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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In this paper, we provide a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. However, as the blocklength decreases, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths over the additive white Gaussian noise (AWGN) channel, the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM) and SpSh are reviewed as energy-efficient shaping techniques. Numerical results show that both have smaller rate losses than CCDM. SpSh—whose sole objective is to maximize the energy efficiency—is shown to have the minimum rate loss amongst all, which is particularly apparent for ultra short blocklengths. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspectives of latency, storage and computations.

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: