ECS 252 Local & Metropolitan Area Networks Assigned: Jan. 26, 1998 Winter 98 Assignment 1 Due: Feb. 3, 1998 (In class) Note: + If you make any assumptions, please write them down clearly. + Do not assume that the person grading your work will correctly "guess" your assumptions. + When multiple solutions to a problem exist, the best solution will fetch the maximum credit. 1. Consider the transmission of digital data (e.g., that from your home computer) through an analog channel (e.g., a telephone line). a) Outline *three* strategies that you can employ to have the analog channel carry your digital data. b) If your digital data is 0 1 1 0 0 0 1 1 1 0 show the transmitted signal for all three cases (using a method that codes one bit per signal, and that is non-differential). c) For all three cases, show the corresponding *differentially*-coded transmitted signal. d) For all three cases, show the corresponding transmitted signal when a *multi-level* coding method is used with 2-bit words. 2. a) Consider an asynchronous communication system with the following parameters: transmitter clock speed f(T), receiver clock speed f(R), X bits per character, one parity bit, and one stop bit. It is required that all bits be sampled in the *middle one-half* of their corresponding signaling interval (i.e., within 25% on either side of their center position). Determine the maximum value of X (in terms of f(T) and f(R)) so that a *framing error* will not occur. b) For the case f(T) = 1 Mbps and f(R) = 971 kbps, determine the maximum value of X. c) For the case f(T) = 1 Mbps and f(R) = 1.07 Mbps, determine the maximum value of X. 3. Consider the CRC error detection mechanism in which the constant P (for CRC generation) is 1 0 1 0 1. The systematic representation (discussed in class, see notes) is employed. The *transmitted* bits (including both message and FCS bits) are 1 0 0 0 1 0 0 0 1. a) What are the message bits? What is the FCS? b) How many different transmitted bit patterns (codes) are possible? c) Give an example of an invalid transmitted code. Briefly explain why this code is invalid. d) Due to noise on the channel, some of the bits can get reversed. If the received bits are 1 1 0 0 1 0 0 1 1, how would the receiver interpret these bits (such as error detected or not detected? if error not detected, what is the transmitted message? if error detected, what is the remainder computed at the receiver?). e) If the probability of a bit error is 0.00001, and all errors are independent, what is the probability of receiving the pattern in part d) when the transmitted code is as given at the beginning of the problem? 4. To transmit packets with virtual-circuit transport, we first set up a virtual-circuit and then transmit the packets. The network is lightly loaded, and our packets do not face any queueing delay. The virtual-circuit set up time is 400 ms. The packets travel over a path that goes through ten nodes, and the links transmit at 56 kbps. Each packet has 400 bits of data, a header of 5 bytes (to indicate the virtual-circuit number and the packet's sequence number), and a trailer of 2 bytes (for error detection). When we use datagram transport, no virtual-circuit is set up, but each packet needs a header of 10 bytes instead of 5 (to indicate the full destination address and source address, in addition to the packet's sequence number). These packets also have the 2-byte trailer. Assume that datagrams also happen to follow the same path through the ten nodes. (a) How long does it take to transmit N packets under each of the two mechanisms? (b) For what values of N is it faster to use virtual-circuit transport? 5. Text (Hammond), pp. 78, Prob. 5. 6. Text (Hammond), pp. 79, Prob. 8. 7. Text (Hammond), pp. 80, Prob. 12.