Multidimensional hybrid modulations for ultra-high-speed optical transport
View Patent ↗Systems and methods are disclosed with a spatial-domain-based multi-dimensional coded-modulation scheme that improves dramatically OSNR sensitivity and tolerance to fiber nonlinearities by using D-dimensional signal constellations, where D=2(2+M)N. The factor 2 originates from two polarizations, 2+M electrical basis functions are selected (2 in-phase/quadrature channels and M pulse-position like basis functions), and N represents the number of orbital angular momentum (OAM) states used in FMFs/MMFs. For single mode fiber applications N is 1.
1. A method for optical communications, the method comprising
a. using a 2(M+2)-dimensional signal-space for single-mode fiber applications, with two phase coordinates (I and Q) and M pulse-position like coordinates per single polarization; and
b. alternatively using a D=2(2+M)N-dimensional space for few-mode fiber (FMF)/multimode fiber (MMF) applications, where the factor 2 originates from two polarizations, and N represents the number of orbital angular momentum (OAM)states used in FMF/MMF applications,
wherein spectral efficiency improvement to pulse position modulation (PPM) can be expressed as
S
E
,
D
-
dim
.
S
E
,
PPM
=
log
2
L
D
/
(
M
/
T
s
)
log
2
M
PPM
/
(
M
PPM
/
T
s
)
=
D
log
2
L
/
M
log
2
M
PPM
/
M
PPM
,
Where S E,D-dim is spectral efficiency for the D-dimensional space,
S E,PPM is spectral efficiency for the PPM,
L is the number of amplitude levels per dimension,
M PPM is the number of pulse-position like coordinates per polarization, and
T s is a symbol duration, and wherein M and N are integers, M≧1, and N≧1.
2. The method of claim 1 , comprising applying the D-dimensional constellations with two phase and M pulse position basis functions per polarization.
3. The method of claim 2 , comprising using N orbital angular momentum (OAM) states as basis functions to form a resulting signal space D=2(2+M)N-dimensional.
4. The method of claim 1 , wherein for the same average symbol energy of 2D constellation, the proposed scheme provides a large Euclidean distance among constellation points to improve OSNR sensitivity.
5. The method of claim 1 , comprising communicating data while tolerating fiber nonlinearities.
6. The method of claim 1 , comprising using quasi-cyclic binary or non-binary LDPC codes with a large girth to provide multi-terabits per second serial optical transmission for long-haul applications.
7. The method of claim 1 , comprising communicating with an aggregate data rate (per single wavelength) determined by:
log
2
(
L
2
(
2
+
M
)
N
)
ch
.
bits
ch
.
sym
.
×
R
s
ch
.
sym
.
s
×
r
info
.
bits
ch
.
bits
,
where r is a code rate and R s is a symbol rate.
8. The method of claim 1 , comprising using a spatially-polarization-multiplexed (2+M)-dimensional system to reduce the receiver complexity.
9. The method of claim 8 , wherein an aggregate data rate of spatially-polarization-multiplexed (2+M)-dimensional system comprises:
2
N
×
log
2
(
L
2
+
M
)
ch
.
bits
ch
.
sym
.
×
R
s
ch
.
sym
.
s
×
r
info
.
bits
ch
.
bits
.
10. The method of claim 1 , comprising iterating extrinsic information between LDPC decoders and an APP demapper until convergence or until a predetermined number of iterations is reached and estimating information streams sent by a transmitter.
11. A system, comprising:
one or more encoders;
an interleaver coupled to the encoders;
an 2(2+M)N-dimensional mapper coupled to the interleaver; and
an 2(2+M) N-dimensional transmitter coupled to the 2(2+M) N-dimensional mapper,
wherein spectral efficiency improvement to pulse position modulation (PPM) can be expressed as
S
E
,
D
-
dim
.
S
E
,
PPM
=
log
2
L
D
/
(
M
/
T
s
)
log
2
M
PPM
/
(
M
PPM
/
T
s
)
=
D
log
2
L
/
M
log
2
M
PPM
/
M
PPM
,
where S E,D-dim is spectral efficiency for the D-dimensional space,
S E,PPM is spectral efficiency for the PPM,
L is the number of amplitude levels per dimension,
M PPM is the number of pulse-position like coordinates per polarization, and
T s is a symbol duration, and wherein M and N are integers, M≧1, and N≧1.
12. The system of claim 11 , comprising a multi-mode fiber/few-mode fiber coupled to the 2(2+M) N-dimensional transmitter.
13. The system of claim 12 , comprising a receiver coupled to the 2(2+M) N-dimensional transmitter.
14. The system of claim 13 , comprising a 2(2+M) N-dimensional demodulator coupled to a multi-mode fiber/few-mode fiber.
15. The system of claim 14 , comprising an a posteriori probability (APP) demapper coupled to the 2(2+M) N-dimensional demodulator to provide symbol log-likelihood ratios (LLRs).
16. The system of claim 14 , comprising a bit LLR calculation block to determine bit LLRs required for iterative decoding in binary LDPC decoders.
17. The system of claim 16 , comprising one or more Low-density parity-check (LDPC) decoders coupled to the bit LLR calculation block.
18. The system of claim 17 , comprising a controller to iterate extrinsic information between the LDPC decoders and APP demapper until convergence or until a predetermined number of iterations has been reached.
19. The system of claim 16 , wherein the outputs of K LDPC decoders are provided as estimates of the K information streams sent by the transmitter.
20. A system, comprising:
one or more encoders;
an interleaver coupled to the encoders;
an 2(2+M)N-dimensional mapper coupled to the interleaver;
an 2(2+M) N-dimensional transmitter coupled to the 2(2+M) N-dimensional mapper;
a multi-mode fiber/few-mode fiber coupled to the 2(2+M) N-dimensional transmitter; and
a receiver coupled to the 2(2+M) N-dimensional transmitter, comprising:
a 2(2+M) N-dimensional demodulator coupled to the multi-mode fiber/few-mode fiber;
an a posteriori probability (APP) demapper coupled to the 2(2+M) N-dimensional demodulator to provide symbol log-likelihood ratios (LLRs);
a bit LLR calculation block to determine bit LLRs required for iterative decoding in binary LDPC decoders; and
one or more Low-density parity-check (LDPC) decoders,
wherein spectral efficiency improvement to pulse position modulation (PPM) can be expressed as
S
E
,
D
-
dim
.
S
E
,
PPM
=
log
2
L
D
/
(
M
/
T
s
)
log
2
M
PPM
/
(
M
PPM
/
T
s
)
=
D
log
2
L
/
M
log
2
M
PPM
/
M
PPM
,
where S E,D-dim is spectral efficiency for the D-dimensional space,
S E,PPM is spectral efficiency for the PPM,
L is the number of amplitude levels per dimension,
M PPM is the number of pulse-position like coordinates per polarization, and
T s is a symbol duration, and wherein M and N are integers, M≧1, and N≧1.