56 Optical Coding Theory with Prime
(a) high-bandwidth optical clock pulses
(e) multiplexed codewords from all stations (after star coupler)
(b) electrical data bits
(c) data-modulated optical pulses (after intensity modulator)
(d) binary (0,1) codewords (after optical encoder)
t
t
t
t
t
TT
c
1
0
1
1
0
01
T
FIGURE 2.2 Signal formats at various stages of an optical transmitter. (Source: Reproduced
with permission from Guu-Chang Yang and Wing C. Kwong, Prime Codes with Applications
to CDMA Optical and Wireless Networks,Norwood,MA:ArtechHouse,Inc.,2002.
c
! 2002
by Artech House, Inc.)
At each receiver, an optical decoder, which operates as an inverse filter of its cor-
responding optical encoder, correlates its own address (signature) codeword with any
received codeword. Assuming chip synchronism, the decoder output is written as a
discrete periodic correlation function, according to Section 1.5. If a codeword arrives
at the correct destination, an autocorrelation function with a high peak is generated.
Otherwise, the codeword is treated as interference and a cross-correlation function
results. So, it is necessary to maximize the autocorrelationpeaksbuttominimizethe
cross-correlation f unctions in order to optimize the d iscrimination between the cor-
rect codewords and interfering codewords. An electrical pulse is generated whenever
an autocorrelation peak is detected at th e thresho ld detector. Such a pulse indicates
the reception of a data bit 1; otherwise, a data bit 0 is recovered.
Prucnal et al. [2] proposed the first-of-its-kind tunable incoherent o ptical encoder,
in which a parallel configuration of fixed fiber-optic delay-lines and intensity modu-
lators was used, for temporal amplitude coding. Figure 2.3 shows the block diagram
of a revised version of such a parallel design. The encoder consists of a 1 ×w optical
power splitter, a set of w electronically tunab le (fiber-optic or waveguide) delay- lines,
Optical Coding Schemes 57
1 x w
power
splitter
w x 1
power
coupler
gated
optical
pulses
to star
coupler
tunable
delay-lines
.
.
.
.
.
.
.
.
.
FIGURE 2.3 Tunable optical encoder in a parallel coding configuration [2, 33].
and a w ×1opticalpowercoupler,wherew is the code weight (or number of pulses)
of the 1-D time-spreading binary (0,1) codes in use. At the encoder inpu t, the power
splitter divides an incoming gated optical pulse, which represents the transmission
of a data bit 1, into w pulses. These w pulses are delayed individually by their own
tunable delay-lines, according to the locations of the mark chips (or bin ar y 1s) in the
address codeword of the intended r eceiver. Finally, these pulses are combined by the
coupler to form the desired codeword for transmission.
As fixed delay-lines were assumed in Prucnal’s original design [2], tunability was
achieved by first generating pulses in all po ssible time- delays an d then selecting on ly
w of them in according to the address codeword of the intended receiver. So, the
original setup required the use of a 1 ×N power splitter, a set of N fixed (fiber-optic
or waveguide) delay-lines, N intensity modulators (one per line), and an N ×1power
coupler, wher e N is the code length. Each of these N delay-lines takes a distinct value
from the set of {0,T
c
,2T
c
,...,(N −1 )T
c
},whereT
c
is the chip-width. The w properly
delayed pulses are selected by closing w intensity modulators.
The setup of the decoder is identical to that o f the encoder, except that only w
fixed-delay paths are needed if a fixed-address-receiver configuration is assumed.
The decoder correlates incoming codewords by accumulating the reversely delayed
pulses to give a high autocorrelation peak if there exists a codeword matching the
decoder’s address codeword. Otherwise, a low cross-correlation function results and
is considered as interference.
The advantage of this parallel cod ing co nfigu ration is the capability of perform-
ing incoherent optical processing without the need for fast-response photodetectors
or high-speed electronics. Also, it can universally generate any 1-D time-spreading
binary (0,1) code, such as all of the p r ime codes in Chapters 3 and 4. However, this
kind of parallel structure creates a very stringent power requirement because each
optical pulse is split into many pulses in the encoders and decoders. In addition, the
number of delay-lines adds up to a huge number, and this kind ofparallelcoding
devices is usually bulky and lossy.
