Note: Descriptions are shown in the official language in which they were submitted.
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COMMUNICATION SYSTEMS AND APPARATUS WITH SYNCHRONOUS
ORTHOGONAL CODING
Field of the Invention
The invention pertains to optical communication systems.
Background
The optical fiber communication infrastructure has expanded rapidly to
satisfy the demands of communication customers requiring inexpensive, high-
bandwidth transmission of voice, data, video, and other data streams.
Inexpensive,
high-speed communication has permitted the rapid expansion of Internet
communication in addition to satisfying more traditional communication demands
such as telephony.
Optical-fiber media have very large available communication bandwidths,
and several approaches have been used to take advantage of this bandwidth. In
one
example, optical carriers have been modulated at high data rates, with data
rates of
2.5 Gbit/s, 10.0 Gbit/s, and higher either installed or demonstrated. Using
higher
data rates, multiple data signals can be combined on a single optical carrier
by
modulating the optical carrier at different times for each of the data signals
to be
combined. This method is known as time-division multiplexing (TDM). Data bits
are recovered from the modulated carrier and the detected bits are assigned to
appropriate data signals, thereby demultiplexing the data signals.
In another method, multiple data streams are used to modulate optical
carriers having different carrier wavelengths. The modulated carriers are
combined
and transmitted on a single optical fiber. To recover the data streams, the
different
carrier wavelengths are separated and the modulation of each carrier
wavelength is
detected. This method is known as wavelength-division multiplexing ("WDM").
While these methods permit the use of more of the available optical fiber
bandwidth, they also exhibit several practical limitations. For example, high-
data-
rate TDM requires optical sources, detectors, and associated electronics that
are
capable of very high-bandwidth operation. Such components are typically
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expensive. WDM systems require frequency-stable and accurately tuned optical
sources. Such sources and other associated components also can be expensive.
An additional method that takes advantage of the high bandwidths available
with optical fibers is known as code-division multiple access ("CDMA"). In
this
method, individual data signals are encoded with corresponding encoders, and
the
coded signals are combined and delivered via optical fiber or other
communication
medium. The data signals are recovered by decoding the combined coded signal
with decoders, each of which corresponds to one (or more) of the encoders used
to
code the data signals. In this method, the separation (demultiplexing) of
different
data signals depends on the codes used by the encoders and decoders. The
number
of data signals that can be combined depends on the number of available codes
and
acceptable levels of channel crosstalk. Available codes tend to produce
unacceptable levels of crosstalk between the decoded signals, i.e., a decoded
data
signal corresponding to a selected data signal contains artifacts due to other
data
signals. Such crosstalk is particularly troublesome in systems in which many
data
signals are to be multiplexed. For these reasons, improved methods and
apparatus
are needed for code-based multiplexing.
Summary of the Invention
Codes and code-based multiplexing methods and apparatus are provided that
permit increased numbers of data signals to be multiplexed while maintaining
channel cross-talk and other coding artifacts at acceptable levels.
Code-based communication systems comprise a coder that applies a code
selected from a set of synchronous, substantially orthogonal codes to a data
stream.
In specific embodiments, the codes are selected from a set of orthogonal codes
and
these codes are applied to data signals as temporal codes. In a representative
embodiment, the codes are temporal phase codes.
Methods of coding a data stream include selecting a time interval and
dividing the time interval into two or more time chips. Each of the time chips
is
assigned a modulation value based on a code. The data stream is divided into
portions corresponding to the time chips, and the modulation values assigned
to the
time chips are coded onto corresponding portions of the data stream. In
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representative examples, the code is a discrete phase code, or a temporal
phase code,
and is selected from a set of synchronous, substantially orthogonal codes. In
a
specific example, the code is selected from the set consisting of the phase
codes:
(4~/3, 2~/3, 0, 2~/3, 4~/3, 0, 0, 0, 0), (4~/3, 0, 4~/3, 0, 0, 2~/3, 2~/3, 0,
0), (0, 4~/3,
2~/3, 0, 2~/3, 4~/3, 0, 0, 0), (2~/3, 4~/3, 0, 0, 0, 0, 4~/3, 2~/3, 0), (0, 0,
0, 4~c/3,
2~/3, 0, 2~/3, 4~/3, 0), (0, 4~/3, 4~/3, 2~/3, 4~c/3, 2~/3, 4~/3, 4n/3, 0),
and (4~/3, 0,
2~/3, 4~/3, 4~/3, 4~/3, 4~/3, 2~/3, 0).
