A Packet Compression/Decompression Approach for Very High Speed Optical Networks*

A .S. Acampm and S. I. AShah Department of Electrical Engineering

and Center for Telecommunications Research

Columbia University, New York, NY 10027-6699

Abstract A technique to produce time-compressed optical packets for transmission over an .ultra high speed optical network is proposed and analytically studied. Unlike other schemes which seek to tap the large optical spectrum by means of wavelength division multiplexing, packet compression seeks to provide a single ultra-high speed channel to be time- shared among a large number of users. While not avoiding the fundan!ental electreoptic bottleneck, which limits the awms speed of any user to a rate no greater than several Gigabits/sec.. use of a high compression ratio (say, greater than 100) can provide an aggregate pool of capacity in the range of a several hundred Gigabits/sec. on a single shared channel. Thus. compression avoids the need to wavelength riiult iplex several hundred 1 Gigabit/sec. channels and fur- ther avoids the need for rapidly tunable optical compo- nents. 'The technique employs two recirculating optical loops

per network node, one to optically compress a fully for- matted electronic packet for transmission onto the network and one to electronically expand such a packet upon re- ception. Depending upon the specific parameters chosen, loss of optical power is shown to limit the packet size to the range of several tens of bits. Despite the significant spontanous emission noise which is thereby produced, it is shown possible to maintain a BER = lo-' and a link margin of 15-30 dB over a wide range of conditions. Fi- nally, compreasion/expansion techniques are shown to in- troduce a new network phenomenon which prohibits a node from accessing (both for transmission and reception) two or more time slots within a contiguous group of slots of number equal to the compression ratio. The effects of this "time-out" phenomenon are shown to the limit the access efficiency to about 50% if the number of users is approxi- mately equal to the compression ratio. The efficiency rises to 90% if the number of users is an order of magnitude higher than the compression ratio.

I) Introduction

Multiuser lightwave packet networks have attracted a great deal of interest by virtue of their potential for supplying

~ ~

'This work was supported by the National Science Founda- tion under grant #ECD-88-lllll . CTR is an NSF research center.

0038

enormous aggregate capacity, estimated to be in the range of several tens of terabits per second [l] - [3]. This high capacity, coupled with the ability to readily integrate mul- timedia traffic on high speed, self routing packet streams, invites a plethora of new, broadband forms of telecommu- nication services. A fundamental constraint, however , is the so-called electreoptic bottleneck, which restricts the access rate of any one user (or any one network port) to a range no greater than several gigabits per seconds.

Wavelength division multiplexing has been considered as one possible means to create and share a large capacity pool (terabits/seconds) among a multitude of relatively lower speed network ports. To provide packet by packet connec- tivity, one such scheme requires optical elements (lasers and optical filters) tunable over the entire range of active wave- lengths' on a time scale short as compared to the packet length, plus a fast controller or scheduler to nonconflict- ingly assign wavelengths to user transmitter/receiver pairs on a packet by packet basis 141-[5]. Another scheme, re- quiring neither wavelength agility nor a fast controller, in- volves passing each packet among the nodes of the network which are connected in a recirculating perfect shuffle pat- tern with a different wav&n&h correeponding to each link [6]-[7]. Electronic atorage and retransmission on a different link ( w h g t h ) oc" at each such relaying node until the pack& teaches its intended destination.

A more diract q p d might CUMM of time compress- ing fully fonrutaied ftred Ie@h e l e d d c packets 8% they are mnverted and t r d t t e d onto the optical medium. Each such ampreseed packet would thereby occupy an op- tical bandwidth more compatible with thst of the medium itself. For example., a 1 Gbit/sec. electronic packet opti- cally compressed by a facter of 100 would occupy an optical spectrum of roughly 100 GHz. The inverse process (time expansion) would then be performed at the receiver. Com- pressed packets generated by different nodes could then be time multiplexed onto the broadcast medium, thereby forming a very high speed packet stream. Each receiving node could then filter and accept only those packets in- tended for l o d reception, much as is done with today's electronic-speed singlechannel local and metropolitan area net works.

In this paper, we consider a specific technique for per- forming such an optical compression/expansion, and ana- lytically evaluate its feasibility. Of paramount m n m is the loss margin of the optical link such that a suitably low

2.5.1 CH 2901 - 7/90/0000-0038 $1.000 1990 IEEE

Bit Error Rate (BER) may be maintained at the receiver in the presence of insertion loss, timing error, and other imperfections in the data link. We.also examine some systems implication of such a compression/expansion ap- proach: although the optical packets produced by such a scheme would occupy considerable optical spectrum, the electro-optic bottleneck still applies and is manifested in a "time out" phenomena which prevents two packets from being accepted or transmitted by a node within a time p e riod equal to the product of the compression factor and the temporal length of the compressed packet.