Figure 2.4 shows the block diagram of a tunable incoherent optical encoder in
58 Optical Coding Theory with Prime
delay-lines
. . .
. . .
DC bias
voltage
power
splitter
T
c
2 x 2
optical
switch
DC bias
voltage
2 x 2
optical
switch
DC bias
voltage
2 x 2
optical
switch
T
c
T
c
T
c
gated
optical
pulses
to star
coupler
absorber
FIGURE 2.4 Tunable optical encoder in a serial coding configuration [33,41,42].
aserialcodingconfiguration[33,41,42].Thissetupimproves the power, size, an d
delay-length requirements of the parallel configuration. The encoder consists of a
series of 2 ×2opticalswitches,whichareconnectedwithtwoseparate(fiber-optic
or waveguide) delay-lines between two adjacent switches. Each pair o f delay-lines
generates a differential time-delay of one chip-width T
c
.TheDC-biasvoltagesofthe
2 ×2opticalswitchesareindividuallycontrolledsothateachswitch is configured
to operate in either 3-dB or bar state independently. At an encoder input, the power
splitter divides an incoming gated optical pulse (of width T
c
), which represents the
transmission of a data bit 1, into two pulses. The amount of differential time-delays is
accumulated as these two pulses pass through a series of bar-state switches. The bar
state allows optical pulses at the two inputs of a switch to directly exit the correspond-
ing outputs without any change. After the proper amount of differential time-delays
has been created, both pulses are combined at a 3-dB-state switch and then split into
four pulses—two pulses at each output. Functioning like a 2 ×2passivecoupler,a
3-dB state switch duplicates optical pulses arriving at its two inputs and makes them
available at the two outputs. The process repeats until the desired number o f pulses,
which are properly arranged accordin g to the add ress codeword of the intended re-
ceiver, is generated. If there are n switches in the 3-dB state, a time-spreading binary
(0,1) codeword with 2
n
pulses can be generated. For example, if the second, sixth,
and thirteenth switches ar e set to the 3-dB state, 2, 6, and 13 chips of differen tial
time-delays are accumulated to generate the codeword 1010001010000101000101.
The setup of the optical decoder is similar to that of the encoder, except that the
3-dB-state 2 ×2opticalswitchesarenowreplacedby2×2passivecouplersifa
fixed-address-receiver configuration is assumed. Only n + 12×2passivecouplers
are needed, and the d elay-lines between two cou plers are usedtogeneratethediffer-
ential time-d elays of two groups of pulses d irectly. For example, to h ave an address
(signature) codeword of 10 100 010 10 000 101000101 in the decoder, four 2 ×2pas-
sive couplers are needed, and the delay-lines between two couplers are arranged to
generate the differential time-delays of 2, 6, and 13 chips, correspondingly.
While this serial configuration improves the power, size, anddelay-lengthrequire-
ments of the parallel configuration, it can only generate certain families of 1-D time-
spreading binary (0, 1) co des th at have replicative pulse separations, such as 1-D
even-spaced codes, 2
n
codes, and 2
n
prime codes in Section 3.5 [33, 41, 42].
Making use of the block structure of some optical codes, such as the 1-D prime
codes in Chapter 3, the power splitting/combining loss and number of optical
Optical Coding Schemes 59
delay-lines
. . .
. . .
gated
optical
pulses
2T
c
T
c
4T
c
2
L-1
T
c
to star
coupler
absorber
DC bias
voltage
2 x 2
optical
switch
DC bias
voltage
2 x 2
optical
switch
DC bias
voltage
2 x 2
optical
switch
DC bias
voltage
2 x 2
optical
switch
FIGURE 2.5 Tunable incoherent optical encoder in an improved serial coding configuration
[33, 41, 42].
switches in the serial coding configuration can be reduced substantially. For instance,
each of the prime codeword s (in Section 3.1) of length p
2
and weight p can be di-
vided into p blocks, and each block has a single one (or a pulse) and p −10s,where
p is a prime number. If all p pulses in a prime code can be generated by a laser with
arepetitionratep /T ,thepowerlosscreatedbypulsesplittingandcombiningatthe
optical splitter and switches can be avoided, where T is the bit period, as explained
in the following.
