Partial Enumerative Sphere Shaping

Gültekin, Yunus Can; Houtum, W.J. van; Koppelaar, Arie; Willems, F.M.J.

doi:10.1109/vtcfall.2019.8891195

Cited by 8 publications

(6 citation statements)

References 13 publications

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“…1 (b) assumes a FEC rate of R c = (m − 1)/m. Lower FEC rates can be used if the bit-level shaping schemes in [36], [41] are considered. Higher FEC code rates (R c > (m − 1)/m) can be used via a straightforward modification of the PAS architecture.…”

Section: B Nonuniform Signalingmentioning

confidence: 99%

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Amari

Goossens

Gültekin

et al. 2019

J. Lightwave Technol.

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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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Section: B Nonuniform Signalingmentioning

confidence: 99%

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Amari

Goossens

Gültekin

et al. 2019

J. Lightwave Technol.

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“…Since symbol-level shaping strategies determine

amplitude bits prior to FEC encoding, they can only be combined with FEC code rates

. To employ lower FEC code rates

, bit-level shaping strategies which only determine a subset of

amplitude bits should be employed as in [ 51 , 57 , 73 ]. To use a higher FEC code rate

, a modified PAS architecture is proposed in [ 28 ] as shown in Figure 3 (bottom).…”

Section: Signaling Schemesmentioning

confidence: 99%

“…The authors of [ 72 ] provided a finite-precision implementation for AC-CCDM. In [ 73 ], a shaper based on ESS was introduced to shape a subset of the amplitude bit-levels, which is referred to as partial ESS. The authors of [ 74 ] introduced the “hierarchical” DM which realizes a nonuniform distribution with hierarchical lookup tables (LUTs) [ 75 ].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

Gültekin

Fehenberger

Alvarado

et al. 2020

Entropy

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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.

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“…The authors of [72] provided a finite-precision implementation for AC-CCDM. In [73], a shaper based on ESS was introduced to shape a subset of the amplitude bit-levels, which is referred to as partial ESS (P-ESS). The authors of [74] introduced the "hierarchical" DM which realizes a nonuniform distribution with hierarchical LUTs.…”

Section: Introductionmentioning

confidence: 99%

“…Since symbol-level shaping strategies determine m − 1 amplitude bits prior to FEC encoding, they can only be combined with FEC code rates Rc ≥ (m − 1)/m. To employ lower FEC code rates Rc < (m − 1)/m, bit-level shaping strategies which only determine a subset of m − 1 amplitude bits should be employed as in[51],[57],[73].…”

mentioning

confidence: 99%

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

Gültekin,

Fehenberger,

Alvarado

et al. 2019

Preprint

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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 the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multisetpartition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh 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. We provide simulation results of the end-toend 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 perspective of latency, storage and computations.

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Partial Enumerative Sphere Shaping

Cited by 8 publications

References 13 publications

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

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