Coders for encoding an optical-data stream include a circulator that receives
the optical-data stream; and an optical fiber that receives the optical-data
stream
from the circulator. The optical fiber includes two or more reflectors
situated and
configured to apply a code to the data stream. The code can be a synchronous,
substantially orthogonal code selected from a set of substantially orthogonal
codes.
Coders for coding an input-data stream include two or more reflectors
situated and configured to selectively reflect portions of the input-data
stream
according to a synchronous code. According to representative embodiments, the
synchronous code is an orthogonal code, a temporal code, a phase code, or a
three-
level phase code. In additional embodiments, the reflectors are defined by
gratings.
Communication methods include selecting a set of synchronous codes and
assigning a synchronous code from the set to each of a plurality of data
channels.
Data streams are encoded corresponding to the data channels based on
respective
synchronous codes. In representative embodiments, encoded data streams are
combined to form a combined, coded data stream. In specific embodiments, the
codes are orthogonal codes, substantially orthogonal codes, or temporal phase
codes.
Additional communication methods include receiving the combined coded
data stream and decoding portions of the combined coded data stream based ~on
the
synchronous codes.
Methods of code-based multiplexing in a wavelength-division multiplexed
(WDM) communication system include selecting at least one carrier signal of a
selected wavelength of the WDM communication system. The carrier signal is
divided into portions that are modulated based on data streams and codes
assigned to
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each portion, wherein the codes are selected from a set of substantially
orthogonal,
temporal codes.
These and other features and advantages of the invention are illustrated
below with reference to the accompanying drawings.
Brief Description of the Drawings
FIG. 1 is a schematic diagram of a code-multiplexed communication system.
FIG. 2A is a schematic diagram of a temporal code template illustrating a
division of a time interval into subintervals ("chips") to which phase or
amplitude
values are assigned based on a code.
FIG. 2B is a schematic diagram of a spectral code template illustrating a
division of a wavelength interval into subintervals ("chips") to which phase
or
amplitude values are assigned based on a code.
FIGS. 3A-3B are schematic diagrams illustrating a data bit prior to encoding,
as encoded, and as decoded, respectively.
FIG. 4 is schematic diagram of a coder that includes gratings defined in an
optical fiber.
FIG. 5 is a schematic block diagram of a single wavelength channel of a
wavelength-division multiplexed (WDM) communication system that includes code-
based multiplexing.
FIG. 6 is a schematic block diagram of a detection system that recovers data
from a decoded data stream.
Detailed Description
With reference to FIG. l, a code-based multiplexed communication system
100 includes channel inputs 103, 104, 105 106 that receive data signals from
respective data sources (not shown in FIG. 1 ). Corresponding channel encoders
108,
109, 110, 111 encode respective data signals and deliver coded data signals to
a
combiner 107. (For convenience, both "encoders" and "decoders" are referred to
herein as "coders.") The combiner 107 combines the coded data signals to form
a
combined, coded data signal and directs the combined, coded data signal to an
optical fiber 112 or other transport medium. The combined, coded data signal
is
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received by a sputter 113 that delivers portions of the combined, coded data
signal to
respective decoders 114, 115, 116, 117 that decode the combined, coded data
signal
and provide decoded data signals to respective channel outputs 119, 120, 121,
122.
Typically, the decoders 114, 115, 116, 117 are matched to corresponding
channel
5 encoders 108, 109, 110, 111.
The operation of the code-based multiplexing communication system 100 of
FIG. 1 includes encoding data signals according to codes applied by the
channel
encoders 108-111 to data signals applied to the respective channel inputs 103-
106.
Generally, the data signals are independent, and each of the channel encoders
108-
111 codes according to a different respective code. The sputter 113 typically
directs
respective portions of the combined, coded data signal to each decoders 114-
117.
