Probabilistic Shaping and Forward Error Correction for Fiber-Optic Communication Systems

Böcherer, Georg; Schulte, Patrick; Steiner, Fabian

doi:10.1109/jlt.2019.2895770

Cited by 172 publications

(80 citation statements)

References 54 publications

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“…where H(·) denotes entropy. It is important to note that by using the more general framework discussed in [43], the achievable rate in (8) can be recovered in a straightforward manner 3 We computed the BMD rate term in (8) as in [16]. However, we also numerically checked that the same results can be obtained using the methodology explained in […”

Section: B Performance Metricsmentioning

confidence: 99%

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Amari

Goossens

Gültekin

et al. 2019

J. Lightwave Technol.

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Probabilistic shaping based on constant composition distribution matching (CCDM) has received considerable attention as a way to increase the capacity of fiber optical communication systems. CCDM suffers from significant rate loss at short blocklengths and requires long blocklengths to achieve high shaping gain, which makes its implementation very challenging. In this paper, we propose to use enumerative sphere shaping (ESS) and investigate its performance for the nonlinear fiber optical channel. ESS has lower rate loss than CCDM at the same shaping rate, which makes it a suitable candidate to be implemented in real-time high-speed optical systems. In this paper, we first show that finite blocklength ESS and CCDM exhibit higher effective signal-to-noise ratio than their infinite blocklength counterparts. These results show that for the nonlinear fiber optical channel, large blocklengths should be avoided. We then show that for a 400 Gb/s dual-polarization 64-QAM WDM transmission system, ESS with short blocklengths outperforms both uniform signaling and CCDM. Gains in terms of both bit-metric decoding rate and bit-error rate are presented. ESS with a blocklength of 200 is shown to provide an extension reach of about 200 km in comparison with CCDM with the same blocklength. The obtained reach increase of ESS with a blocklength of 200 over uniform signaling is approximately 450 km (approximately 19%).

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Section: B Performance Metricsmentioning

confidence: 99%

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Amari

Goossens

Gültekin

et al. 2019

J. Lightwave Technol.

View full text Add to dashboard Cite

show abstract

“…We introduce R −1 BMD (·) as the inverse function. Its relation to other SD FEC metrics, e.g., the normalized generalized mutual information (NGMI) [25] is explained in [15].…”

Section: Signaling and Achievable Ratesmentioning

confidence: 99%

One and Two Bit Message Passing for SC-LDPC Codes With Higher-Order Modulation

Steiner

Yacoub

Matuz

et al. 2019

J. Lightwave Technol.

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Low complexity decoding algorithms are necessary to meet data rate requirements in excess of 1 Tbps. In this paper, we study one and two bit message passing algorithms for belief propagation decoding of low-density parity-check (LDPC) codes and analyze them by density evolution. The variable nodes (VNs) exploit soft information from the channel output. To decrease the data flow, the messages exchanged between check nodes (CNs) and VNs are represented by one or two bits. The newly proposed quaternary message passing (QMP) algorithm is compared asymptotically and in finite length simulations to binary message passing (BMP) and ternary message passing (TMP) for spectrally efficient communication with higher-order modulation and probabilistic amplitude shaping (PAS). To showcase the potential for high throughput forward error correction, spatially coupled LDPC codes and a target spectral efficiency (SE) of 3 bits/QAM symbol are considered. Gains of about 0.7 dB and 0.1 dB are observed compared to BMP and TMP, respectively. The gap to unquantized belief propagation (BP) decoding is reduced to about 0.75 dB. For smaller code rates, the gain of QMP compared to TMP is more pronounced and amounts to 0.24 dB in the considered example.Index Terms-Quantized LDPC decoders, binary message passing, ternary message passing, quaternary message passing, higher-order modulation, probabilistic amplitude shaping

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“…On the contrary, a probabilistically shaped constellation is uniformly spaced with varying probabilities per symbol. The latter attracted increased attention in the last several years, due to its higher shaping gain, rate adaptability, and the possibility of using Gray code for symbol labeling [17]- [19].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Coded Modulation for IM/DD Free-Space Optical Backhauling: A Probabilistic Shaping Approach

Elzanaty

Alouini

2020

IEEE Trans. Commun.

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In this paper, we propose a practical adaptive coding modulation scheme to approach the capacity of free-space optical (FSO) channels with intensity modulation/direct detection based on probabilistic shaping. The encoder efficiently adapts the transmission rate to the signal-to-noise ratio, accounting for the fading induced by the atmospheric turbulence. The transponder can support an arbitrarily large number of transmission modes using a low complexity channel encoder with a small set of supported rates. Hence, it can provide a solution for FSO backhauling in terrestrial and satellite communication systems to achieve higher spectral efficiency. We propose two algorithms to determine the capacity and capacity-achieving distribution of the scheme with unipolar M-ary pulse amplitude modulation (M-PAM) signaling. Then, the signal constellation is probabilistically shaped according to the optimal distribution, and the shaped signal is channel encoded by an efficient binary forward error correction scheme. Extensive numerical results and simulations are provided to evaluate the performance. The proposed scheme yields a rate close to the tightest lower bound on the capacity of FSO channels. For instance, the coded modulator operates within 0.2 dB from the M-PAM capacity, and it outperforms uniform signaling with more than 1.7 dB, at a transmission rate of 3 bits per channel use.

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Probabilistic Shaping and Forward Error Correction for Fiber-Optic Communication Systems

Cited by 172 publications

References 54 publications

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

One and Two Bit Message Passing for SC-LDPC Codes With Higher-Order Modulation

Adaptive Coded Modulation for IM/DD Free-Space Optical Backhauling: A Probabilistic Shaping Approach

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