With 1 parity bit, we can detect all 1-bit errors. Show that at least one generalization fails, as follows:
(a) Show that if messages m are 8 bits long, then there is no error detection code e = e(m) of size 2 bits that can detect all 2-bit errors.
(b) Find an N (not necessarily minimal) such that no 32-bit error detection code applied to N-bit blocks can detect all errors altering up to 8 bits.

 Consider an ARQ algorithm running over a 40-km point-to-point fiber link.
(a) Compute the one-way propagation delay for this link, assuming that the speed of light is 2 × 108 m/s in the fiber.
(b) Suggest a suitable timeout value for the ARQ algorithm to use.
(c) Why might it still be possible for the ARQ algorithm to time out and retransmit a frame, given this timeout value?

 Suppose you are designing a sliding window protocol for a 1-Mbps point-to-point link to the moon, which has a one-way latency of 1.25 seconds. Assuming that each frame carries 1 KB of
data, what is the minimum number of bits you need for the sequence number?

 Suppose you are designing a sliding window protocol for a 1-Mbps point-to-point link to the stationary satellite revolving around the Earth at an altitude of 3 × 104 km. Assuming that each frame carries 1 KB of data, what is the minimum number of bits you need for the sequence number in the following cases? Assume the speed of light is 3 × 108 m/s.
(a) RWS=1
(b) RWS=SWS
Draw a timeline diagram for the sliding window algorithm with SWS = RWS = 3 frames, for the following two situations. Use a timeout interval of about 2 × RTT.
(a) Frame 4 is lost.
(b) Frames 4 to 6 are lost.

Suppose that we run the sliding window algorithm with SWS = 5 and RWS = 3, and no out-of-order arrivals.
(a) Find the smallest value for MaxSeqNum. You may assume that it suffices to find the smallest MaxSeqNum such that if DATA[MaxSeqNum] is in the receive window, then DATA[0]
can no longer arrive.
(b) Give an example showing that MaxSeqNum − 1 is not sufficient.
(c) State a general rule for the minimum MaxSeqNum in terms of SWS and RWS.