Therefore, each of the decoders 114-117 receives data corresponding to several
(or
all) of the data signals, and the decoding process pernlits recovery of
selected data
signals from the combined, coded data signal. Communication channels are
typically selected by assigning codes for encoding and decoding a data signal
assigned to a particular data channel. The codes can be permanently assigned
and
coded by dedicated encoders/decoders. Alternatively, the codes can be
reconfigurably assigned so that the coders are programmable to encode/decode a
variety of codes.
A decoded signal produced by a selected decoder generally includes some
crosstalk or other contributions from data signals coded by channel encoders
that are
not matched to the selected decoder. Such contributions can interfere with
data
recovery from the decoded signal, increasing the bit-error rate of the
corresponding
communication channel. These contributions depend on the codes assigned to the
channels. The codes coded by the channel encoders/decoders can have a variety
of
forms, and these forms can determine many properties of a code-based
multiplexing
communication system, including channel cross-talk levels and bit-error rates.
Codes for code-based multiplexing can be conveniently designed based on
code templates. A representative code template 200 is illustrated
schematically in
FIG. 2A. The code template 200 spans a time interval T~oDE and is divided into
8
time intervals ("chips") 201-208 each having a duration T~HIP~ As shown in
FIG.
2A, the chips 201-208 have equal durations, but chips of unequal duration can
be
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used. A spread-spectrum bandwidth is given by the inverse of the chip duration
T~H~p, and data streams coded with a selected code typically have a bandwidth
of
approximately the spread-spectrum bandwidth. A code based on the code template
200 specifies an amplitude, phase, or combination of amplitude and phase to be
coded onto an optical signal at times corresponding to the various chips. For
a
communication system that codes several channels, codes (based on the code
template 200) are assigned to each of the channels. These codes form a set
referred
to as a "code set."
A data signal to be coded (encoded or decoded) is based on a time-varying
field, such as an electromagnetic field. An electric field of such a signal
can be
represented as E(t~) = Ale"°~, wherein A~ is an amplitude and cps is a
phase of a jth
chip, and j is an integer. Various combinations of amplitudes and phases can
be
used to define a code set. In a particular example, codes can assign a
constant field
amplitude (A = A~ for all j) but with phases cps that vary from chip to chip.
Other
codes assign different field amplitudes for two or more of the chips, and
additional
codes have chips that assign varying combinations of amplitude and phase to
each of
the chips.
As shown in FIG. 2A, the code template 200 represents either temporal
phase codes or amplitude codes, or a combination thereof. One specific code
type is
a multiple-level phase code in which one of several values of phase are
assigned to
the code chips while the amplitudes are the same. A representative phase code
of
three chips can be written as a row vector (cps, cp2, cp3). A code set that
includes
similar codes is listed below in Table 1. A code defined by a limited number
of
phase or amplitudes is referred to as a "discrete code." As a representative
example,
three phases can be used to define a seven- or nine-chip code such that each
of the
chips is assigned one of the three phases.
The code template 200 of FIG. 2A is a temporal code template. With
reference to FIG. 2B, a spectral code template 220 spans a wavelength range
~,~oDE
and includes wavelength (or spectral) chips 221-228 that span a wavelength
range
~,.CH~p. Spectral coding can be represented as coding that produces an
electric field as
a function of frequency E(f ) = Ale"~~, wherein fj is a frequency, and A~ is
an '
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amplitude and cps is a phase of a jth chip. The chips of a spectral code can
assign
various.combinations of amplitude A~ and phase cps town optical signal or
other
signal. Code templates, codes, and code sets for temporal coding, including
temporal phase coding, are adaptable to spectral coding. Because code-based
multiplexing based on spectral coding tends to be less compatible than
temporal
coding with wavelength-division multiplexing ("WDM"), embodiments based on
temporal coding are described herein.
As shown in FIGS. 2A-2B, the code templates 200, 220 include a continuous
time interval T~oDE or spectral range ~,,~oDE, respectively. However. code
templates
I0 can include discontinuous time intervals and spectral ranges. The
amplitudes and/or
phases assigned to code chips can be binary levels or multiple levels, or can
be
continuous values.
