698 Photonic Packet Switching time domain or in the frequency domain. The codes are carefully designed so that many transmitters can transmit simultaneously without interfering with one another, and the receiver can pick out a desired transmitter's signal from the others by suitably despreading the received signal. OCDMA networks were a popular research topic in the late 1980s and early 1990s, but they suffer from even more problems than PPS networks employing high-speed TDM. See [Sal89, SB89, PSF86, FV88] for a sampling of papers on this topic, and see [Gre93] for a good overview. Problems 12.1 In the packet multiplexing illustrated in Figure 12.7, show that the delay encoun- tered by pulse i, i = 1, 2, . . . , l, on passing through the k compression stages is (2 k - i)(T - ). Using the fact that the pulses are separated by time T at the input, now show that pulse i occurs at the output at time (2 k - 1)(T - ) + (i - 1) . Thus the pulses are separated by a time interval of at the output. Show that a compressed data packet of length l bits, obtained by the packet multi- plexing technique illustrated in Figure 12.7, can be decompressed, in principle, by passing it through a series of k = log l expansion stages, where the j th expansion stage is as shown in Figure 12.29. What should be the switching time of the on-off switches used in this scheme? Consider the tunable delay shown in Figure 12.14. Assume that a delay of xT /2 k-1 is to be realized, where x is a k-bit integer. Consider the binary representation of x, and find an expression for the control inputs c 1 , . . . , c k . Assume that if c i = 1, switch i is set in the bar state, and if c i = 0, switch i is set in the cross state. Consider the fiber loop mirror shown in Figure 12.9, and show that the nonlinear element should introduce a phase shift of between the clockwise and counterclock- wise signals in order for all the energy entering the directional coupler from arm A to be transferred to arm B. We have seen that many photonic packet-switching proposals use a lower-rate header compared to the payload. Suppose the maximum header bit rate is 1 Gb/s and headers are 10 bytes long. The payload data rate is 100 Gb/s. (a) We would like the duration of the payload to be 90% of the overall packet duration (including header and payload). What size does the payload need to be? (b) If we wanted the maximum payload size to be 1000 bytes and maintain the same efficiency, at what rate would the header have to be transmitted? (c) Suppose we need a minimum of 1 s to process the header. This time is accounted for as an additional guard band in the overall packet, in addition 12.2 12.3 12.4 12.5