Homework 1 (Due Oct. 13)

1. Write a program to simulate a slotted ALOHA system with N users and transmission probability p per user. Assume each user always has a frame to send. (Use your favorite programming platform)

a) Plot the achievable throughput as a function of N and p.

b) Then find a distributed adaptive policy on your own (i.e., adaptively change p; use your own judgements and creativity) to increase the throughput relative to the case when the transmission probability p is fixed. Compare the results and also with the analytical result given in the viewgraphs.

2. Do the exercise for the viewgraph numbered week1/124. Show which messages are exchanged until the tree is built. Show all the details. Then assume port 3a fails. Write what happens next in terms of the configuration messages and the newly built tree.

3. A bit stream 10011101 is transmitted using the CRC method. The generator is 1001. Show the actual bit string transmitted. Suppose the third bit from the left is inverted during transmission. Show that this error is detected at the receiver's end. Repeat this exercise when the leftmost two and three bits are inverted.