Code-multiplexed data can have temporally overlapping bits ("dense code-
multiplexing") or non-overlapping bits ("sparse multiplexing"). In
addition,~the
code-multiplexed data signals can be based on a common clock or otherwise
synchronized, and code-based multiplexing systems comprising such signals are
referred to as "synchronous code-multiplexed." Channel cross-talk and channel
bit-
error rates in synchronous code-based systems can be controlled by controlling
the
temporal placement of codes relative to each other and by using codes that
produce
relatively small levels of cross-talk or other artifacts at selected times,
and that
permit higher levels of cross-talk or other artifacts at other times. Such
control is
particularly useful in dense code-multiplexed systems. If spectral codes are
used,
spectral placement of coding artifacts can be controlled.
With reference to FIG. 3A, representative data streams 301, 303 are shown
prior to encoding. The data streams 301, 303 are represented as sequential
bits 305-
307 (011), 308-310 (I10) , respectively. The data streams 301, 303 are based
on a
common clock frequency. In addition, the bits 305-307 of the data stream 301
are in
phase with corresponding hits 308-310, respectively, of the data stream 303.
For
example, the bits 306, 309' ale approximately simultaneous. However, such
simultaneity is unnecessary, and a constant phase difference (delay) between
corresponding bits of the data streams 301, 303 is satisfactory.
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FIGS. 3B-3C illustrate the data streams 301, 303 after encoding and
decoding, respectively. Referring to FIG. 3C, decoded bits 315-317 correspond
to
the bits 305-307 but include contributions 318 due to the presence of bits of
the data
stream 303 in the combined data signal that is decoded. The degradation in bit
error
rate and other data errors are reduced by encoding and decoding the data
streams
301, 303 based on codes such that the contributions 318 do not appear at
specified
latch times TLATCH at which the bits are electronically latched, i.e.,
assigned "0" or
" 1 " values based on the value of the decoded signal at the latch times
T~,TCH- Codes
that provide a zero-cross-talk time or time interval (or a low cross-talk time
or time
interval) reduce the magnitude of the contributions 318 and are referred to
herein as
"synchronous, substantially orthogonal codes." With such codes, the
contributions
318 (such as crosstalk) are time-displaced from the temporal positions T~,TCH
at
which data bits are recovered from the decoded signal. Typically the
contributions
318 are displaced from the temporal positions TLArcH ~d spread over a time
interval
of as much as approximately (2N~hips' 1 ) TcHCp, wherein N~h;Ps is a number of
chips in
a selected code.
Prior to coding, each of the bits 305-307, 308-310 of FIG. 3A can span a
spectral bandwidth as large a spectral bandwidth used in a WDIvI system,
typically
20-40 GHz. The bits can be provided in many ways, including direct or external
modulation of standard communications-grade lasers. In addition, the
coding/decoding illustrated in FIGS. 3A-3B is exemplary, and features shown
therein are not limiting. For example, the bits 305-307, 308-310 need not be
substantially shorter than the clock period T~LOCK, and the bits can have
Fourier-
transform-limited spectra, or other spectra such as a frequency chirp.
The selection of synchronous, substantially orthogonal codes to reduce
crosstalk depends on the decoding process and physical limitations in
encoders/decoders. If a signal (such as an electric field) is coded with a
code m from
a set of M codes and is decoded by a decoder designed to match a code n, then
an
output power P"",(t) produced by decoding a signal coded with the mth code and
decoded with the nth code is preferably small. In particular, Pm~(t=0) =
Poi"",
wherein Smn is the Kronecker delta function (8m"= 1 for m = n and Sm"= 0
otherwise). Codes that satisfy the condition Pm~(t=0) = Po&"" are referred to
as
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"synchronous, orthogonal codes," and can provide low cross-talk in a code-
based
optical communication system. In contrast, substantially orthogonal codes can
have
some nonzero component at t = 0, but small enough to permit accurate data
recovery
even in the presence of unmatched data signals.
In coders (encoders and decoders) that code an electric field by performing a
cross-correlation of a coded input electric field Em(t) and a decoder code
that is
matched to a code n, corresponding to a field E"(t), the output power is:
2
Pmn (t) - f ut'Em (t' )En (t + t, )
wherein * denotes complex conjugation of the code function. At time t = 0, the
pOWer pn"(l) 1S:
2
pmn (t - O) - f dt,Em (t' )En (t 1 ) ~
which is the squared modulus of an overlap integral between the input code
(code m)
and the complex conjugate of the decoder code (code n). Thus, at a selected
time,
orthogonal codes satisfy the relationship:
J~tI Em (t1 )En (t' ) = poV mn
This relationship is a standard definition of orthogonality between two
complex
functions. Thus, any set of orthogonal functions as defined above may be used
to
construct synchronous, orthogonal encoders and decoders. Orthogonal spectral
codes satisfy a similar spectral relationship, i.e.,
2
f dfEm(f)En(f) -po~mn~
wherein f is frequency, and Em is a frequency-dependent coded field. Thus, a
set of
orthogonal codes can be used to define either temporal or spectral codes, or
both.
