Compressed Shaping: Concept and FPGA Demonstration

Probabilistic shaping (PS) has been widely studied and applied to optical fiber communications. The encoder of PS expends the number of bit slots and controls the probability distribution of channel input symbols. Not only studies focused on PS but also most works on optical fiber communications have assumed source uniformity (i.e. equal probability of marks and spaces) so far. On the other hand, the source information is in general nonuniform, unless bit-scrambling or other source coding techniques to balance the bit probability is performed. Interestingly, one can exploit the source nonuniformity to reduce the entropy of the channel input symbols with the PS encoder, which leads to smaller required signal-to-noise ratio at a given input logic rate. This benefit is equivalent to a combination of data compression and PS, and thus we call this technique compressed shaping. In this work, we explain its theoretical background in detail, and verify the concept by both numerical simulation and a field programmable gate array (FPGA) implementation of such a system. In particular, we find that compressed shaping can reduce power consumption in forward error correction decoding by up to 90% in nonuniform source cases. The additional hardware resources required for compressed shaping are not significant compared with forward error correction coding, and an error insertion test is successfully demonstrated with the FPGA.Comment: 10 pages, 12 figure

Post-FEC BER Benchmarking for Bit-Interleaved Coded Modulation with Probabilistic Shaping

Accurate performance benchmarking after forward error correction (FEC) decoding is essential for system design in optical fiber communications. Generalized mutual information (GMI) has been shown to be successful at benchmarking the bit-error rate (BER) after FEC decoding (post-FEC BER) for systems with soft-decision (SD) FEC without probabilistic shaping (PS). However, GMI is not relevant to benchmark post-FEC BER for systems with SD-FEC and PS. For such systems, normalized GMI (NGMI), asymmetric information (ASI), and achievable FEC rate have been proposed instead. They are good at benchmarking post-FEC BER or to give an FEC limit in bit-interleaved coded modulation (BICM) with PS, but their relation has not been clearly explained so far. In this paper, we define generalized L-values under mismatched decoding, which are connected to the GMI and ASI. We then show that NGMI, ASI, and achievable FEC rate are theoretically equal under matched decoding but not under mismatched decoding. We also examine BER before FEC decoding (pre-FEC BER) and ASI over Gaussian and nonlinear fiber-optic channels with approximately matched decoding. ASI always shows better correlation with post-FEC BER than pre-FEC BER for BICM with PS. On the other hand, post-FEC BER can differ at a given ASI when we change the bit mapping, which describes how each bit in a codeword is assigned to a bit tributary.Comment: 14 pages, 8 figure

2048-QAM transmission at 15 GBd over 100 km using geometric constellation shaping

We experimentally investigated a pilot-aided digital signal processing (DSP) chain in combination with high-order geometric constellation shaping to increase the achievable information rates (AIRs) in standard intradyne coherent transmission systems. We show that the AIR of our system at 15 GBd was maximised using geometrically-shaped (GS) 2048 quadrature amplitude modulation (QAM), reaching 18.0 b/4D-symbol in back-to-back transmission and 16.9 b/4D-symbol after transmission through 100 km of a single-mode fibre after subtracting the pilot overhead (OH). This represents the highest-order GS format demonstrated to date, supporting the highest AIR of any standard intradyne system using conventional optics and 8-bit electronics. Detailed characterisation of the DSP, transceiver performance, and transmission modelling has also been carried out to provide insight into sources of impairments and directions for further improvement

Compensation of Laser Phase Noise Using DSP in Multichannel Fiber-Optic Communications

One of the main impairments that limit the throughput of fiber-optic communication systems is laser phase noise, where the phase of the laser output drifts with time. This impairment can be highly correlated across channels that share lasers in multichannel fiber-optic systems based on, e.g., wavelength-division multiplexing using frequency combs or space-division multiplexing. In this thesis, potential improvements in the system tolerance to laser phase noise that are obtained through the use of joint-channel digital signal processing are investigated. To accomplish this, a simple multichannel phase-noise model is proposed, in which the phase noise is arbitrarily correlated across the channels. Using this model, high-performance pilot-aided phase-noise compensation and data-detection algorithms are designed for multichannel fiber-optic systems using Bayesian-inference frameworks. Through Monte Carlo simulations of coded transmission in the presence of moderate laser phase noise, it is shown that joint-channel processing can yield close to a 1 dB improvement in power efficiency. It is further shown that the algorithms are highly dependent on the positions of pilots across time and channels. Hence, the problem of identifying effective pilot distributions is studied.The proposed phase-noise model and algorithms are validated using experimental data based on uncoded space-division multiplexed transmission through a weakly-coupled, homogeneous, single-mode, 3-core fiber. It is found that the performance improvements predicted by simulations based on the model are reasonably close to the experimental results. Moreover, joint-channel processing is found to increase the maximum tolerable transmission distance by up to 10% for practical pilot rates.Various phenomena decorrelate the laser phase noise between channels in multichannel transmission, reducing the potency of schemes that exploit this correlation. One such phenomenon is intercore skew, where the spatial channels experience different propagation velocities. The effect of intercore skew on the performance of joint-core phase-noise compensation is studied. Assuming that the channels are aligned in the receiver, joint-core processing is found to be beneficial in the presence of skew if the linewidth of the local oscillator is lower than the light-source laser linewidth.In the case that the laser phase noise is completely uncorrelated across channels in multichannel transmission, it is shown that the system performance can be improved by applying transmitter-side multidimensional signal rotations. This is found by numerically optimizing rotations of four-dimensional signals that are transmitted through two channels. Structured four-dimensional rotations based on Hadamard matrices are found to be near-optimal. Moreover, in the case of high signal-to-noise ratios and high signal dimensionalities, Hadamard-based rotations are found to increase the achievable information rate by up to 0.25 bits per complex symbol for transmission of higher-order modulations

Voronoi Constellations for Coherent Fiber-Optic Communication Systems

The increasing demand for higher data rates is driving the adoption of high-spectral-efficiency (SE) transmission in communication systems. The well-known 1.53 dB gap between Shannon\u27s capacity and the mutual information (MI) of uniform quadrature amplitude modulation (QAM) formats indicates the importance of power efficiency, particularly in high-SE transmission scenarios, such as fiber-optic communication systems and wireless backhaul links. Shaping techniques are the only way to close this gap, by adapting the uniform input distribution to the capacity-achieving distribution. The two categories of shaping are probabilistic shaping (PS) and geometric shaping (GS). Various methods have been proposed for performing PS and GS, each with distinct implementation complexity and performance characteristics. In general, the complexity of these methods grows dramatically with the SE and number of dimensions.Among different methods, multidimensional Voronoi constellations (VCs) provide a good trade-off between high shaping gains and low-complexity encoding/decoding algorithms due to their nice geometric structures. However, VCs with high shaping gains are usually very large and the huge cardinality makes system analysis and design cumbersome, which motives this thesis.In this thesis, we develop a set of methods to make VCs applicable to communication systems with a low complexity. The encoding and decoding, labeling, and coded modulation schemes of VCs are investigated. Various system performance metrics including uncoded/coded bit error rate, MI, and generalized mutual information (GMI) are studied and compared with QAM formats for both the additive white Gaussian noise channel and nonlinear fiber channels. We show that the proposed methods preserve high shaping gains of VCs, enabling significant improvements on system performance for high-SE transmission in both the additive white Gaussian noise channel and nonlinear fiber channel. In addition, we propose general algorithms for estimating the MI and GMI, and approximating the log-likelihood ratios in soft-decision forward error correction codes for very large constellations