Research Status and Progress of Probabilistic Shaping Techniques in Optical Communication

Xiang Liu; Jiao Zhang; Min Zhu; Bingchang Hua; Yuancheng Cai; Mingzheng Lei; Yucong Zou; Aijie Li

doi:10.3788/LOP202259.1100004

Laser & Optoelectronics Progress, Volume. 59, Issue 11, 1100004(2022)

Research Status and Progress of Probabilistic Shaping Techniques in Optical Communication

Xiang Liu^1,2, Jiao Zhang^1,2、*, Min Zhu^1,2、**, Bingchang Hua², Yuancheng Cai^1,2, Mingzheng Lei², Yucong Zou², and Aijie Li²

Author Affiliations

¹National Mobile Communication Research Laboratory, Southeast University, Nanjing 210096, Jiangsu , China

²Purple Mountain Laboratories, Nanjing 211111, Jiangsu , China

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Abstract Get PDF(in Chinese)

Figures & Tables(22)

Fig. 1. Capacity of the ideal AWGN channel with Gaussian inputs and with equiprobable $M$ -PAM inputs^[5]

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Fig. 2. 16QAM probabilistic shaping. (a) 16QAM; (b) PS-16QAM

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Fig. 3. Schematic diagram of PS-16QAM probabilistic shaping. (a) Probability distribution; (b) signal constellation

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Fig. 4. Basic framework of probabilistic shaping technology

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Fig. 5. System symbols and performance indicators^[74-76]

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Fig. 6. CCDM implementation block diagram^[23]. (a) Principle block diagram; (b) schematic drawings

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Fig. 7. PS-8ASK with three parameter values $v$

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Fig. 8. Effect of changing shaping factor $v$ on GMI of transmitted and received symbols

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Fig. 9. Arithmetic coding probabilistic shaping scheme. (a) PAS scheme^[24]; (b) PDM /MPDM scheme^[49]; (c) 2D-DM scheme^[56]

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Fig. 10. Influence degree of arithmetic coding probabilistic shaping scheme index

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Fig. 11. Arithmetic coding PS performance parameter index comparison

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Fig. 12. Performance chart^[28]. (a) AIR and SNR; (b) FER and SNR

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Fig. 13. Symbol-level labeling PS scheme. (a) Outer maps to the inner layer^[64]; (b) set partition^[60-61]

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Fig. 14. Schematic of probabilistic shaping based on symbol-level labeling^[9]

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Fig. 15. Non-uniform signal designed for PS scheme. (a) Huffman code^[66] ; (b) bisection-based^[67]

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Table 1. Comparison of characteristics and shortcomings of AC probabilistic shaping scheme

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Table 1. Comparison of characteristics and shortcomings of AC probabilistic shaping scheme

AC shaping scheme		Ref.	Characteristic	Shortcoming
Serial structure	CCDM	［23］	Lower complexity，asymptotically optimal	High latency，rate loss
Serial structure	PAS	［24］	Rate adaption，lower BER	High complexity，rate loss
Parallel structure	PDM	［44］	High throughput，lower complexity	A gap to the MB distribution
	MPDM	［49］	Flexible output composition，lower rate loss	High hardware requirements
	MDDM	［56］	Approaching MB，multi-dimensional	High hardware requirements

Table 2. PAS related parameter rate
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Table 2. PAS related parameter rate
Signal $R_{p s}$ $R_{f e c}$ $η = m R_{p s} R_{f e c}$
$2^{m}$ -ASK $\frac{R_{d m} \cdot (m - 1) + γ}{m - 1 + γ}$ $\frac{m - 1 + γ}{m}$ $R_{d m} \cdot (m - 1) + γ$
$2^{m}$ -QAM $\frac{R_{d m} \cdot (m - 2) + 2 γ}{m - 2 + 2 γ}$ $\frac{m - 2 + 2 γ}{m}$ $R_{d m} \cdot (m - 2) + 2 γ$
$2^{m}$ -ND $\frac{R_{d m} \cdot (m - N) + N γ}{m - N + N γ}$ $\frac{m - N + N γ}{m}$ $R_{d m} \cdot (m - N) + N γ$

Table 3. Gaps of uniform ASK and PS to capacity C

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Table 3. Gaps of uniform ASK and PS to capacity C