The proposed compression scheme employs a recirculat- ing fiber loop driven by an information-modulated stream of very narrow optical pulses. By appropiately choosing the length of the loop, it is possible to successively de- lay the earlier pulses by multiples of the temporal dura- tion of the compressed packet. Eventually, an entire com- pressed packet circulates in the loop and can be discharged onto the network medium by firing a waveguide switch.

' A second packet cannot be formed concurrently with the first, thereby producing the aforementioned "time out" ef- fect. The expander uses a second recirculating loop to cap- ture and recirculate the desired packet, producing a replica of the entire packet on each recirculation. A two-input high speed electro-conductive switch, with inputs driven by packet replicas and the original stream of narrow pulses, respectively, performs the logical equivalent of an optical "AND", producing individual uncompressed electronic bits. As with compression, two packets cannot be concurrently expanded.

Techniques for optimizing the parameters of the recir- culating loops are introduced to minimize the BER, and consideration is also given to the use of optical amplifiers within the loops to improve the performance further. Typ- ical results are as follows. Assume an electronic data rate of 1 Gigabit/sec, an optical compression factor of 100, a semiconductor laser at each node which can couple 10 milli- watts of average power into single mode fiber and compres- sion/expansion loops with 1 dB recirculation loss. Then , for a packet length of 30 bits, the transmitter-to-receiver link margin is 10 dB relative to the quantum limit for a BER of Thus, under these conditions, a receiver 10 dB inferior to the quantum limit cannot accomodate any transmission loss; alternatively a transmission loss of 10 dB would require a quantum limited receiver. To pro- vide a link margin of 30 dB under identical conditions as specified above, the packet length must be reduced to 15 bits. Clearly, greater recirculation loop loss in the com- pressor/expander would further reduce the packet length (in bits). Also, results are dependent on the electronic data rates, but not on the compression ratio, and reducing the electronic data rate will permit use of proportionately longer packets.

Typical results obtained through the use of optical am- plifiers are as follows. We assume operation at power lev- els below those needed to produce gain saturation at the output of the amplifiers (if necessary, optical attenuation

would be inserted prior to the compression loop to insure this, thereby cutting into the link margin). When optical amplifiers are introduced into the compression and expan- sion loops, considerable quantum noise is generated, and link margins are computed relative to the resulting shot noise limit. Then, again assuming an electronic data rate of 1 Gigabit/sec., a 10 milliwatt laser will provide a 20 dB link margin for a 75 bit packet if the round-trip loop gain (product of loop loss and the amplifier gain) is equal to 0.9. For same conditions and same link margin, the packet size grows to 150 bits for a loop gain of 0.95, and to 700 bits for a loop gain of 0.99 (these results are independent of the compression factor;clearly, the compression factor must be at least as great as the number of bits in the packet).

To study the effects of the time out phenomena, we con- sider simple network models such as the passive linear bus or the passive broadcast star. Important systems issues such as pulse and packet synchronization, media access, and network control as needed to permit capture of the cor- rect packet by each receiving node, are not considered here, and we focus only on the capacity degradation that arises from time-out. We show the surprising result that time-out at the transmitter does not reduce the aggregate capacity of the network for these simple, single channel-time multi- plexed networks. However, time-out at the receiver has a pronounced effect on the capacity of the network, becoming quite serious as the number of network nodes deminishes to a value lower than the compression ratio. Results for a compression ratio of 100 show that the usable capacity is reduced 'by a factor of 91% for a network containing 10 nodes ( i.e., if the data rate of the compressed packet is 100 Gbits/sec., then a useful capacity of only 9 Gbits/sec. is produced). If the number of nodes increases to 100, then a usable capacityof 51 Gbits/sec. results, and for 1000 nodes, a usable capacity of 90 Gbits/sec. is produced. Similar re- sults apply at other compression ratios.

In Section 11, we describe the compression/expansion techniques in greater detail, and present some network en- vironments where such approaches may prove useful. In section 111, we present the BER and link margin analysis for two cases:l) no optical amplifiers and 2) one amplifier in each of the compression and expansion loops. Section IV contains the analysis of the effect of time-out on the aggregate capacity for simple network architectures.

1I)A Packet Compressor/Expander

The basic approach for producing an information- modulated compressed packet is shown in Figure 1. A mode locked or gain switched laser generates a stream of narrow pulses, each pulse of width T seconds, with a period of T seconds. An electronically driven light valve modulates this pulse stream either by passing or blocking individual pulses (data rate = bits/sec ; light passed corresponds to a log- ical one and light blocked corresponds to a logical zero). A small fraction of the energy of each pulse is passively coupled into the recirculation loop, the length of which is

2.5.2 0039

chosen to be T - T - e, where c is small compared with T ;

energy not coupled into the loop is absorbed (see Figure la).

