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Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping
Entropy ( IF 2.7 ) Pub Date : 2020-05-21 , DOI: 10.3390/e22050581
Yunus Can Gültekin , Tobias Fehenberger , Alex Alvarado , Frans M. J. Willems

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.

中文翻译:

有限块长度的概率整形:分布匹配和球面整形

在本文中,我们对用于短块长度概率幅度整形的分布匹配 (DM) 和球体整形 (SpSh) 算法进行了系统比较。对于渐近大块长度,已知恒定成分分布匹配 (CCDM) 可生成目标容量实现分布。然而,随着块长度的减少,由此产生的速率损失会降低 CCDM 的效率。我们声称,对于加性高斯白噪声 (AWGN) 信道上的如此短的块长度,整形的目标应该重新表述为在给定速率(而不是匹配分布)下获得最节能的信号空间。根据这种解释,多组分区 DM (MPDM) 和 SpSh 被视为节能整形技术。数值结果表明,两者的速率损失都比 CCDM 小。SpSh——其唯一目标是最大限度地提高能量效率——被证明具有最小的速率损失,这对于超短块长度尤为明显。我们提供了端到端解码性能的仿真结果,表明使用 MPDM 和 SpSh 在块长度约为 200 的情况下,与统一信令相比,功率效率可提高多达 1 dB。 最后,我们讨论了这些算法的复杂性从延迟、存储和计算的角度来看。
更新日期:2020-05-21
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