A Unified Understanding of the Many Forms of
Optical Code Division Multiplexing
Eli Yablonovitch
Rick Wesel
Bahram Jalali
Ming Wu
Ingrid Verbauwhede
Can FPGA’s + Modulator/PhotoDetector Array
Mimic any form of OCDMA?
Princeton
USC
UC Davis
Telcordia
Purdue Univ.
Matched Filtering
in Time Domain
(non-coherent)
Matched Filtering in
the Spectral Domain
(coherent)
l1
l3
l4
Time
Time
Modulators
Transmitter
Data
FPGA
DWDM
DEMUX
Wavelength
Code
From
Network
To Network
DWDM
MUX
Multi-wavelength
Laser Source
l4
l2
Receiver
Voltage
l3
Wavelength
l2
l1
Wavelength
Block Diagram
Threshold
Level
(valid
data)
Time
Time
Photodetectors
FPGA
Data
FPGA Encryption
PLL
Input data
LVDS Output
Switch Matrix
Protocol
LVDS Input
Input clock
System clock
Output clock
Output data
Delay Module
Code Generator
LVDS: Low Voltage Differential Signaling
PLL: Phase-Locked Loop
Therefore FPGA’s + Modulator/PhotoDetector Array
can easily duplicate the performance of Matched
Filtering in Time Domain (non-coherent)
Therefore Princeton scheme and
USC scheme can
be emulated by
our FPGA approach
Equivalence Between Spectral Phase Encoding And Time Sequential Encoding:

Frequency
Wavelength MUX
Spectral Phase Decoder
(a)
Data
threshold
detector
t
time
(a) Sequential brief individual pulses, have a broad spectrum as indicated by the colors.
The plus and minus signs in (a) indicate various phase shifts induced on the spectral components
of one pulse. The phase shifts can be decoded by a matched filter, producing a single big pulse
that can be monitored by a threshold detector.
Sum
Delay
Buffer
(b)
Frequency

FPGA
t
time
Photo-receiver
array
Data
(b) With no loss of generality, the pulses can be spectrally filtered, and each spectral component
sent to a phase sensitive photo-receiver. The retrieved information can be stored and processed
in a Field Programmable Gate Array, which is fully equivalent to direct-sequence radio CDMA.
sidebands
sidebands
+
l
sidebands
+ carrier
carrier
carrier
optical
electrical
l
Figure 1: Coherent detection without a local oscillator.
The ring is a carrier add/drop separation filter.
sidebands
l1
EDFA
l1l
sidebands
+
carrier
add/
drop
l2
l3
l
+
carrier
2
carrier
optical
electrical
180
hybrid
coupler
in-phase quadrature
signal
signal
Figure 4: Tandem single side band receiver, not requiring a local
oscillator, avoids duplicate side-bands.
Direct Sequence Spread Spectrum:
carrier
wave
cos(t)
signal(t)
code(t)
mixer
code(t)  signal(t)
1
time
-1
Transmitter
cos(t)  code(t)  signal(t)
time
mixer
chip time
local
oscillator
cos(t)
cos(t)  code(t)  signal(t)
mixer
Receiver
cos2(t)
 code(t)
 signal(t)
local code
generator
code(t)
cos2(t)
 code2(t)
 signal(t)=
time
(1/2)signal(t)
mixer
A Direct Sequence radio CDMA system imposes random phase shifts +1 or –1 on
the signals in much the same way as the channelized optical spectral
phase decoder/encoder, described in a previous vugraph.
Therefore FPGA’s + Modulator/PhotoDetector Array
can do Spectral Phase Encoding if Coherent detectors
are used
Therefore UC Davis scheme and
Telcordia scheme and
Purdue scheme can
be emulated by
our FPGA approach
The different approaches are all equivalent since, the frequency  time rectangular cell
changes shape, but its area is preserved, in accordance with the “Uncertainty Principle”.

frequency
Conventional Wavelength/Time matrix.
Frequency and time are treated
on an equal footing.
time
t

frequency
time between pulses
time
t
Spectral Phase Encoding.
Each color of each pulse will be
coded with a different phase shift,
producing narrow slicing of the spectrum,
but relatively long periods between pulses.

frequency
chip time
channel 1
channel 2
time
Direct-Sequence Time-Domain
Spread-Spectrum CDMA.
Each channel occupies a broad
frequency spectrum corresponding
to the inverse of the chip time.
t
Successive Decoding
• We can decode the first user by treating
others as noise, then the first user’s ones
become erasures for the other users.
Proceed in this way until finish decoding
all the users.
• This is called successive decoding. For
binary OR channel, this process does not
lose capacity as compared to joint
decoding.
Successive Decoding: The Z-Channel
• Successive decoding for n users:
– User with lowest rate is decoded first
– Other users are treated as noise
– The decoded data of the first user is used in the
decoding of the remaining users
• First user sees a “Z-channel”
x0
x 1
1  a1
a1
y0
y 1
• Where ai = 1-(1-p)n-i is the probability that at
least one of the n-i remaining users transmits
a1
Simple codes
• In order to have a hardware demo working
for the May meeting, some very simple
codes were produced.
• This demo consists of two transmitter and
two receivers
• Both receivers decode the information
independently
Simple Codes for Demo
• Short codes have been designed for a
simple demo for 2 users
• These were chosen to be as simple to
encode and decode as possible
• Each bit is encoded separately
• Bit synchronism is assumed, blocked
asynchronism is allowed
• Coordination is required
• These codes are error free
Simple codes for Demo (2)
1
Rate 1/4
0
Receiver 1 looks for
position of 0 (which
always exists)
0
Source 1
If 1 or 2, decide 1
1
If 3 or 4, decide 0
1
2
3
4
Sum Rate 5/12
Rate 1/6
Receiver 2 looks for
FIRST position of 0.
If 1, 3 or 5, decide 1
If 2, 4 or 6, decide 0
0
Source 2
1
1
2
3
4
5
6
Worst Case :
block i
block i+1
FPGA Setup for initial
successive decoding Demo
Transmitter 1
FPGA
Data
Generator
CW
Laser
FPGA
Receiver 1
Bit Error
Rate Tester
Decoder
Encoder
Modulator
Wavelength
Coupler
Transmitter 2
FPGA
Data
Generator
CW
Laser
Photodetector
Photodetector
FPGA
Decoder
Encoder
Modulator
Receiver 2
Bit Error
Rate Tester