The active switch is set in the "bar"state such that the loop is closed and very little energy is coupled onto the transmission medium. Now, T seconds after the first pulse of the forming packet enters the loop, it has gone once around and has completely passed the passive coupler (the coupler is reciprocal and a small fraction of the energy is coupled back out: a combination of this loss and other losses in the loop, compounded as the pulse recirculates again and again, ultimately limits the number of bits which can be carried in the packet). At this moment, the second pulse enters the loop, with the leading edge appearing c seconds after the trailing edge of the first pulse. After another T seconds have elapsed, the doublet has passed the passive coupler the third pulse arrives and is coupled into the loop, as shown in Figure l(b). After NT seconds, N bits are circulating in the loop, one bit every T + C seconds as shown in Figure. l(c). The packet length in bits, N, is chosen such that after the last bit has passed the active switch, sufficient time elapses to set the switch in the "cross" state before the first pulse again approaches, thereby coupling the entire optical packet onto the transmission medium as shown in Figure l(d).

By means of this scheme, an N-bit electronic packet of length (N-l)T + T seconds has been compressed into an optical packet of length (N-~)(T + c)+ T ; for T > T and T > e , a compression factor of $ has been achieved. Typi- cally, T might be in the range of several pico-seconds, and T in the range of several nano-seconds. In this paper, for exemplary purposes only, we choose T = 1 nsec., 7 5 10 picoseconds, yielding a compression ratio greater than 100 and an optical data rate greater than 100 Gbits/sec. The number of bits, N, in the packet must be smaller than the compression ratio to prevent bits from overlapping in the recirculation loop. In fact, N must be sufficiently small to provide enough time margin, 200-300 psec., to fire the ac- tive switch. The switch cannot fire much faster than this; if such a switch could change state arbitarily quickly, then an active switch, rather than a passive coupler, could be used to couple the pulses of the modulated pulse stream into the loop, preventing energy loss by opening the loop to accept a new pulse immediately after the packet forming in the loop has passed, and closing the loop as the packet passes again, BP was suggested in [SI. For the parameters of interest in this paper, the switching transient would need to be of the order of C, or a fraction of a picosecond, much smaller than the state-of-theart in electro-optic switching. We note that the link margin results to be presented are independent of the compression ratio, and higher compres- sion ratios may be used if suitably narrow optical pulses can be generated and detected.

The packet expander, shown in Figure 2, operates in an analogous fashion. Here, the active switch is set in the "cross" state to completely couple the correct one of the ar- riving compressed optical packets into a recirculating loop

of length 2'--7-c ; after the packet has entered the loop, the switch is reaet to the "bar" state, closing the loop to pre- vent unwanted packets from entering. Each time the c a p tured packet propagates past the passive coupler, a small portion of its energy is leaked out to the detector, and a sequence of such replicas is thereby produced with a period of T - T - e, This sequence, along with a stream of narrow pulses produced by a mode locked laser, form the inputs to a photoconductive switch which serves, essentially, as an electro-optic "AND" gate: only if light is present on both inputs will a narrow electronic pulse be produced. The phase of the mode locked laser, its repetition rate and pulse length, and tlie period of the delayed replicas of the compressed optical packet have been selected so that the photoconductive switch produces an electronic replica of the first bit in the first packet of the sequence, the second bit of the second packet of the sequence, and so forth until the bit of the packet has been electronically replicated. An electronic amplifier, filter and pulse regenerator then produce the electronically detected and expanded version of the captured compressed packet.

Accompanying timing diagrams, drawn simply for a com- pression factor of 6 to illustrate the approach, appear in Figure 3. The modulating information, is the sequence 101101. We note the 7-second advancement in time occur- ing on each revolution of the packet as it develops in the compression loop. Upon discharge onto the medium, the fully compressed packet is time multiplexed with packets from other users. The switch in the expansion loop opens for, and captures, only the desired packet. Again, as the packet recirculates around the loop, we note a 7-second ad- vancement in time. Since the mode locked laser produces a pulse stream with a T-second period, this ?-second ad- vancement results in a different bit being reproduced at the output of the optical AND gate. Finally, we note the fully expanded and reproduced electronic signal 101101.