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The integrals given above describe continuous codes having arbitrarily small
chips. These continuous codes can be based on continuous functions. Generally,
code sets include codes based on a limited number of chips, and a temporal or
spectral interval is segmented to define a series of temporal or spectral
chips as
5 shown in the code templates of FIGS. 2A-2B. With division into chips, the
single-
time orthogonality relationship written above becomes:
Nchips
Em \t j )En It j ) - pa Smn '
j
10 Equivalently, the relationship may be written as:
Nchips
~Em~tj)En~tj)-elf po~mW
J
wherein cp is an arbitrary phase factor. This expression is equivalent to a
dot
product of a vector representing an mth code and a vector corresponding to a
complex conjugate of a an nth code, wherein both vectors include l~~hips
components.
Writing the mth and nth codes in terms of corresponding amplitudes and phases,
the
orthogonality relationship becomes:
Nchips
'4j '4j exI)~I~Cvj~ Cpj )~ - 2~~ pa lsmn
J
For amplitude codes (in which all phase terms are equal), the relationship is:
Nchips
~'4~ '4J =e~~ pa~mn
j
Therefore, any set of orthogonal real vectors with N~n~ps components forms a
set of
synchronous, orthogonal codes.
For phase-only, synchronous, orthogonal codes, the orthogonality
relationship is:
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Nchips
m n i~
exp(i(Cpf -Cpj )) = 2 Nchipssmn
l
Codes and code sets can be obtained analytically based on these orthogonality
relationships. Monte Carlo methods can also be used to search for synchronous,
orthogonal code sets. In addition, codes such as Walsh codes, Hadamard codes,
Gold codes, and Kasami codes can be adapted for coding as described above.
One simple method of obtaining code sets includes quantizing the phase
levels of the codes into Nph~e equally spaced phase levels. Coders based on
codes
having a discrete phase levels also permit simpler manufacturing processes.
For
quantized phase levels, the orthogonality relationship is:
Nchips 2~ 2~c
i~
exp(i ( N ~ m - N 2 n )) = a Nchips ~mn ~
J phases phases
wherein ~n E ~0,1,..., Np,,~es. -1~. Such a code set is shown in Table 1. The
code set
of Table 1 includes seven codes each having nine chips, wherein Np,,ases = 3.
Table 1
Code (P1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9
1 4~/3 2~/3 0 2~/3 4~/3 0 0 0 0
2 4~/3 p 4~/3 0 0 2~/3 2~/3 0 0
3 0 4~/3 2~/3 0 2~/3 4~/3 0 0 0
4 2~/3 4~/3 0 0 0 0 4~/3 2~/3 0
5 0 0 0 4~/3 2~/3 0 2~/3 4n/3 0
6 0 4~/3 4~/3 2~c/34~/3 2n/3 4~/3 4~/3 0
4~/3 0 2~/3 4~/3 4~/3 4~/3 4~/3 2~c/30
Temporal phase coding using code sets such as those of Table 1 can be as
robust as
amplitude-based coding with respect to signal-transmission degradations caused
by
attenuation and cross-talk. Additional code sets can be obtained as described
above.
In a specific example, a 2.5 Gbitls data stream having TBiT = 400 ps is
encoded with codes of the code set of Table 1. The chip duration To~P is
selected as
approximately TBIT/N~n~Ps = 400/9 ps = 44.4 psec. To avoid intersymbol
interference,
bits of the input data stream are typically configured to have a bit duration
of about
200 psec because the decoding process can produce outputs in a time interval
of as
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much as (2N~h~ps -1 ) TCHIP~ The bandwidth of the 2.5 Gbit/s is selected to be
about
1/T~HIP or about 23 GHZ.
