Coding Based on Large⁃Scale SPAD Array Ranging Application

Fig. 3. Simulation results of code structure and correlation characteristics of each sequence. (a) m-sequence; (b) Chebyshev sequence; (c) Tent sequence; (d) Logistic sequence; (e) improved Logistic sequence

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Fig. 4. Lyapunov exponent of improved Logistic mapping before and after concatenation

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Fig. 5. Variation of autocorrelation PSLD and cross-correlation PSLD in composite Logistic sequence. (a) Difference between autocorrelated PSLD and sum of cross-correlated PSLDs; (b) distribution of sum of cross-correlated PSLDs

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Table 1. Mapping method and binarization threshold of four chaotic sequences^[15]

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Table 1. Mapping method and binarization threshold of four chaotic sequences^[15]

Sequence type	Mapping method	Probability density function	Threshold	Remark
Chebyshev sequence	$x_{n + 1} = c o s [p a r c c o s (x_{n})],$ x_n∈（-1，1）	$ρ (x) = \{\begin{matrix} \frac{1}{π \sqrt[]{1 - x^{2}}}, & - 1 < x < 1 \\ 0, & o t h e r w i s e \end{matrix}$	0	Symbol p denotes an integer greater than or equal to 2
Tent sequence	$x_{n + 1} = \{\begin{matrix} \frac{x_{n}}{a}, & 0 < x_{n} < a \\ \frac{1 - x_{n}}{1 - a}, & a \leq x_{n} \leq 1 \end{matrix}$	$ρ (x) = \{\begin{matrix} 1, & 0 < x < 1 \\ 0, & o t h e r w i s e \end{matrix}$	0.5	Probability density is the distribution of standard type mapping，where $a = 0.5$
Logistic sequence	$x_{n + 1} = μ x_{n} (1 - x_{n}), x_{n} \in (0,1)$	$ρ (x) = \{\begin{matrix} \frac{1}{π \sqrt[]{x (1 - x)}}, & 0 < x < 1 \\ 0, & o t h e r w i s e \end{matrix}$	0.5	Probability density is the distribution of full mapping，where $μ = 4$
Improved Logistic sequence	$x_{n + 1} = 1 - λ x_{n}^{2}, x_{n} \in (- 1,1)$	$ρ (x) = \{\begin{matrix} \frac{1}{π \sqrt[]{1 - x^{2}}}, & - 1 < x < 1 \\ 0, & o t h e r w i s e \end{matrix}$	0	Probability density is the distribution of full mapping，where $λ = 2$

Table 2. Variation of normalized PSLD of different sequences with distance (code length)

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Table 2. Variation of normalized PSLD of different sequences with distance (code length)

Sequence type	Normalized PSLD
	R_max=2.45 km（N_L=16383）		R_max=4.9 km（N_L=32767）		R_max=9.8 km（N_L=65535）
	Autocorrelation	Cross- correlation/10^-4	Autocorrelation	Cross- correlation/10^-4	Autocorrelation	Cross- correlation/10^-4
m-sequence	0.9912	18.9221	0.9933	3.9674	0.9852	1.9837
Chebyshev sequence	0.9709	6.7139	0.9792	14.0381	0.9855	27.6184
Tent sequence	0.9717	4.2725	0.9806	2.7466	0.9844	6.5440
Logistic sequence	0.9759	34.7900	0.9751	18.9209	0.9850	10.0708
Improved Logistic sequence	0.9737	12.8174	0.9810	4.8828	0.9852	3.2043

Table 3. Normalized PSLD distribution under different array sizes

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Table 3. Normalized PSLD distribution under different array sizes

Sequence type	Quantity of sequences $S$	Difference between maximum and minimum autocorrelation PSLD $d$	Mean value of cross‑ correlation PSLD $μ$
Improved Logistic sequence	10	$2.6 \times 10^{- 3}$	$9.3534 \times 10^{- 4}$
	50	$5.6 \times 10^{- 3}$	$8.4719 \times 10^{- 4}$
	100	$5.6 \times 10^{- 3}$	$8.6157 \times 10^{- 4}$
	200	$5.6 \times 10^{- 3}$	$8.5650 \times 10^{- 4}$
Cascaded Logistic sequence	10	$4.9 \times 10^{- 3}$	$9.4681 \times 10^{- 4}$
	50	$4.9 \times 10^{- 3}$	$8.6456 \times 10^{- 4}$
	100	$5.1 \times 10^{- 3}$	$8.5553 \times 10^{- 4}$
	200	$6.2 \times 10^{- 3}$	$8.5583 \times 10^{- 4}$
Composite Logistic sequence	10	$4.2 \times 10^{- 3}$	$10.0000 \times 10^{- 4}$
	50	$6.5 \times 10^{- 3}$	$9.0926 \times 10^{- 4}$
	100	$9.1 \times 10^{- 3}$	$9.1483 \times 10^{- 4}$
	200	$9.6 \times 10^{- 3}$	$9.1799 \times 10^{- 4}$

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Qingyu Pan, Chao Wang, Jiawei Ren, Dapeng Wang, Yijun Zhu. Coding Based on Large⁃Scale SPAD Array Ranging Application[J]. Chinese Journal of Lasers, 2023, 50(19): 1906004

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Paper Information

Category: Fiber optics and optical communication

Received: Aug. 29, 2022

Accepted: Oct. 21, 2022

Published Online: Oct. 18, 2023

The Author Email: Wang Chao (xxgcwangchao@163.com)

DOI:10.3788/CJL221187

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Mapping method and binarization threshold of four chaotic sequences[15]

Table 1. Mapping method and binarization threshold of four chaotic sequences[15]

Table 2. Variation of normalized PSLD of different sequences with distance (code length)

Table 2. Variation of normalized PSLD of different sequences with distance (code length)

Table 3. Normalized PSLD distribution under different array sizes

Table 3. Normalized PSLD distribution under different array sizes

Table 1. Mapping method and binarization threshold of four chaotic sequences^[15]

Table 1. Mapping method and binarization threshold of four chaotic sequences^[15]