Constellation	Rate /bit	Capacity C SNR /dB	Uniform SNR /dB	Gap /dB	$X^{Ω}$ SNR /dB	Gap /dB	Shaping gain /dB
4-ASK	1	4.7712	5.1181	0.3469	4.8180	0.0468	0.3001
8-ASK	2	11.7609	12.6187	0.8578	11.8425	0.0816	0.7762
16-ASK	3	17.9934	19.1681	1.1747	18.0910	0.0976	1.0771
32-ASK	4	24.0654	25.4140	1.3486	24.1706	0.1052	1.2434
64-ASK	5	30.0988	31.5384	1.4396	30.2078	0.1090	1.3306

Table 4. Rate loss under different block length n

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Table 4. Rate loss under different block length n

Architecture	$k$	$k / n$	$H (\tilde{A}) / H (\bar{A})$	$R_{l o s s}$
CCDM/PAS	367	1.6991	1.7490	0.0499
	367	2.2378	2.3132	0.0754
	367	6.7963	6.9523	0.1560
MPDM	374	1.7315	1.7490	0.0175
	374	2.2262	2.2727	0.0465
	374	6.9259	6.9913	0.0654
Sphere	374	1.7315	1.7459	0.0133
	374	2.2262	2.2496	0.0234
	374	6.9259	6.9684	0.0425

Table 5. Research of PS technology in optical fiber transmission system

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Table 5. Research of PS technology in optical fiber transmission system

Optical fiber transmission system
Ref.	Institution	Signal	Distance /km	Rate	Characteristic
［19］	University of Arizona	8/16/32QAM	100	12.5 Gbaud	Superior performance
［29］	Beijing University of Posts and Telecommunications	PAM8	2	28 Gb/s	Low complexity and improve BER
［33］	Technical University of Munich	16/64QAM	B2B	-	Higher sensitivity gains and close to the gap to capacity
［34］	Huazhong University of Science and Technology	256QAM	75	50.2 Gb/s	Superior net date rate and suitable for multicarrier systems
［71］	Fudan University	32QAM	1	108.29 Gb/s	Better receiver sensitivity gain
［83］	Huaqiao University	PAM8	20	16.8 Gbaud	Fewer PS redundancy
［84］	Huawei Technologies/China Telecom Beijing Research Institute	16QAM	1142	200 Gb/s	Real-time and improve performance，energy-efficiency

Table 6. Research of PS technology in ROF transmission system

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Table 6. Research of PS technology in ROF transmission system

ROF transmission system
Ref.	Institution	Signal	Distance /m	Rate /（Gb·s^-1）	Characteristic
［51］	Zhejiang University	16QAM-OFDM	20	>100	Ultrahigh data rate
［54］	Hunan University	64QAM	0.5	1.81	Flexibility and small capacity granularity
［85］	Fudan University	512QAM、128QAM	1	208.4	Increase the maximal AIR
［86］	Beijing University of Posts and Telecommunications	16QAM	40	12.144	BER performance，higher bit rate
［87］	University of Antioquia	8/16QAM	-	10	Better performance、longer transmission distance
［88］	Georgia Institude of Technology	16QAM-OFDM	4	25.9	First experimental demonstration

Table 7. Research of PS technology in VLC transmission system

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Table 7. Research of PS technology in VLC transmission system

VLC transmission system
Ref.	Tx	Rx	Signal	Rate	Institution
［40］	LED	PD	PAM4	2 Gb/s	Beijing University of Posts and Telecommunications
［90］	LED	PD	256QAM	204.1 Mb/s	Huazhong University of Science and Technology
［91］	LED	PD	64QAM	50.75 Mb/s	University of Shanghai for Science and Technology
［92］	LD	APD	DMT	10.23 Gb/s	National Taiwan University/Fudan University
［93］	LED	PIN	16QAM	1.70 Gb/s	Fudan University

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Xiang Liu, Jiao Zhang, Min Zhu, Bingchang Hua, Yuancheng Cai, Mingzheng Lei, Yucong Zou, Aijie Li. Research Status and Progress of Probabilistic Shaping Techniques in Optical Communication[J]. Laser & Optoelectronics Progress, 2022, 59(11): 1100004

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