Problem 3. Consider a file of size F bits transmitted over a line with bandwidth B bps. The file is broken into
N packets of size P (i.e., $F = NP$) bits each, and an error-correcting code of size C is appended to each packet.
The error-correcting code can detect and correct up to K bit flips. Let each bit be flipped independently with
probability p.
• What is the probability that a corrupted packet is accepted at the destination?
• What is the probability that the entire file is correctly received?
• Compute the above probabilities for F = 1 Mbyte, N = 1024, P = 1 KByte, C = 8 bits, K = 3, and
$p = 10^{-5}$.
