Rate Adaptation and Reach Increase by Probabilistically Shaped 64-QAM: An Experimental Demonstration
TL;DR: A transmission system with adjustable data rate for single-carrier coherent optical transmission is proposed, which enables high-speed transmission close to the Shannon limit, and it is experimentally demonstrated that the optical transmission of probabilistically shaped 64-QAM signals outperforms the transmission reach of regular 16- QAM and regular 64-ZAM signals.
Abstract: A transmission system with adjustable data rate for single-carrier coherent optical transmission is proposed, which enables high-speed transmission close to the Shannon limit. The proposed system is based on probabilistically shaped 64-QAM modulation formats. Adjustable shaping is combined with a fixed-QAM modulation and a fixed forward-error correction code to realize a system with adjustable net data rate that can operate over a large reach range. At the transmitter, an adjustable distribution matcher performs the shaping. At the receiver, an inverse distribution matcher is used. Probabilistic shaping is implemented into a coherent optical transmission system for 64-QAM at 32 Gbaud to realize adjustable operation modes for net data rates ranging from 200 to 300 Gb/s. It is experimentally demonstrated that the optical transmission of probabilistically shaped 64-QAM signals outperforms the transmission reach of regular 16-QAM and regular 64-QAM signals by more than 40% in the transmission reach.
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TL;DR: A hierarchical DM (HiDM) scheme, having fully parallelized input–output interfaces and a pipelined architecture that can efficiently perform the DM/invDM without the complex operations of previously proposed methods such as constant composition DM is proposed.
Abstract: The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the FEC coding and decoding lies inside the shaping algorithms. PS can seemingly achieve performance close to the Shannon limit, although there are practical implementation challenges that need to be carefully addressed. We propose a hierarchical DM (HiDM) scheme, having fully parallelized input–output interfaces and a pipelined architecture that can efficiently perform the DM/invDM without the complex operations of previously proposed methods such as constant composition DM. Furthermore, HiDM can operate at a significantly larger post-FEC bit error rate (BER) for the same post-invDM BER performance, which facilitates simulations. These benefits come at the cost of a slightly larger rate loss and required signal-to-noise ratio at a given post-FEC BER.
75 citations
Cites background from "Rate Adaptation and Reach Increase ..."
...in [20] and examined for a fiber-optic channel in [21]....
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TL;DR: Transmission of a probabilistically shaped polarization-division multiplexed 3-GBd 4096-QAM signal over up to 200 km of backward Raman amplified Corning® Vascade® EX2000 fiber is demonstrated.
Abstract: We demonstrate transmission of a probabilistically shaped polarization-division multiplexed 3-GBd 4096-QAM signal over up to 200 km of backward Raman amplified Corning® Vascade® EX2000 fiber. The 3-GBd signal with a root-raised-cosine roll-off of 0.01 has the potential to generate a spectral efficiency of 19.77 bit/s/Hz over 50 km of fiber.
74 citations
TL;DR: In this article, the authors proposed a 4D-PS-9/12-56APSK modulation format with hybrid probabilistic and geometric constellation shaping to improve the performance of nonlinearity compensation over conventional 2D formats.
Abstract: We demonstrate 70.46 Tb/s transmission over 7,600 km and 71.65 Tb/s transmission over 6,970 km with C+L band EDFAs using a multidimensional coded modulation format with hybrid probabilistic and geometric constellation shaping. The proposed format (4D-PS-9/12-56APSK) is designed to approach Shannon limit and to improve the performance of nonlinearity compensation over conventional and probabilistically shaped 2-D formats. The receiver DSP uses multistage nonlinearity compensation that includes fast least-mean-square equalizer and generalized filter in addition to digital back propagation. The adaptive linear filters are aided by coded modulation decisions. We study the contribution of each algorithm and show an average total nonlinearity compensation benefit of 1.4 dBQ at the designed amplifier power.
71 citations
Cites background or methods from "Rate Adaptation and Reach Increase ..."
...formations have been implemented using prefix codes [6], [18], many-to-one mappings combined with a turbo code [19], distribution matching [3], [20], [21] or cut-and-paste method [22]....
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...formats [3], [4] with spectral efficiency 8 bits/s/Hz [5], [6], transmission fibers [7], [8], and the use of broadband amplification [9]–[12] have enabled recent laboratory SMF capacity achievements [9]–[12]....
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...In general, PS can outperform circular based GS by up to few tenths of a dB in shaping gain for the same number of constellation points [3]....
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TL;DR: In this paper, the authors proposed to use enumerative sphere shaping (ESS) and investigate its performance for the nonlinear fiber optical channel, which 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.
