Shaping Lightwaves in Time and Frequency for Optical Fiber Communication

Cho, Junho; Chen, Xi; Raybon, G.; Che, Di; Burrows, E.C.; Olsson, Samuel L. I.; Tkach, R.W.

doi:10.21203/rs.3.rs-452651/v1

Cited by 4 publications

(5 citation statements)

References 37 publications

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“…B-ESS modifies the ESS algorithm such that shaped channel inputs with limited energy variations are generated. Transmitted signals with high energy variations generate a larger nonlinear interference during propagation over fiber [17], [18]. Consequently, we demonstrated that B-ESS provides significant SNR gains over ESS and K-ESS, and up to 10% rate increase.…”

Section: Introductionmentioning

confidence: 77%

Band-ESS: Streaming Enumerative Coding with Applications to Probabilistic Shaping

Gültekin¹,

Willems²,

Alvarado³

2022

Preprint

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Probabilistic amplitude shaping (PAS) is on track to become the de facto coded modulation standard for communication systems aiming to operate close to channel capacity at high transmission rates. The essential component of PAS that breeds this widespread interest is the amplitude shaping block, through which the channel input distribution is controlled. This block is responsible for converting bit strings into amplitude sequences with certain properties, e.g., fixed composition, limited energy, limited energy variation, etc. Recently, band-trellis enumerative sphere shaping (B-ESS) was introduced as an amplitude shaping technique that achieves limited energy variations which is useful in optical communication scenarios. B-ESS operates based on a trellis diagram in which sequences with high energy variations are pruned. In this work, we study the implementation of B-ESS. We first show that thanks to the trellis structure obtained by this pruning, B-ESS can be implemented with very low storage complexity. The trellis computation is shown to be reduced to a set of recursive multiplications with a scalar factor. Then we show that this scalar factor can be adjusted such that the trellis computation is further simplified and realized with only binary shifts. This shift-based B-ESS (1) can be implemented for arbitrarily long blocklengths without incurring an increase in complexity, and (2) can operate in a streaming mode similar to convolutional coding.

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Section: Introductionmentioning

confidence: 77%

Band-ESS: Streaming Enumerative Coding with Applications to Probabilistic Shaping

Gültekin¹,

Willems²,

Alvarado³

2022

Preprint

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show abstract

“…For instance, it has been shown that the amount of nonlinear interference generated by a propagating signal depends not only on its average power (second-order moment), but also on its fourth-order moment (when symbols are i.i.d.) [23], [33]- [35] or, more in general, on the variations of the instantaneous power over a finite temporal window [19], [21], [36]. In this case, the use of a shorter block length N is expected to be beneficial, as it introduces a constraint on the energy of each block of N symbols.…”

Section: Probabilistic Amplitude Shapingmentioning

confidence: 99%

“…The nonlinear interference due to DM was analyzed in [19] for the CCDM, while the kurtosis-limited sphere shaping, which selects the sequences with minimum energy and low kurtosis, showed superior performance in the nonlinear regime with respect to equivalent-length ESS in a single-span scenario but not for a multi-span link [20]. Furthermore, it was shown that the nonlinear shaping gain improves by properly packing shaped sequences in time and frequency [21].…”

mentioning

confidence: 99%

On the Nonlinear Shaping Gain With Probabilistic Shaping and Carrier Phase Recovery

Civelli

Forestieri

Secondini

2023

J. Lightwave Technol.

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The performance of different probabilistic amplitude shaping (PAS) techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques-namely, sphere shaping, shell mapping with different number of shells, and constant composition DM-and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations (1 × 180 km, 15 × 80 km, and 27 × 80 km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm.

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“…For instance, it has been shown that the amount of nonlinear interference generated by a propagating signal depends not only on its average power (second-order moment), but also on its fourth-order moment (when symbols are i.i.d.) [22], [32]- [34] or, more in general, on the variations of the instantaneous power over a finite temporal window [18], [20], [35]. In this case, the use of a shorter block length N is expected to be beneficial, as it introduces a constraint on the energy of each block of N symbols.…”

Section: Probabilistic Amplitude Shapingmentioning

confidence: 99%

“…The nonlinear interference due to DM was analyzed in [18] for the CCDM, while the kurtosis-limited sphere shaping, which selects the sequences with minimum energy and low kurtosis, showed superior performance in the nonlinear regime with respect to equivalent-length ESS in a single-span scenario but not for a multi-span link [19]. Furthermore, it was shown that the nonlinear shaping gain improves by properly packing shaped sequences in time and frequency [20].…”

mentioning

confidence: 99%

On the Nonlinear Shaping Gain with Probabilistic Shaping and Carrier Phase Recovery

Civelli¹,

Parente²,

Forestieri³

et al. 2022

Preprint

View full text Add to dashboard Cite

The performance of different probabilistic amplitude shaping (PAS) techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery. Different PAS implementations are considered, based on different distribution matching (DM) techniques-namely, sphere shaping, shell mapping with different number of shells, and constant composition DM-and amplitude-to-symbol maps. When carrier phase recovery is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when carrier phase recovery is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations (1 × 180 km, 15 × 80 km, and 27 × 80 km single-mode-fiber links), and also including laser phase noise, except when inline dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation model and explains the interaction of carrier phase recovery and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a carrier phase recovery algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the carrier phase recovery algorithm.

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Shaping Lightwaves in Time and Frequency for Optical Fiber Communication

Cited by 4 publications

References 37 publications

Band-ESS: Streaming Enumerative Coding with Applications to Probabilistic Shaping

Band-ESS: Streaming Enumerative Coding with Applications to Probabilistic Shaping

On the Nonlinear Shaping Gain With Probabilistic Shaping and Carrier Phase Recovery

On the Nonlinear Shaping Gain with Probabilistic Shaping and Carrier Phase Recovery

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