Some network architectures where such compres- sorslexpanders might be used appear in Figure 4. In Fig- ure 4(a) is the classical linear bus; packets formed by com- pressors geographically distributed along the length of the bus are time multiplexed onto the transmit bus and sent past receivers on the receive bus, with expanders capturing t h e packets intended for local reception. A second archi- tecture appears in Figure 4(b). h e , compressed packets produced by geographically separated nodes are linearly su- perimposed and broadcast past all receivers by a centrally located passive star coupler. Eh& node ti- its com- p d packet transmimion so as not to overlap in time with other packets. A third architecture appears in Fig- ure 4(c), which, for exemplary purposes, is drawn for an 8 node network. Here, the nodes are arranged in a recir- culating perfect s h d e pattern [2],[6],[7], with a physically separate fiber used for each interconnecting link. In ad- dition to compressors and expanders, each node contains a small optical switching matrix, which may, for example, be constructed from electronically controlled Lithium Nio- bate waveguide switches, to interconnect the compressors

2.5.3 0040

and expanders to the inbound and outbound links respec- tively. Control over the optical switch matrices may be provided, for example, via a much slower control network operating as an overlay to the higK speed data network. Packets arriving at a node not intended for local reception are placed by the switching matrix onto the outbound link, and a packet can be accepted from the compressor only if an empty time slot exists on the outbound link; priority for the outbound links is given to the packets already in flight, since the switching nodes do not contain any optical buffers. If two or more packets wish to exit the same outbound link, one will be misrouted (hot-potato routing). The capacity of such a scheme is potentidy enormous since, unlike the single channel architectures of Figure 4(a) and Figure 4(b), this approach employs many optical channels operating in parallel. Performance of such a scheme in terms of the aggregate capacity produced is reported elsewhere [9].

1II)Link Budget Analysis

We now consider the optical power required, and the re- sulting loss margin of the optical link, to produce an ac- ceptable BER with an optical compression/decompression scheme using recirculating loops. Two situations will be considered : (1) entirely passive compression and expan- sion as represented in Figure 1, and (2) the use of optical amplifiers within the compression and expansion loops to partially offset the loop loss, thereby permitting the gener- ation of longer packets.

A)Passive Compression and Expansion

In this case, the goal is to maximize the optical power pro- duced at the receiver. Power losses occur in the passive couplers, the loops themselves and in the transmission link separating a transmitter and a receiver.

Let PI be the pulsed power produced by the mode locked laser at the transmitter, let /3 be the coupling coefficient of the passive coupler ( i.e., if the incident power is PI then the power coupled into the loop is PPI), and let a be the optical loss in traversing a loop, including the fiber loss and the insertion losses of the coupler and the switch, but excluding the loss arrising from the loop power leaking out through the coupler (i.e., after one complete pass through the loop, a pulse of power p is reduced to a level of a[l-P]p). Assume that the only system losses occur within the loop. At the transmitter, the first pulse of the packet traverses the loop N - 1 times, the second pulse N - 2, etc. Thus, upon ejection from the transmission loop, the j t h pulse in the packet, P/T) is of power level

The receiving loop is the mirror image of the transmitter. Here, the packet that will ultimately yield the last detected bit passes through the loop N-1 times, the packet that will

yield the next to the last bit passes through the loop N- 2 times, etc. Thus, upon exiting the receiving loop, the pulse that will ultimately produce the j t h detected bit has a power level, Pj, given by:

pj = PjT'PC$(l - P ) J = PIPZcUN(l - P ) N E PR (2)

We note, due to the mirror-symmetry of the two loops, that all the pulsei'have the same level of power when they exit the receiving loop. For a fixed N, 'the dgsigner must now select /3 to maximize PR. Differentiating Equation (2) with respect to P, one obtains the result :

2 N + 2 Poptimum = - (3)

(4)

Assume a receiver which operates at the quantum limit, i.e., 10 photons per bit needed to produce a BER of lo-', then,

where hv is the energy per photon. Hence the required pulsed power from the mode locked laser is :

Finally, the average laser power needed to operate at the quantum limit is given by :

(7) TPI - 10hv(N + 2)(N+2)

4TaNNN Pa, = - - T

Plotted in Figure 5 as a function of N is the required average laser power for select values of the loop loss, a, for an electronic data rate of 1 Gbits/sec. From these curves, we can readily find the true laser power needed for realis- tic cases (non-zero transmission loss, receiver not operating at the quantum limit, etc.) by simply adding the loss to the power required for quantum limited performance. For example, suppose the cummulative transmission loss (light valve, fiber medium, splitting in star couplers, etc.) is 15 dB and the receiver performance is 10 dB poorer than the quantum limit, then the true power needed at the trans- mitter would be 25 dB higher than shown.

Another way to present these results is shown in Figure 6. Here, we plot the allowable loss (transmission loss, receiver degradation from the quantum limit, timing errors, etc.) vs. the number of bits in the packet for selected values of

2.5.4 004 1

the loop loss and for two specific values of available laser power at the transmitter : 1 milliwatt and 10 milliwatts. We see here, for example, with 10 milliwatts of power, if the loop loss can be contained to 1 dB (admittedly difficult with an active switch in the loop), then a packet length of ‘LO bits will, enjoy a link margin of 20 dB relative to the quantum limit; a 14 bit packet would enjoy a margin of 30 dB. Under the same conditions, but for an electronic data rate of 100 Megabits/sec., a 30 bit packet will enjoy a margin of ‘20 dB. since the absolute link margin scales iiiversely with the electronic data rate.

