Coded multidimensional pulse amplitude modulation for ultra-high-speed optical transport

1. An optical communication method, comprising:

using subcarriers as individual bases functions, obtaining signal constellation points of an N-dimensional pulse amplitude modulation (ND-PAM) constellation diagram as an N-dimensional Cartesian product of a one-dimensional PAM; and

transmitting the N-dimensional signal constellation point over all N orthogonal subcarriers serving as individual bases functions;

comprising receiving the ND-PAM signals;

comprising splitting the ND-PAM signals into two orthogonal polarizations that are used as input into two coherent detectors;

comprising using the coherent detector outputs as real and imaginary parts of a complex sequence stream;

comprising splitting the stream into N-branches, where a kth branch determines projection along a kth coordinate; and

comprising using the projections in a posteriori probability (APP) demapper.

2. The method of claim 1 , wherein the one dimensional PAM comprises amplitude signal constellation points X={(2i−1−L)d, i=1, 2, . . . , L}, wherein 2d is a Euclidean distance between two neighboring points and L is the number of constellation points in one dimensional PAM, and wherein the ND-PAM comprises

X

N

=

X

×

X

×

…

×

X

⁢

︸

N

⁢

⁢

times

=

{

(

x

1

,

x

2

,

…

⁢

,

x

N

)

|

x

i

∈

X

,

∀

1

≤

i

≤

N

}

.

3. The method of claim 1 , comprising encoding b independent data streams using an LDPC (n,k) code of rate r=k/n, where n denotes a codeword length and k is an information word length.

4. The method of claim 3 , comprising writing codewords row-wise into a b×n bit interleaver.

5. The method of claim 4 , wherein the number of constellation points in ND-PAM is determined by M=L N where L is the number of constellation points in one dimensional PAM, and the number of bits per symbol is b=log 2 (L N ), comprising taking codeword bits from the bit interleaver column-wise at every symbol slot i and provided to an ND mapper to select one constellation point out of L N , depending on information content.

6. The method of claim 1 , comprising performing an N-dimensional mapper as a look-up table (LUT) with b input bits serving as a memory address that selects the N-coordinates of an ND-PAM signal constellation point.

7. The method of claim 1 , comprising imposing coordinates on orthogonal subcarrier, wherein a kth coordinate is multiplied by exp[j2πkt/T] (k−−N/2, . . . ,N/2−1) where t denotes time and T denotes a period.

8. The method of claim 7 , comprising adding all coordinates, upon multiplication with exp[j2πkt/T], to provide real and imaginary parts of a signal used as in-phase and quadrature signals for Mach-Zehnder modulators (MZMs).

9. The method of claim 8 , comprising combining signals at the output of I/Q modulators into single stream with a polarization-beam splitter (PBS).

10. The method of claim 1 , comprising determining symbol log-likelihood ratios (LLRs) as

λ( S i )=log [ P ( S i S 0 |R i )/ Pi =( S i ≠S 0 |R i )],

where P(S i |R i ) is determined by Bayes' rule as:

P

⁡

(

S

i

|

R

i

)

=

P

⁡

(

R

i

|

S

i

)

⁢

P

⁡

(

S

i

)

/

∑

S

′

⁢

P

⁡

(

R

i

|

S

i

′

)

⁢

P

⁡

(

S

i

′

)

.

11. The method of claim 1 , comprising determining bit LLRs to be used in LDPC decoding as:

L

⁡

(

v

^

j

)

=

log

[

∑

S

i

⁢

:

⁢

v

j

=

0

⁢

exp

⁡

(

λ

⁡

(

S

i

)

)

/

∑

S

i

⁢

:

⁢

v

j

=

1

⁢

exp

⁡

(

λ

⁢

(

S

i

)

)

]

where s i denotes a transmitted signal constellation point, R i denotes a received) constellation point, where so denotes a referent constellation point, and P(R i |S i ) denotes a conditional probability estimated by collection of histograms., P(s) denotes a priori probability of symbol S, while {circumflex over (v)} j (jε{0, 1, . . . , n−1}) is the jth bit estimate of a codeword v.

12. The method of claim 11 , where the bit LLRs are forwarded to LDPC decoders to provide extrinsic bit LLRs for demapping.