Statistical properties of nonlinear distortion of a polarization-multiplexed OFDM signal in long-haul fiber links

A. S. Skidin; O. S. Sidelnikov; M. P. Fedoruk

doi:10.1364/OL.402401

Optics Letters
Vol. 45,
Issue 19,
pp. 5550-5553
(2020)
•https://doi.org/10.1364/OL.402401

Statistical properties of nonlinear distortion of a polarization-multiplexed OFDM signal in long-haul fiber links

A. S. Skidin, O. S. Sidelnikov, and M. P. Fedoruk

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A. S. Skidin, O. S. Sidelnikov, and M. P. Fedoruk, "Statistical properties of nonlinear distortion of a polarization-multiplexed OFDM signal in long-haul fiber links," Opt. Lett. 45, 5550-5553 (2020)

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Table of Contents Category
- Fiber Optics and Optical Communications
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About this Article
History
- Original Manuscript: July 9, 2020
- Revised Manuscript: August 21, 2020
- Manuscript Accepted: August 25, 2020
- Published: September 30, 2020

Abstract

We investigate nonlinear transmission regimes of a polarization-multiplexed 16-quadrature amplitude modulation (PDM-16-QAM) orthogonal frequency-division multiplexed (OFDM) signal in a long-haul optical link. We study the dependence between the strength of nonlinear distortion and statistical properties of a PDM-OFDM signal. We also consider the constellation shaping-based solutions that allow to significantly reduce the bit error rate (up to three to 12 times at the cost of 5%–20% signal redundancy) and propose a method to analytically optimize the symbol distribution for higher-order modulation formats using only the initial signal.

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Input data:

pattern length $m$ ; alphabet power $q$ ;
output block length $n$ ;
source data block $N$ , $0 \leq N < V (n)$ , where $V (n) = \sum_{i = 0}^{q^{m} - 1} V (n, i)$ ;
set of one entry codewords, $Q_{m}$ .
Output data:
encoded block $E$ of length $n$ ( $E = e_{0} e_{1} \dots e_{n - 1}$ ).
Internal variables:
$d = bit [0.\bf m - 1]; i = bit [0.\bf m - 1];$
int $j$ ;
Find the start pattern $d$ : $d = max {p \| N \geq \sum_{i = 0}^{p - 1} V (n, i)}$ ;
$j \leftarrow n - m + 1$ ;
$(e_{j} e_{j + 1} \dots e_{j + m - 1})_{q} \leftarrow d$ ;
$N \leftarrow N - \sum_{i = 0}^{d - 1} V (n, i)$ ;
for $j \leftarrow (n - m)$ down to 1;
$e_{j} \leftarrow max {p \| 0 \leq p < q,$
$N \geq \sum_{i = 0}^{p - 1} V (j + m - 1, i e_{j + 1} e_{j + 2} \dots e_{j + m - 1}) = φ (p)}$ ;
if $e_{j + 1} e_{j + 2} \dots e_{j + m} \notin Q_{m}$ then $N \leftarrow N - φ (e_{j})$ .

Input data:

pattern length $m$ ; alphabet power $q$ ;
encoded $q$ -ary data block $E$ of length $n$ ( $E = e_{0} e_{1} \dots e_{n - 1}$ );
set of prohibited codewords $D_{m}$ ;
set of one entry codewords, $Q_{m}$ .
Output data: number of the encoded sequence, $N$ ,
$0 \leq N < V (n)$ .
Internal variables:
$d = bit [0.\bf n - 1]; i = bit [0.\bf n - 1];$
Find initial pattern $d$ : $d = max {p \| N \geq \sum_{i = 0}^{p - 1} V (m, i)}$ ;
$j \leftarrow m - n + 1$ ;
$d \leftarrow (e_{j} e_{j + 1} \dots e_{j + n - 1})_{q}$ ;
$N \leftarrow \sum_{i = 0}^{d - 1} V (m, i)$ ;
for $j \leftarrow (m - n)$ down to 1
$φ (p) \leftarrow \sum_{i = 0}^{p - 1} V (j + n - 1, i e_{j + 1} e_{j + 2} \dots e_{j + n - 1})$ ;
if $e_{j + 1} e_{j + 2} \dots e_{j + n} \in D_{m}$
STOP: the codeword is incorrect;
if $e_{j + 1} e_{j + 2} \dots e_{j + n} \notin Q_{m}$ then $N \leftarrow N + φ (e_{j})$ .

Input data:

pattern length $m$ ; alphabet power $q$ ;
output block length $n$ ;
source data block $N$ , $0 \leq N < V (n)$ , where $V (n) = \sum_{i = 0}^{q^{m} - 1} V (n, i)$ ;
set of one entry codewords, $Q_{m}$ .
Output data:
encoded block $E$ of length $n$ ( $E = e_{0} e_{1} \dots e_{n - 1}$ ).
Internal variables:
$d = bit [0.\bf m - 1]; i = bit [0.\bf m - 1];$
int $j$ ;
Find the start pattern $d$ : $d = max {p \| N \geq \sum_{i = 0}^{p - 1} V (n, i)}$ ;
$j \leftarrow n - m + 1$ ;
$(e_{j} e_{j + 1} \dots e_{j + m - 1})_{q} \leftarrow d$ ;
$N \leftarrow N - \sum_{i = 0}^{d - 1} V (n, i)$ ;
for $j \leftarrow (n - m)$ down to 1;
$e_{j} \leftarrow max {p \| 0 \leq p < q,$
$N \geq \sum_{i = 0}^{p - 1} V (j + m - 1, i e_{j + 1} e_{j + 2} \dots e_{j + m - 1}) = φ (p)}$ ;
if $e_{j + 1} e_{j + 2} \dots e_{j + m} \notin Q_{m}$ then $N \leftarrow N - φ (e_{j})$ .

Input data:

pattern length $m$ ; alphabet power $q$ ;
encoded $q$ -ary data block $E$ of length $n$ ( $E = e_{0} e_{1} \dots e_{n - 1}$ );
set of prohibited codewords $D_{m}$ ;
set of one entry codewords, $Q_{m}$ .
Output data: number of the encoded sequence, $N$ ,
$0 \leq N < V (n)$ .
Internal variables:
$d = bit [0.\bf n - 1]; i = bit [0.\bf n - 1];$
Find initial pattern $d$ : $d = max {p \| N \geq \sum_{i = 0}^{p - 1} V (m, i)}$ ;
$j \leftarrow m - n + 1$ ;
$d \leftarrow (e_{j} e_{j + 1} \dots e_{j + n - 1})_{q}$ ;
$N \leftarrow \sum_{i = 0}^{d - 1} V (m, i)$ ;
for $j \leftarrow (m - n)$ down to 1
$φ (p) \leftarrow \sum_{i = 0}^{p - 1} V (j + n - 1, i e_{j + 1} e_{j + 2} \dots e_{j + n - 1})$ ;
if $e_{j + 1} e_{j + 2} \dots e_{j + n} \in D_{m}$
STOP: the codeword is incorrect;
if $e_{j + 1} e_{j + 2} \dots e_{j + n} \notin Q_{m}$ then $N \leftarrow N + φ (e_{j})$ .

Abstract

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Figures (3)

Tables (2)

Equations (3)

Optics Letters