Abstract: 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%)
66 citations
TL;DR: In this article, a detailed analysis regarding the effect of the number of hidden units and the length of the word of symbols that trains the LSTM algorithm and corresponds to the considered channel memory is conducted in order to reveal the limits of LSTMs based receiver with respect to performance and complexity.
Abstract: We introduce for the first time the utilization of Long short-term memory (LSTM) neural network architectures for the compensation of fiber nonlinearities in digital coherent systems. We conduct numerical simulations considering either C-band or O-band transmission systems for single channel and multi-channel 16-QAM modulation format with polarization multiplexing. A detailed analysis regarding the effect of the number of hidden units and the length of the word of symbols that trains the LSTM algorithm and corresponds to the considered channel memory is conducted in order to reveal the limits of LSTM based receiver with respect to performance and complexity. The numerical results show that LSTM Neural Networks can be very efficient as post processors of optical receivers which classify data that have undergone non-linear impairments in fiber and provide superior performance compared to digital back propagation, especially in the multi-channel transmission scenario. The complexity analysis shows that LSTM becomes more complex as the number of hidden units and the channel memory increase, however LSTM can be less complex than Digital Back Propagation in long distances (>1000 km).
65 citations
References
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Book•
01 Jan 1968TL;DR: This chapter discusses Coding for Discrete Sources, Techniques for Coding and Decoding, and Source Coding with a Fidelity Criterion.
Abstract: Communication Systems and Information Theory. A Measure of Information. Coding for Discrete Sources. Discrete Memoryless Channels and Capacity. The Noisy-Channel Coding Theorem. Techniques for Coding and Decoding. Memoryless Channels with Discrete Time. Waveform Channels. Source Coding with a Fidelity Criterion. Index.
6,684 citations
TL;DR: In this article, the capacity limit of fiber-optic communication systems (or fiber channels?) is estimated based on information theory and the relationship between the commonly used signal to noise ratio and the optical signal-to-noise ratio is discussed.
Abstract: We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.
2,135 citations
"Rate Adaptation and Reach Increase ..." refers background in this paper
...In particular, [19] estimates lower bounds on the capacity, while [20] derives an upper...
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TL;DR: The fundamental mechanism that explains why “convolutional-like” or “spatially coupled” codes perform so well is described, and it is conjecture that for a large range of graphical systems a similar saturation of the “dynamical” threshold occurs once individual components are coupled sufficiently strongly.
Abstract: Convolutional low-density parity-check (LDPC) ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed to date, all of which share the good performance characteristics of convolutional LDPC ensembles. We describe the fundamental mechanism that explains why “convolutional-like” or “spatially coupled” codes perform so well. In essence, the spatial coupling of individual codes increases the belief-propagation (BP) threshold of the new ensemble to its maximum possible value, namely the maximum a posteriori (MAP) threshold of the underlying ensemble. For this reason, we call this phenomenon “threshold saturation.” This gives an entirely new way of approaching capacity. One significant advantage of this construction is that one can create capacity-approaching ensembles with an error correcting radius that is increasing in the blocklength. Although we prove the “threshold saturation” only for a specific ensemble and for the binary erasure channel (BEC), empirically the phenomenon occurs for a wide class of ensembles and channels. More generally, we conjecture that for a large range of graphical systems a similar saturation of the “dynamical” threshold occurs once individual components are coupled sufficiently strongly. This might give rise to improved algorithms and new techniques for analysis.
736 citations
TL;DR: A new coded modulation scheme is proposed that operates within less than 1.1 dB of the AWGN capacity 1/2 log2(1 + SNR) at any spectral efficiency between 1 and 5 bits/s/Hz by using only 5 modes.
Abstract: A new coded modulation scheme is proposed. At the transmitter, the concatenation of a distribution matcher and a systematic binary encoder performs probabilistic signal shaping and channel coding. At the receiver, the output of a bitwise demapper is fed to a binary decoder. No iterative demapping is performed. Rate adaption is achieved by adjusting the input distribution and the transmission power. The scheme is applied to bipolar amplitude-shift keying (ASK) constellations with equidistant signal points and it is directly applicable to two-dimensional quadrature amplitude modulation (QAM). The scheme is implemented by using the DVB-S2 low-density parity-check (LDPC) codes. At a frame error rate of $10^{-3}$ , the new scheme operates within less than 1.1 dB of the AWGN capacity $\frac{1}{2}\log_2(1+{\mathsf{SNR}})$ at any spectral efficiency between 1 and 5 bits/s/Hz by using only 5 modes, i.e., 4-ASK with code rate 2/3, 8-ASK with 3/4, 16-ASK and 32-ASK with 5/6, and 64-ASK with 9/10.
642 citations