Marked Multi-Layer Optical Spatial Pulse Position Modulation

Input bits $(b_{1} b_{2})$	Mapping symbol
	1st layer		2nd layer
	$s_{1}$	$u_{1}$	$s_{2}$	$u_{2}$
000 000	${[\begin{matrix} 1 & 0 & \begin{matrix} 0 & 0 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} A & 0 & \begin{matrix} A & 0 \end{matrix} \end{matrix}]$	${[\begin{matrix} 0 & 1 & \begin{matrix} 0 & 0 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} 0 & A & \begin{matrix} A & 0 \end{matrix} \end{matrix}]$
000 001	${[\begin{matrix} 1 & 0 & \begin{matrix} 0 & 0 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} A & 0 & \begin{matrix} A & 0 \end{matrix} \end{matrix}]$	${[\begin{matrix} 0 & 1 & \begin{matrix} 0 & 0 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} 0 & A & \begin{matrix} 0 & A \end{matrix} \end{matrix}]$
000 010	${[\begin{matrix} 1 & 0 & \begin{matrix} 0 & 0 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} A & 0 & \begin{matrix} A & 0 \end{matrix} \end{matrix}]$	${[\begin{matrix} 0 & 0 & \begin{matrix} 1 & 0 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} 0 & A & \begin{matrix} A & 0 \end{matrix} \end{matrix}]$
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
111 101	${[\begin{matrix} 0 & 0 & \begin{matrix} 0 & 1 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} A & 0 & \begin{matrix} 0 & A \end{matrix} \end{matrix}]$	${[\begin{matrix} 0 & 0 & \begin{matrix} 1 & 0 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} 0 & A & \begin{matrix} 0 & A \end{matrix} \end{matrix}]$
111 110	${[\begin{matrix} 0 & 0 & \begin{matrix} 0 & 1 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} A & 0 & \begin{matrix} 0 & A \end{matrix} \end{matrix}]$	${[\begin{matrix} 0 & 0 & \begin{matrix} 0 & 0 & 1 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} 0 & A & \begin{matrix} A & 0 \end{matrix} \end{matrix}]$
111 111	${[\begin{matrix} 0 & 0 & \begin{matrix} 0 & 1 & 0 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} A & 0 & \begin{matrix} 0 & A \end{matrix} \end{matrix}]$	${[\begin{matrix} 0 & 0 & \begin{matrix} 0 & 0 & 1 \end{matrix} \end{matrix}]}^{T}$	$[\begin{matrix} 0 & A & \begin{matrix} 0 & A \end{matrix} \end{matrix}]$

Table 2. Computational complexities of ML and SD algorithms
View table
Table 2. Computational complexities of ML and SD algorithms
Decoding algorithm Total complexity
ML $(N_{S S K}^{2} + \dots + N_{S S K}^{L})$ · $(L K)$ · $[2 N_{t} N_{r} (L + K) + 2 N_{r} (L + K) - 1]$
SD $(N_{S S K}^{2} + \dots + N_{S S K}^{L})$ · $(L K)$ · $[2 N_{t} N_{r} (L + K) + N_{r} (L + K) - 1]$

Table 3. Spectral efficiency and transmission rate of different OSM schemes

View table

Table 3. Spectral efficiency and transmission rate of different OSM schemes

Modulation scheme	Spectral efficiency /（bit·s^-1·Hz^-1）	Transmission rate /bpcu
K-SPPM^［10］	$l b (N_{t} K) / K$	$l b (N_{t} K)$
K-GSPPM^［11］	$[⌊l b C_{N_{t}}^{2}⌋ + 2 l b K] / K$	$⌊l b C_{N_{t}}^{2}⌋ + 2 l b K$
（L，K）-MMLOSPPM	$L l b (K N_{S S K}) / (L + K)$	$L l b (K N_{S S K})$

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Huiqin Wang, Guiqing Ye, Qingbin Peng, Zhongxian Bao, Minghua Cao. Marked Multi-Layer Optical Spatial Pulse Position Modulation[J]. Acta Optica Sinica, 2022, 42(14): 1406003

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