B)Amplifier in the Compression and Expansion Loops

We haw seen that the loss in the compression and expan- sion loops can seriously limit the size of the packets used in ttic proposed schenw. To partially offset this loss, thereby permitting the formation of longer packets, we consider the introductidn of optical amplifiers in the recirculating loops as shown in Figure 7. The gain of the amplifiers is selected such that the overall gain in traversingeither loop (coupling loss. fibcr loss. insertion loss, amplifier gain, etc.) is slightly lcss than unity to prevent oscilation. Let the overall gain bc :

where G is the gain of the amplifier. Although. in principle, an optical amplifier can be used

such that y is arbitarily close to unity, thereby permitting longer length packets, such an amplifier generates sponta- neous emission noise which ultimately limits performance. The noise produced at the output of the amplifier,Pn, is given by [lo]:

&hvA(G - 1) Pn = N2 - NI (9)

where Nl,z are the population of the lower and the upper states, respectively, and A is the optical bandwidth of the amplifier; for our purposes, we assume the presence of an optical filter, limiting the noise bandwidth to a factor of 10 greater than the signal bandwidth, i.e., 6 = $!. While this introduces a factor of 10 more noise power than the minimum possible (and seemingly, would reduce thq: link. margin by 10 dB), the signal and noise power can now be considered to add non-coherently at the receiver. Sifice the number of photo-electrons generated at the receiver in one bit interval is proportional to the average power (sig- nal plus noise) incident upon the photodetector over a r- second interval, use of a noise bandwidth equal to the signal bandwidth could cause undesirable coherence between sig- nal and noise to occur over some r-second intervals. Such coherence could cause a partial concellation of the signal by the optical coherently noise prior to the detector, thereby

reducing the link margin by more than the 10 dB which would occur through the use of a noise filter with 10 times the signal bandwidth. When the bandwidth of the noise filter is a factor of 10 greater than the signal bandwidth, the coherence time of the noise is reduced by a factor of 10 (to a value of 6) and, when counting photoelectrons produced over a r-second interval, the contribution of the signal times noise beat term caused by the squarelaw na- ture of the photodetector (which responds to incident power and not field intensity) is be assumed to integrate to zero since the noise phase varies rapidly relative to the integra- tion period T. This same effect permits us to treat the noise build-up in the compression and expansion loops as an in- coherent power addition (again, we assume that a factor of 10 is sufficiently high so that, over the 7-second integration period of the the optical receiver, the phases of the spon- taneous noise contributions to the total noise build-up on successive passes around the loop vary sufficiently rapidly that the noise-times-noise terms of the individual contribu- tions, as produced by the photodectector, integrate to zero; the contributions to the noise build-up generated on succes- sive passea around the loop are therefore assumed to add non-coherently, or power-wise, rather than voltagewise). In Equation (g), for most practical cases, + e 2.

When an amplifier is placed in the recircu&.i& loop, the noise produced at its output is the sum of the spontanously generated noise, plus any noise appearing at its input am- plified by the gain G. When the loop is closed (activeswitch in the “bar” state), the noise will begin to build up, rdect- ing repeated amplification of the recirculating noise. After one pass (T seconds), the noise power at the output of the amplifier is given by:

After the loop has been closed for an amount of time equal to N revolutions ( the time needed to form a packet of length N ), the noise level has risen to:

0042

2.5.5

If the loop were never opened, then the steady state noise power P,, would be given by:

Unlike the completely passive case (no amplifier) an asymmetry is now rqpparent. All pulses in the packet are corrupted by the same noise power in the compression loop. However, in the expansion loop, the replica of the packet from which the first bit will be detected sees only the “first pass” noise (see Eq. lo), while the replica of the packet from which the last pulse will be detected sees the

pass noise” (see Eq. 11). Thus, the last bit experiences the most noise corruption, and we will assess the detectibility

(2) ( p 0 + pR) In [L + P R ] 4

[(k) po][-L(po + p R ) ] >> [(--) 2r po][i + PO x

(18) Po of only this most corrupted bit.

Referring to Figure 7, let L be the transmission attenua- tion between transmitter and receiver, i.e., power emerging from the transmission link, po, is equal to Lp;, where pi is the incident power. Then, the signal power, PR, from

appropriately modified) :

Finally, since the average number of photeelectrona pro- second interval is large for both logical “zeron duced in a

and logical uone”,

which the last bit will be detected is given by (see Eq. 2,

(19) Po ln[ l+ -1 PR

and PR = PI/327NL (13)

Also, the corrupting noise power, Po, has a value given by

Po = (pNLrN+PN)P . (14)

where the first term in Equation (13) arises from the noise ‘1 = ;Jp,o (21 1 generated in the compression loop and t,he second term arises from the noise generated in the expansion loop.

