Sebastiaan Goossens, Sjoerd van der Heide, Menno van den Hout, Abdelkerim Amari, Yunus Can Gültekin, Olga Vassilieva, Inwoong Kim, Tadashi Ikeuchi, Frans M. J. Willems, Alex Alvarado, Chigo Okonkwo
We transmit probabilistic enumerative sphere shaped dual-polarization 64-QAM at 350Gbit/s/channel over 1610km SSMF using a short blocklength of 200. A reach increase of 15% over constant composition distribution matching with identical blocklength is demonstrated.
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We show that a 0.9 dB SNR improvement can be obtained via short-blocklength enumerative sphere shaping for single-span transmission at 56 GBd. This gain vanishes for higher symbol rates and a larger number of spans.
The performance of enumerative sphere shaping (ESS), constant composition distribution matching (CCDM), and uniform signalling are compared at the same forward error correction rate. ESS is shown to offer a reach increase of approximately 10% and 22% compared to CCDM and uniform signalling, respectively.
The effect of decreasing the kurtosis of channel inputs is investigated for the first time with an algorithmic shaping implementation. No significant gains in decoding performance are observed for multi-span systems, while an increase in reach is obtained for single-span transmission.
Introducing RSESS: An Open Source Enumerative Sphere Shaping Implementation Coded in Rust
本文提出了用于概率星座整形（PCS）的枚举球面整形（ESS）算法的 Rust 开源实现及 Python 绑定，并在 AWGN 信道上验证了其性能。
We study the effective SNR behavior of various enumerative amplitude shaping algorithms. We show that their relative behavior can be explained via the temporal autocorrelation function or via the energy dispersion index.
Probabilistic amplitude shaping (PAS) is on track to become the de facto coded modulation standard for communication systems aiming to operate close to channel capacity at high transmission rates. The essential component of PAS that breeds this widespread interest is the amplitude shaping block, through which the channel input distribution is controlled. This block is responsible for converting bit strings into amplitude sequences with certain properties, e.g., fixed composition, limited energy, limited energy variation, etc. Recently, band-trellis enumerative sphere shaping (B-ESS) was introd…
The dependency between the Gaussianity of the input distribution for the additive white Gaussian noise (AWGN) channel and the gap-to-capacity is discussed. We show that a set of particular approximations to the Maxwell-Boltzmann (MB) distribution virtually closes most of the shaping gap. We relate these symbol-level distributions to bit-level distributions, and demonstrate that they correspond to keeping some of the amplitude bit-levels uniform and independent of the others. Then we propose partial enumerative sphere shaping (P-ESS) to realize such distributions in the probabilistic amplitude …
Probabilistic amplitude shaping (PAS) combines an outer shaping layer with an inner, systematic forward error correction (FEC) layer to close the shaping gap. Proposed for PAS, constant composition distribution matching (CCDM) produces amplitude sequences with a fixed empirical distribution. We show that CCDM suffers from high rate losses for small block lengths, and we propose to use Enumerative Sphere Shaping (ESS) instead. ESS minimizes the rate loss at any block length. Furthermore, we discuss the computational complexity of ESS and demonstrate that it is significantly smaller than shell m…
Adaptive Probabilistic Constellation Shaping based on Enumerative Sphere Shaping for FSO Channel with Turbulence and Pointing Errors
本文提出一种基于枚举球形整形的自适应概率星座整形技术，通过提升频谱利用和控制精度，在湍流和指向误差环境下实现高可靠性通信。
Multi-dimensional Energy Limitation in Sphere Shaping for Nonlinear Interference Noise Mitigation
本文提出四维能量限制的枚举球形整形方法，用于降低速率损失并抑制非线性干扰，在单跨段和WDM仿真中比传统ESS提升0.19 bit/4D-symbol，但增益在多跨段系统中扩展性有限。
Band-trellis enumerative sphere shaping is proposed to decrease the energy variations in channel input sequences. Against sphere shaping, 0.74 dB SNR gain and up to 9% increase in data rates are demonstrated for single-span systems.
Compressed Shaping: Concept and FPGA Demonstration
本文提出结合数据压缩与概率成形的压缩成形技术，利用非均匀信源降低信道输入符号熵，并通过仿真和 FPGA 实现验证其可显著降低 FEC 解码功耗。
In this paper, we study amplitude shaping schemes for the probabilistic amplitude shaping (PAS) framework as well as algorithms for constant-composition distribution matching (CCDM). Huffman-coded sphere shaping (HCSS) is discussed in detail, which internally uses Huffman coding to determine the composition to be used and relies on conventional CCDM algorithms for mapping and demapping. Numerical simulations show that HCSS closes the performance gap between distribution matching schemes and sphere shaping techniques such as enumerative sphere shaping (ESS). HCSS is based on an architecture tha…
Nonlinear interference (NLI) generated during the propagation of an optical waveform through the fiber depends on the fourth order standardized moment of the channel input distribution, also known as kurtosis. Probabilistically-shaped inputs optimized for the linear Gaussian channel have a Gaussian-like distribution with high kurtosis. For optical channels, this leads to an increase in NLI power and consequently, a decrease in effective signal-to-noise ratio (SNR). In this work, we propose kurtosis-limited enumerative sphere shaping (K-ESS) as an algorithm to generate low-kurtosis shaped input…
In this paper, we provide for the first time 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. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining t…
Intensity Fluctuation Spectra as a Design Guide for Nonlinear-Tolerant Constellation Shaping
本文提出了一种统一框架，通过强度波动谱与星座塑形的块级能量统计关联，为非线性容忍的高速率WDM系统设计提供了降低低频内容的指导。
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