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: Focusing on the optical transport and switching layer, aspects of large-scale spatial multiplexing, massive opto-electronic arrays and holistic optics-electronics-DSP integration, as well as optical node architectures for switching and multiplexed of spatial and spectral superchannels are covered.
Abstract: Celebrating the 20th anniversary of Optics Express, this paper reviews the evolution of optical fiber communication systems, and through a look at the previous 20 years attempts to extrapolate fiber-optic technology needs and potential solution paths over the coming 20 years. Well aware that 20-year extrapolations are inherently associated with great uncertainties, we still hope that taking a significantly longer-term view than most texts in this field will provide the reader with a broader perspective and will encourage the much needed out-of-the-box thinking to solve the very significant technology scaling problems ahead of us. Focusing on the optical transport and switching layer, we cover aspects of large-scale spatial multiplexing, massive opto-electronic arrays and holistic optics-electronics-DSP integration, as well as optical node architectures for switching and multiplexing of spatial and spectral superchannels.
498 citations
TL;DR: The star-shaped 16-ary quadrature amplitude modulation scheme shows superiority over the PS-Square-16QAM in terms of the BER improvement.
Abstract: We investigate and compare the performance of star-shaped 16-ary quadrature amplitude modulation (Star-16QAM) and square-shaped 16QAM (Square-16QAM) in the probabilistic shaping (PS) and uniform schemes with coherent detection. With the help of PS technology, the bit error ratio (BER) improvement achieved in the PS-Star-16QAM scheme is greater than that of the PS-Square-16QAM when compared with the uniform schemes in our numerical simulation and experiment. Therefore, the PS-Star-16QAM shows superiority over the PS-Square-16QAM in terms of the BER improvement.
308 citations
Cites methods from "Rate Adaptation and Reach Increase ..."
...The application of PS in optical communication is able to operate the systems more approach to the Shannon limit thus outperforming conventional modulation formats [2]–[4], [11]....
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TL;DR: In this paper, the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR, was investigated.
Abstract: Different aspects of probabilistic shaping for a multispan optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multispan wavelength division multiplexing optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1400 to 3000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and full-field split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multi-span fiber system.
278 citations
TL;DR: This manuscript discusses the motivations for jointly utilizing transmission techniques such as probabilistic shaping and digital sub-carrier multiplexing in digital coherent optical transmissions systems and describes the key-building blocks of modern high-speed DSP-based transponders working at up to 800G per wave.
Abstract: The design of application-specific integrated circuits (ASIC) is at the core of modern ultra-high-speed transponders employing advanced digital signal processing (DSP) algorithms. This manuscript discusses the motivations for jointly utilizing transmission techniques such as probabilistic shaping and digital sub-carrier multiplexing in digital coherent optical transmissions systems. First, we describe the key-building blocks of modern high-speed DSP-based transponders working at up to 800G per wave. Second, we show the benefits of these transmission methods in terms of system level performance. Finally, we report, to the best of our knowledge, the first long-haul experimental transmission – e.g., over 1000 km – with a real-time 7 nm DSP ASIC and digital coherent optics (DCO) capable of data rates up to 1.6 Tb/s using two waves (2 × 800G).
181 citations
Cites background or methods from "Rate Adaptation and Reach Increase ..."
...For square shaped constellations with points located on a Cartesian grid such as 64QAM, this becomes even easier by applying the corresponding 1-D distribution on I- and Q-dimensions separately [37]....
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...Probabilistic shaping (PS) [37] and geometric shaping (GS) [38] are possible approaches to constellation shaping....
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TL;DR: A layered PS-FEC architecture consisting of a PS encoder and an FEC encoder is introduced, of which probabilistic amplitude shaping is a practical instance and achievable PS encoding rates and FEC decoding rates are derived using information-theoretic arguments.
Abstract: This tutorial paper provides a foundation for integrating probabilistic shaping (PS) and forward error correction (FEC). A layered PS-FEC architecture consisting of a PS encoder and an FEC encoder is introduced, of which probabilistic amplitude shaping is a practical instance. Achievable PS encoding rates and achievable FEC decoding rates are derived using information-theoretic arguments. The developed tools are applied to the design and performance assessment of optical transponders based on measurements from optical transmission experiments.
170 citations
Cites methods from "Rate Adaptation and Reach Increase ..."
...In the left plot, we illustrate the achievable FEC rates for the transmission experiment of [9]....
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...For this, the measurement x and y were taken from the transmission experiment in [9] which investigates four shaped modes OP 1 (H(X) = 5....
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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