Let us now focus on the detection of the last bit in the packet. If this bit is a logical zero, then the receiver sees only the amplifier noise Po (see Eq. 13). In the r second interval corresponding to this bit, the number of photo- electrons generated, 9, is a Poisson distributed random vari- able with mean value :

Thus, the optimum threshold is approximately equal to the geometric mean of the number of photoelectrons pro- duced by a logical “one” and a logical “zero”,

With the threshold set as in Equation (21), we calculate the BER as follows. Let P(c/O) and P ( + ) be the proba- bilities of error given a logical “zero” and a logical “one ” respectively. Then,

m 1 - -Er (15) P ( E / o ) = Jzd-- hv dn (22) PO7

E[9/01 = hv pe(po+pR) me

Assuming that this is large, the Poisson distribution p(v/O) may be approximated by a Gaussian distribution

\ I

(16) where Q(x) is the complementary error function :

Similarly, when the last bit is a logical one, the optical power seen by the detector is PR + Po, and :

Also, -(n;--TP &&7EzG 1 Wdn (25)

p w ) -= 2% P,+P, 7 (17) P ( + ) = J Fe he -m

The optimum receiver sets its threshold 9 for distin- guishing between zeros and ones at that value such that p(n/O) = p(n/l) because the probabilit‘ies of a one or zero being transmitted are the same. From Equation (15) and (16), and after much simplification, we find that 17 satisfies = Q (/T’ - = P(c/O) (26)

the following equation : Thus, the probability of bit error is the same for both a

logical “zero” and a logical “one” and the BER is given by Equation (23).

Before presenting numerical results, some observations

2.5.6 0043

are in order. First, from Equation (9), (11) and (14), we note that the term $ is independent of T , since, as previ- ously explained, the noise bandwidth of the amplifier was arbitrarily fixed at through the use of an optical filter. Second, we observe that the BER is dependent upon several parameters: the number of bits in a packet N, the overall loop gain y ’< 1. the coupling coefficient p, the amplifier gain G, the laser power P I , and the transmission loss L. From Equation (8), we see that if we specify 7 (close to one. but with sufficient margin such that if the passband gain of the amplifier should peak, oscillations do not oc- cur), then the gain G must pffset the loop losses a(1 - p). IGnally from Equation (14). since LyN is typically much sinaller than unity.

% pPN (27)

\Ve chose to present our results in the following manner. Starting with an objective BER=lO-’, and for select values of N, 7 . and 0, find 3 and G which provide the desired H K I l with the smallest PIL. Then, for fixed PI, the largest possible transmission loss can be tolerated.

I n Figure S . we plot the allowable loss vs. packet size fm select values of round trip loop gain y and for loop loss parameter ci = 1 dB. Because an amplifier is present, the rrsults arc relatively insensitive to a (the link margin de- creases by approximately l dB for every l dB increase in 0). The laser power levels chosen are 1 mw and 10 mw average, and the electronic data rate is 1 Gbit/sec. As be- fore, the results directly scale with the data rate. Typical results for a link margin of 30 dB and a laser average power of 1 milliwatt indicate that a packet length of 30 bits can be supported if the round-trip loop gain is set at 0.9. With better amplifier stabilization, the round-trip gain could be increased to 0.95, permitting a packet size of 70 bits. With very good amplifier stabilization, the round-trip loop gain might be as high as 0.99, permitting use of packets con- taining 230 bits. Any attenuation of the pulses produced by the mode locked laser prior to the compression loop, as might be needed to avoid gain saturation of the amplifier within that loop, will correspondingly reduce the link mar- gins. Erbium-doped fiber amplifiers, as opposed to semi- conductor amplifiers, might be better suited in this regard.

IV)Effects of Time-out

We will now assess the effects of compression/expansion time out on the aggregate information-bearing capacity of the simple single channel network architecture of Fig 3(a&b). Many important issues such as receiver synchro-

. nization, media access, network control to enable selection of correct packets for local reception, etc, are not consid- ered here, and we focus exclusively on the time out effects. Since protocol conversion cannot be done at the compressed data rates such as we are considering in this paper, these

’ other system issues are non-trivial and are the subject of

on-going research. The effects of compression on the aggregate capacity are

studied with the aid of Figure 9. We assume that all nodes have electronic buffers which are always filled with infor- mation waiting to be transmitted (we seek to calculate the maximum throughput on the channels; hence, we assume that there are always packets awaiting transmission, and compute the rate of successful deliveries). Each packet is equally likely to be destined for any node, and the media access is such that all available transmit time slots are oc- cupied subject to time out constraints. Upon command, a node fetches one fixed length packet from its transmit buffer, optically compEesses it, and discharges it onto the medium in the designated time slot. After placing a packet onto the medium, a node cannot place a second packet onto the medium until C - 1 time slots have passed, where C is the compression ratio. There are M nodes. We see that, by construction, all time slots are occupied if M 2 C, and no inefficiency can result from transmitter time out. We study this case first.

