EE 333, Communication Networks Mid-Term Exam (2014-15S)

Maximum Marks = 30 Time = 2 hours

1. Your friend has designed a new ARQ technique which he/she wants to use to transmit data from A to B. In this scheme, A transmits data in the form of blocks where each block has N packets. After A sends all the N packets (in N consecutive slots), B tells A the sequence numbers of ALL the packets that it did not receive correctly. A then repeats only those packets. B now tells A which of these packets were in error and A then repeats only those packets. This process continues until B tells A that all packets of the block have been received correctly. Once A hears this, it can go ahead and send the next block. For the following, assume that the packet length is T (fixed), propagation delay is d in each of the links A-B and B-A and that the ACK length is small enough to be neglected. Assume also that α is the probability that a packet is correctly received at B and that the ACKs from B to A are always correctly received. We also assume that A always has enough packets to send to B, i.e. it never runs out of packets to send (a) For N=1, what is the average efficiency with which the A-B link can be used? [2] (b) For N=2, what is the average efficiency with which the A-B link can be used? [4] (c) For N=3, what is the average efficiency with which the A-B link can be used if we assume d=0 (only for part (c))? [4] For notational convenience, use b=d/T as the normalized propagation delay (in one direction) 2. (a) Using the CRC approach, a code word of n bits is generated using a generator polynomial of the type g(x)=(1+x)P(x) where P(x) is chosen to be a Primitive Polynomial which exactly divides (xn+1) but not any (xm+1) for m<n. [5] For this code, show that Cyclically Right Shifting a code word by one bit will generate another valid code word. [Note: Please answer briefly and clearly. Garbled, confused and confusing answers will not be considered.]

(b) The CRC-8 generator polynomial 8 2( ) 1g x x x x is used to encode a data word. The resultant

code word is 17 14 12 11 10 9 7 5 4 2( ) 1C x x x x x x x x x x x x

The receiver receives 17 14 12 11 8 7 5( )C x x x x x x x x x

Assume that the sender monitors its own transmission and can also see what the receiver will receive.

What can the sender say about whether or not the received code word ( )C x will be accepted by the

receiver as a code word without errors? [5] Show all your steps – no marks for unsupported guess-work! 3. Consider a Slotted ALOHA system with three users where the transmission probability in a slot is q for both “Thinking” and “Blocked” users. The system state is defined as the number of backlogged users

with jP =P{j backlogged users in the system}

(a) Draw the State Transition Diagram for the system clearly labelling the state transition probabilities in the diagram. (You need not show the j→j type of transitions.) [4] (b) Derive expressions for P1 and P2 in terms of q and P0. [3] (c) What is the maximum throughput of this system and the value of q at which this is achieved? [3]