Probabilistic shaping: a step closer to the Shannon limit in channel capacity for optical communications

Shu, Chester; Zhang, Qiulin; Shatin, N.T.

doi:10.1049/el.2020.2505

“…The relationships between EPCS and ν for 64QAM, 256QAM and 1024QAM, i.e., M = 4, 8, and 16, respectively, and with different code-rates. The amplitudes are shaped according to the pmf in(14). The two expressions of approximation in(27) are plotted with dashed cyan and red curves, which can be seen to be close to the true values.…”

mentioning

confidence: 79%

“…■ Property 4 put a stringent constraint on how much entropy-loss can be tolerated with the PCS scheme, in order to outperform a conventional approach in throughput. Since typically the target BLER is set to P b ≤ 10% in NR, this means that with PCS δ H should not be higher than 10%, and this limits the parameter ν in (14). When P b is large, δ H can increase.…”

Section: A a Necessary Conditionmentioning

confidence: 99%

“…The idea of using Gaussian signaling in modulation can be traced back to 1980s, proposed by G. D. Forney in his seminal papers [3]- [5], which is simpler than the trellis coded modulation (TCM) [6]. Since then, techniques of improving modulation have been extensively studied in literature inducing probabilistic constellation shaping (PCS) [7]- [10], geometrical constellation shaping (GCS) [11]- [14], and probabilistic amplitude shaping (PAS) [15]- [17]. PCS produces a QAM constellation whose transmission probabilities of different constellation symbols obey a predetermined Gaussian distribution, and is applied to reduce the gap between the capacity and the achievable rate.…”

Section: Introductionmentioning

confidence: 99%

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Supporting Probabilistic Constellation Shaping in 5G-NR

Hu¹,

Wang²,

Semnov³

2022

Preprint

1

0

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In this paper, we consider applying probabilistic constellation shaping (PCS) to the fifth-generation new-radio (5G-NR) system. We propose a practical PCS transceiver design which is fully backward compatible to the existing 5G-NR system, and can bring significant improvements in block-error rate (BLER) and throughput. Further, we derive the properties of average-power, entropy-loss, and peak-to-average power-ratio (PAPR) increment in connection to the proposed PCS design. We show that an effective PCS can set the variance of a zero-mean Gaussian distribution for shaping to be around 0.5,making both the PAPR-increment and the entropy-loss to be at acceptable levels. Furthermore, we derive a necessary condition for PCS to attain a higher throughput than a uniform constellation. It shows that the normalized entropy-loss with PCS must be smaller than the BLER attained from transmissions with a uniform constellation. This is a critical observation and provides an important insight for the PCS design. Moreover, we also illustrate that the proposed PCS scheme can provide additional flexibilities in adjusting the effective code-rate without affecting the encoder. As a result, transitions among different MCSs can be smoother even with an adaptive modulation and coding scheme (MCS), and a better throughput-envelope can be obtained as signal-to-noise ratio (SNR) changes.

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“…The pmfs are specified according to (14), and for fair comparisons among different code-rates, we adjust ν, instead of ν, in all simulations. In addition, we use a heuristic adjustment to make all values N m to be integers, which sets N m = ⌊N p m ⌋.…”

Section: A Simulation Setupsmentioning

confidence: 99%

Supporting Probabilistic Constellation Shaping in 5G-NR Evolution

Hu¹,

Wang²,

Semnov³

2022

Preprint

0

View full text Add to dashboard Cite

In this paper, we consider applying probabilistic constellation shaping (PCS) to the fifth-generation new-radio (5G-NR) system. We propose a practical PCS transceiver design which is fully backward compatible to the existing 5G-NR system, and can bring significant improvements in block-error rate (BLER) and throughput. Further, we derive the properties of average-power, entropy-loss, and peak-to-average power-ratio (PAPR) increment in connection to the proposed PCS design. We show that an effective PCS can set the variance of a zero-mean Gaussian distribution for shaping to be around 0.5,making both the PAPR-increment and the entropy-loss to be at acceptable levels. Furthermore, we derive a necessary condition for PCS to attain a higher throughput than a uniform constellation. It shows that the normalized entropy-loss with PCS must be smaller than the BLER attained from transmissions with a uniform constellation. This is a critical observation and provides an important insight for the PCS design. Moreover, we also illustrate that the proposed PCS scheme can provide additional flexibilities in adjusting the effective code-rate without affecting the encoder. As a result, transitions among different MCSs can be smoother even with an adaptive modulation and coding scheme (MCS), and a better throughput-envelope can be obtained as signal-to-noise ratio (SNR) changes.

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“…As can be seen, the transmission-probability decreases as the amplitude of a constellation symbol increases. GCS [10]- [13], on the other hand, keeps the transmission-probabilities uniform, but the geometrical locations of constellation symbols are shaped to be Gaussian. A widely applied shaping technique that has been commercialized in optical and fiber systems [14]- [16], is PAS, which is also a special case of PCS.…”

Section: Introductionmentioning

confidence: 99%

Supporting Probabilistic Constellation Shaping in 5G-NR Evolution

Hu¹,

Wang²,

Semnov³

2022

Preprint

0

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It is well-known that probabilistic constellation shaping (PCS) provides a shaping-gain of 1.53dB asymptotically as signal-to-noie (SNR) increases. This is however, under ideal assumptions that the considered system operates in optimal sense and can achieve the Shannon capacity. While in practice the system can operate below the capacity, and in particular when block-error rate (BLER) and throughput are considered which are the most relevant merits, the benefits of PCS are unclear. In this paper, we propose a PCS-transceiver for the fifth-generation new-radio (5G-NR) that supports quadrature-amplitude-modulation (QAM) constellations shaped with PCS, namely, PCS-QAM. We put a special interest in the throughput achieved under a stringent BLER constraint, and validate the effectiveness of PCS with practical detection and decoding algorithms, in comparison to conventional uniform QAM constellations, namely, Uniform-QAM. We also analyze the properties of power-gain, entropy-loss, and peak-to-average power-ratio (PAPR), in connections to the PCS design. Further, we derive a necessary and sufficient condition for a PCS-QAM to outperform a Uniform-QAM in throughput, and prove that the normalized entropy-loss with the PCS-QAM must be less than the BLER obtained with the Uniform-QAM. Furthermore, we demonstrate that the PCS-transceiver is flexible in rate-adaption without affecting the encoder, and yields a better throughput-envelope by mitigating the SNR-gaps between two adjacent modulation and coding scheme (MCS) indexes in 5G-NR.

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Probabilistic shaping: a step closer to the Shannon limit in channel capacity for optical communications

Cited by 12 publications

References 7 publications

Supporting Probabilistic Constellation Shaping in 5G-NR

Supporting Probabilistic Constellation Shaping in 5G-NR

Supporting Probabilistic Constellation Shaping in 5G-NR Evolution

Supporting Probabilistic Constellation Shaping in 5G-NR Evolution

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