Shown in Figure 2.5 is an improved serial tunable encoder. It consists of a series
of L + 12×2opticalswitches,whichareconnectedwithtwoseparate(fiber-optic or
waveguide) delay-lines between two adjacent switches, where L = -log
2
p. and -·.
is the ceiling function [33,41,42]. The DC-bias voltages of the 2×2opticalswitches
are individually contro lled so that each switch is configuredtooperateineithercross
or bar state independently. While the bar state allows an optical pulse at an input of
aswitchtodirectlyexitthecorrespondingoutput,thecrossstateallowsthepulseto
cross over to the op posite o utput. Th e differential time-delays are all distinct and as-
signed with values equal to the product of the chip-width T
c
and consecutive powers
of 2. This design is based on the tunable O-TDMA coder proposedbyPrucnaletal.
in [83, 84], in which any discrete time delay of {0,T
c
,2T
c
,...,(p −1)T
c
} chips can
be generated by setting the 2 ×2opticalswitchesineithercrossorbarstates,accord-
ingly. The last 2 ×2opticalswitchisusedtoroutetheproperlydelayedpulsetothe
output of the encoder. With this last switch in place, the use of intensity modulators
for performing electro-optic conversion of data bits (see Figures 2.1 and 2.2) can be
eliminated. This is because all p pulses within a bit period can be simply routed to
the unused output of the last switch for every data bit 0. Similarly, as in the 2
n
prime
codewords in Section 3.5, a block m ay have no pulse but all p 0s, any optical pulse
within such a block can also be routed to this unused output.
Because optical pulses are now entering this improved serialencoderatarateof
p/T , p-fold increases in the speed of electronics and the repetition rate of lasers are
required, as compared to the serial design in Figure 2.4. Nevertheless, there is no
power loss due to splitting and combining of optical pulses, and only -log
2
p.+ 1
optical switches are required in the improved serial design,resultinginsubstantial
cost savings and size reduction, and mak in g the design more suitable for waveguide
implementation.
60 Optical Coding Theory with Prime
2.2 1-D TEMPORAL PHASE CODING
Temporal amplitude coding can only accommodate 1-D binary (0, 1) codes and is
restricted to the use of incoherent processing and detectionbecauseopticalintensity
is used for transmission. This kind of incoherent system is usually asynchronous in
nature because these optical codes, such as the prime codes inChapter3,arede-
signed to operate without system-wise time synchronization. Due to nonscheduled
transmission and nonzero mutual interference, temporal amplitude coding supports
only a limited number of subscribers and even fewer simultaneous u sers befo r e a
rapid deterioration of code p erformance occurs. By introducing 0 o r
π
phase shifts to
optical pulses, temporal phase coding supports orthogonal bipolar (−1, +1) co d es,
such as maximal-length sequences and Walsh codes [48, 49], with zero (in-phase)
cross-correlation functions. Rather than using OOK, temp oral phase coding trans-
mits a conjugated form of the bipolar codewords in use for databit0s,resultingin
better code performance than temporal amplitude coding [10–13, 15, 16]. However,
this kind of coherent system is usually synchronous in naturebecausebipolarcodes
require system-wise synchronization in order to maintain code orthogonality. Also,
the need for phase preservation in optical fibers often hinders the development of
temporal phase coding.
power
splitter
power
coupler
temporal-
phase-coded
bipolar code
t
t
optical
pulse
tunable phase
modulators
fixed
delay-
lines
0 0 0 π π 0 π
(b)
(a)
2x2
coupler
integrator, sampler,
& threshold detector
optical
encoder
tunable
delay-line
pulsed
laser
balanced
photodetector
recovered
data bits
maximal-length
sequence of length 7
+1 +1 +1 -1 -1 +1 -1
0 0 0 π π 0 π
electrical
path
temporal-
phase-coded
bipolar code
FIGURE 2.6 Temporal phase coding: (a) tunable encoder; (b) tunable decoder [10–13, 15,
16].
Figure 2.6 shows a typical tunable coherent encoder and decoder for temporal
phase coding [10–13, 15, 16]. Assume that bipolar codes of length and weight of
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.