We assume that each node has the means to determine which packet is intended for local reception (perhaps a slower-speed network controller running in parallel with the high speed data channel provides this information). A node will seize and expand all packets intended for lo- cal reception, again subject to time out constraints: all packets destined for a given node and arriving within C-1 time slots of the last reception by that node cannot be ac- cepted and are ultimately captured by a fictitious collector of rejected packets. We assume that these rejected pack- ets are randomly reinjected onto the transmit bus, thereby denying access to new packets within those time slots occu- pied by previously rejected packets (in practice, the rejected packet collector might be an optical switch which removes successfully-delivered packets from the stream and passes rejected packets back onto the trnasmit bus, although this might void the aforementioned random reinjection assump- tion).

Referring now to Figure 10, we see a typical sequence of receiving events at a given node. After acceptance of a packet, a window of C-1 time slots is created during which all other packets destined for reception at that node are rejected. This is followed by a random interval, possibly of length zero, during which no packet is destined for that node. The first packet addressed to the given node after the time-out interval is accepted, and thus starts a new cycle.

We see, that once per cycle, a packet is accepted at the node and some random number of packets, binomially distributed between 0 and C-1, are rejected. We assume that the packet contained in any time slot is randomly dis- tributed for any node, and that the destination of all adja- cent packets are independent; any dependencies which may have arisen by the virtue of the previously rejected packets are removed by the fictitious rejected packet collector/re- inserter which collects all rejected packets over a long time interval and randomly chooses packets to be reinserted. On the average, the number of packets collected is equal to the

2.5.7 0044

number of packets reinserted. Let r be the number of packets rejected by a given node

during any cycle. Then, since the probability that a packet in a given time slot is addressed to that node is given by 1 M ’ -

On average, E[r] packets are rejected by a given node for every packet accepted. The acceptance ratio, therefore, is:

c-1 M S C - 1

1 - q =

is the fraction of packets which must be reinserted at some later time. Since all nodes are identical, Equation (31) is the transmission inefficiency arising from the time out at the receiver, and the aggregate capacity is equal to the optical data ra!e of the channel multiplied by the efficiency

The same result is obtained forM < C. Under this con- dition, it might appear that the time-out at the transmitter also plays a role, but this is not so. Consider an empty net- work which commences operation at some given time. The first M time slots will be filled, since each node always has some packets awaiting transmission. The next C-M time slots are empty. Of these initial M transmitted packets, some number J1, between 0 and M-1, will be rejected by their intended receivers. Consider, now, the next group of C transmit time slots. Of these, Jlwill be filled by rein- serted packets, and the smaller of M or C - JI time slots will be filled by new packets. Of these, at most M will be accepted, implying that of this second group of C slots, at least J1 must be rejected.

Let the number rejected be J2, where J1 5 J2 5 C. This number, J2, must be re-inserted in the third group of C slots, along with the smaller of M or C - Jz new packets. Proceeding in this fashion, we see that rejected packets will eventually cause every time slot within a contiguous group of C time slots on the transmit bus to be occupied by either a re-inserted packet or a newly generated packet, with no transmit time lost because a given node was denied access to an unoccupied transmit time slot as a result of its transmitter time out interval.

After a long period of time has elasped, the fictitious rejected packet controller/reinserter has again randomized

7 (Eq. 30).

and reinserted packets so that the results (30) and (31), originally derived for the case M 2 C , apply also when

The transmission efficiency,(30), is plotted in Figure 11 as a function of M for select values of time-out interval C. We see that for small compression ratios, the transmission inefficiency rises rapidly with the number of users. This is as expected; when the number of users is large as compared with the compression ratio, then it becomes less likely that two or more packets will arrive for a given node during a contiguous interval of C time slots. However, as thlnumber of users diminishes, receiver time-out has an increasingly serious effect. For a compression ratio of C = 100, a 100 user network enjoys a transmission efficiency of only 50%: For the same compression ratio, the number of users must increase to about 1000 before the efficiency rises to 90%.

M < C.