An encoder 400 for encoding an optical data stream as specified by a
selected code is illustrated in FIG. 4. The encoder 400 includes a circulator
401 and
a fiber-grating codes 403. The fiber-grating codes 403 comprises gratings 411-
415
or other reflectors that direct portions of the optical data stream as
specified by a
code. The gratings 411-415 are formed as periodic variations in refractive
index of a
core or cladding of an optical fiber. An uncoded bit 405 is directed to the
circulator
401 and then to an input 421 of the fiber-grating codes 403. Portions of the
uncoded
bit 405 are reflected by the gratings 411-415, are returned to the circulator
401, and
form a coded bit 407. The relative positions and reflectances of the
gratings~411-
415 are selected based on the phases and amplitudes of the chips of a selected
code.
A decoder matched to the encoder 400 can be made by arranging the fiber-
grating
codes 403 so that the coded output (and typically portions of unmatched coded
outputs produced by encodings with a different code of a code set) is directed
from
the circulator 401 to a surface 423 of the fiber-grating codes 403.
Positions of gratings such as the grating 411-415 correspond to a selected
code. If the reflectances of such gratings are low, then the placement of the
gratings
is readily accomplished based on the phases to be coded. If the grating
reflectances
are large, an input data stream is depleted as the data stream propagates
through the
gratings. Grating placement in such a codes can be determined using a
simulated
annealing process implemented as a design program on a computer.
FIG. 5 is a schematic diagram of a single WDM channel that includes four
code-based channels. A laser 501 supplies power to a sputter 503 at a selected
WDM wavelength 7,,". The sputter 503 directs portions of the laser power to
modulators 511-514 that modulate respective portions according to data based
on
data from data sources such as a data source 515 (not shown in FIG. 5). The
respective modulated portions from the modulators 511-514 are directed to
corresponding encoders 521-524 that encode the modulated portions. A combines
530 receives and combines the modulated, coded power portions and directs the
combined power to a WDM multiplexes (not shown). Data is recovered by
extracting power at the selected WDM wavelength and directing portions of this
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power to respective decoders 531-534 that correspond to the encoders 521-524,
respectively. Typically an encoder and decoder are matched so that the decoder
processes the data signal produced by the encoder so that data can be
recovered.
Corresponding receiver modules 541-544 recover data for each of the channels.
As
illustrated in FIG. 5, code-based multiplexing is implemented on a single WDM
wavelength 7~~, data signals can be code-multiplexed on two or more such WDM
wavelengths.
With reference to FIG. 6, a detection system 600 that receives a decoded
optical data stream 601 includes a detector 603 that converts the decoded
optical
data stream 601 to an electrical data stream 605, typically a time-varying
electrical
voltage or current. Typically, the detector 603 includes a photodetector 613
and an
amplifier 615. The electrical signal 605 is delivered to a data recovery
module 607
that provides a data output 609 that, in the absence of data recovery error,
corresponds to the data transmitted, prior to encoding and decoding. A latch
time
controller 611 is configured to adjust a latch time or times to vary times at
which the
data recovery module 607 identifies a bit as a "0" bit or a "1" bit.
Typically, the
detector 603 partially time-integrates the data stream 601 and the latch
controller
permits adjustment of a latch time TLATCH SO that contributions of coding
artifacts do
not substantially increase an error rate in the data output. Such adjustment
is based
on a code set used for encoding/decoding or an error rate detected in the data
output
609.
The code-based communication methods and apparatus described herein
permit passive coding of optical and other signals, produce low levels of
decoding
artifacts at latch times, and permit higher levels at other times.
Communication
methods based on frequency shifting such as those used in wireless code-
division
multiple-access systems use active coders and produce decoding artifacts (such
as
cross-talk) at different frequencies that are not displaced from the latch
times.
Passive coders are especially attractive for optical communication because of
the
expense and complexity of active coders for use at optical carrier
frequencies.
Encoding and decoding of an uncoded data stream is illustrated above, but
coded
data streams can be recoded in order to further identify a destination for the
data
stream.
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Aspects of the invention have been described with reference to several
representative embodiments, but the invention is not limited to these
embodiments.
It will be obvious to those skilled in the art that these embodiments can be
modified
and that such modifications remain within the spirit and scope of the
invention. We
claim all that is encompassed by the appended claims.
