Approaching waterfilling capacity of parallel channels by higher order modulation and probabilistic amplitude shaping

Steiner, Fabian; Schulte, Patrick; Böcherer, Georg

doi:10.1109/ciss.2018.8362291

Cited by 31 publications

(35 citation statements)

References 17 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.

View full text Add to dashboard Cite

show abstract

“…2. We note here that a similar gap-to-capacity analysis is provided for product distributions 2 in [9]. Next, we will build an amplitude shaping block to realize output distributions resembling the approximate distributions in (5).…”

Section: B Partially Maxwell-boltzmann-distributed Inputsmentioning

confidence: 96%

Partial Enumerative Sphere Shaping

Gültekin

Houtum²,

Koppelaar

et al. 2019

2019 IEEE 90th Vehicular Technology Conference (VTC2019-Fall)

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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 shaping (PAS) framework. Simulations over the AWGN channel exhibit that shaping 2 amplitude bits of 16-ASK have almost the same performance as shaping 3 bits, which is 1.3 dB more powerefficient than uniform signaling at a rate of 3 bit/symbol. In this way, required storage and computational complexity of shaping are reduced by factors of 6 and 3, respectively.

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“…However, this requires a prohibitively complex hardware implementation. Recently, several attempts have been made to find a better balance between performance and complexity [31]- [35], [38]- [44]. In [38], [39], fixedlength to fixed-length conversion was used, which is simple enough to implement, but the performance is limited.…”

Section: Implementation Issuesmentioning

confidence: 99%

“…In [42]- [44], separate DM is applied to each modulation bit level for efficient implementation, and bit-wise DM like [37], [39], [41] can be combined with it. Its performance mainly depends on the bit-wise DM, and it is also useful for approaching the water-filling capacity on transmission over parallel channels having different SNRs [43]- [45].…”

Section: Implementation Issuesmentioning

confidence: 99%

Hierarchical Distribution Matching for Probabilistically Shaped Coded Modulation

Yoshida

Karlsson

Agrell

2019

J. Lightwave Technol.

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The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the FEC coding and decoding lies inside the shaping algorithms. PS can seemingly achieve performance close to the Shannon limit, although there are practical implementation challenges that need to be carefully addressed. We propose a hierarchical DM (HiDM) scheme, having fully parallelized input/output interfaces and a pipelined architecture that can efficiently perform the DM/invDM without the complex operations of previously proposed methods such as constant composition DM (CCDM). Furthermore, HiDM can operate at a significantly larger post-FEC bit error rate (BER) for the same post-invDM BER performance, which facilitates simulations. These benefits come at the cost of a slightly larger rate loss and required signal-to-noise ratio at a given post-FEC BER.

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Approaching waterfilling capacity of parallel channels by higher order modulation and probabilistic amplitude shaping

Cited by 31 publications

References 17 publications

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Partial Enumerative Sphere Shaping

Hierarchical Distribution Matching for Probabilistically Shaped Coded Modulation

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