (assuming each office can hold up to 10 desks)?
2) How many ways can you put 10 indistinguishable desks into 3 grad students offices (assuming each office can hold up to 10 desks)?
Explanation / Answer
(1)
Number of ways in which the 16 error bits can be distributed amongst 128 bit positions = 128C16*(16!)
Number of ways in which the 16 error bits can be distributed such that each 8-bit word has an error bit = 816
So,
Probability that the message will be received accurately = (816)/(128C16*(16!)) = 1.44*10-19
Hope this helps !
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