Linear dispersion polarization-time codes and equalization in polarization multiplexed coherent optical system
A method of optical communication comprising encoding four modulated symbols to generate four encoded symbols in two orthogonal polarizations and transmitting the four encoded symbols in two successive time slots. An optical communication apparatus comprising a processor configured to receive two sequences of digital symbols in a plurality of time slots, wherein the two sequences correspond to two components of two orthogonal polarizations, wherein one digital symbol per polarization is received in each of the plurality of time slots, divide each of the two sequences into a plurality of groups using a modulo operation of time, wherein each group comprises two digital symbols received in two consecutive time slots, and adaptively equalize the four digital symbols of the two consecutive time slots using a 4×4 matrix to generate four modulated symbols, wherein the 4×4 matrix comprises 16 tap-vectors.
1. A method of optical communication comprising:
encoding four modulated symbols, denoted as S 1 , S 2 , S 3 , and S 4 , to generate four encoded symbols, denoted as S X 1 , S Y 1 , S X 2 , and S Y 2 , in two orthogonal polarizations, denoted as a X polarization and a Y polarization, using formulas:
S X 1 =S 1 +Z 3
S X 2 =−S 2 −Z 4
S Y 1 =S 2 −Z 4
S Y 2 =S 1 −Z 3 ,
wherein Z 3 and Z 4 are computed as:
[
Z
3
Z
4
]
=
M
[
S
3
S
4
]
,
where M is about
1
7
[
1
+
ⅈ
-
1
+
2
ⅈ
1
+
2
ⅈ
1
-
ⅈ
]
;
transmitting S X 1 and S Y 1 in a first time slot; and
transmitting S X 2 and S Y 2 in a second time slot successive to the first time slot.
2. The method of claim 1 , wherein the method is implemented in a multi-carrier optical communication system.
3. The method of claim 1 , wherein the method is implemented in a single-carrier optical communication system.
4. An optical communication apparatus comprising:
a processor configured to encode four modulated symbols, denoted as S 1 , S 2 , S 3 , and S 4 , to generate four encoded symbols, denoted as S X 1 , S Y 1 , S X 2 , and S Y 2 , in two orthogonal polarizations, denoted as a X polarization and a Y polarization, using formulas:
S X 1 =S 1 +Z 3
S X 2 =−S 2 −Z 4
S Y 1 =S 2 −Z 4
S Y 2 =S 1 −Z 3 ,
wherein Z 3 and Z 4 are computed as:
[
Z
3
Z
4
]
=
M
[
S
3
S
4
]
,
where M is about
1
7
[
1
+
ⅈ
-
1
+
2
ⅈ
1
+
2
ⅈ
1
-
ⅈ
]
;
and
a transceiver coupled to the processor and configured to:
transmit S X 1 and S Y 1 in a first time slot; and
transmit S X 2 and S Y 2 in a second time slot successive to the first time slot.
5. The apparatus of claim 4 , wherein the transceiver is configured to transmit a multi-carrier optical signal.
6. The apparatus of claim 4 , wherein the transceiver is configured to transmit a single-carrier optical signal.