V) Conclusion

2.5.8

We have seen that, in principle, compression of fully- formated packets in the optical domain offers the poten- tial to better exploit the optical spectrum with conven- tional multi-user packet network architectures (broadcast bus, broadcast star). With this approach, a single ultra- high speed channel is created and shared among a multi- tude of lower speed users. The fundamental opto-electronic bottleneck is not overcome, because each user is limited by transmitter and receiver time-out to an effective peak rate constrained by electronic data rates (say, several giga- bits/sec.). However, by employing a high compression ratio (C > loo), an aggregate capacity of several hundred Giga- bits/sec. may be created. For a number of network users or nodes exactly equal to the compression ratio, time-out at the receiver limits the effective utilization of this capacity to about 50%; for a number of nodes ten times greater than the compression ratio, the efficiency rises to about 90%.

Losses in the compression and expansion recirculation loops for the specifically proposed compression/expansion techniques limit the size of the packet, in bits, to a range (say, under 50) which is small compared to the packet sizes currently under consideration for broadband multimedia applications (approximately 500 bits including information and header). To produce these longer packets with ac- ceptably low BER, it necessary to partially offset the loop losses by introducing optical amplifiers directly into the 1oops.Although considerable spontanous noise is generated, our analysis shows that a resonably high link margin (20- 40 dB) can be maintained for other loss mechanisms which have not been taken icto account (timing jitter, backoff to avoid gain saturation, inefficiencies in the photo-conductive switch, dispersion and loss in the interconnecting fiber net- work, etc.)

While our study has shown the theoretical feasibility of optical packet compression and expansion techniques, tech- nical feasibility must be established by means of hardware implementation. This and higher level systems issues (me- dia access and control of a bus operating at speeds far be-

0045

yorid electronic processing capabilities) are the subjects of on- going research.

References

1 "Special issue on Fiber Optic for Local Communica- tions", IEEE, Journal SPI. Areas Comm.,Vol. SAC-3, Nov. 1985.

2 A.S.r\campora and M.J.Karol,"An Overview of Light- wave Packet Networks" ,IEEE Network Maga:ine, \.'01.3. No.1 .Jan.1989. I

3 5pccial Issue on Optical Multiuser Networks", ZEEE .Yrtirork r\lngnzine. vo1.3. No.2, March 1989.

4 I , . ' ( : .K~ov~k~,~SIul t ichannel Coherent Optical Com- iiiiuiications Systems," Joirrnal of Lightwave Tech., vol. LT-5. no. 8. pp.1,095-1,102, 1987.

5 ILGlanc?. et al.."Densely Spaced WDM Optical Star Sctwork." Elecftvn. Left.. ~01.33, no.19, pp. 1002- 1003. 19d6.

6 A .S. Aranipora. "A Multichannel Multihop Local Light wave Setwork- JEEE Globecom. '87 Conferrence Rrcord. Tokyo. Sov. 1987.

i A .S.Acampora.M. J.E;arol and M.G.Hluchyj,"Terabit 1,ightwave Setworks: A Multihop Approach",AT&T

nical Journal. Vol.66, h'0.6, Nov./Dec. 1987.

S Ii.P.Jackson, et.al.*Optical Fiber Delay Line Signal Processing", IEEE Trans. Microwave Theory and

, Tech., Vol. MTT-3, No. 3, March 1985.

9 A.S.Acampora and S.I.A.Shah,"A Comparison of Hot Potato and Store & Forward Multihop Lightwave Net- works", submitted to IEEE Trans. Comm.

10 A.Yariv,OpticalElectrunia, Holt,Rinehart and Win- ston, 1985.

E- c-w-L (.)

MM

0046

2.5.9

N& 1

e, - P O $ 0 10 15

Number of BitdPacket 5

Figure 6(b) : Loop Loss 3 dB

Figure 5 : Power required vs Number of Bitspacket at the Quantum Limit (No Amplifier Case)

I I I , Electronic Data Rate = 1 GB/s. \ \ h p h s 1 dB \

Input Power to mw

-Input Power 1 mw

I

30 40 2o Number of Biteacket 10

Figure 6(a) : Loop LOSS 1 dB

Figurr; 6 : Allowable Loss Margin Relative to the Quantum Limit VS Number of BitsPacket Information Rate = lGB/s., No Amplifier in the Compmp. Loop

2.5.10 0047

BlDarrmL h m R . l o = 1 GBh.

A v s y c ~ ~ = ~ ~ W

QMLoop&=0.99' Loop pin =0.95 -- -- Loap pin = 0.90

-

-

-

lo00 Number of BitsPacket

0 500 Figure 8(a): Average Laser Power = 1 mw

60

Q 20 3 - a

0 lo00

Number of BiWacket 500 0

Figure 8@): Average Laser Power = 10 mw F i y c 8: Allowable Loss Margin for an Ideal Receiver vs

Number of BitsPacket.

1

0.8 8 $0.6

.f 0.4 z & 0.2

x

8

0' I

0 500 lo00 Number of Users

Figure 11: Trans. Efliciency vs # of Users for various Compression Ratios

2.5.1 1