# Research on Key Technologies of Elastic Satellite Optical Network Based on Optical Service Unit
## 2 Methods
### OISL-OSU Service Slicing
#### 2.2.2 RS(255,223) Interleaving and Encoding  
After two decades of development, terrestrial OTNs have adopted the RS(255,239) encoding scheme with an interleaving depth of sixteen. This decision was made after careful consideration of service and channel characteristics to achieve a balance between minimizing delay and effectively combating burst errors. In contrast, OISL-OSU functionality exhibits significantly lower link stability compared to terrestrial OTNs. Therefore, within the framework of the mature terrestrial system, further optimization of the data interleaving depth is necessary. Consequently, this paper proposes the use of the RS(255,223) encoding scheme with an interleaving depth of thirty-two. In inter-satellite laser links, the fixed-step accuracy of optical head movement introduces instability into the communication channel. As a result, the RS decoder may encounter data streams containing consecutive symbol errors spanning dozens of symbols with a certain probability. The RS(255,223) encoding scheme, with its interleaving depth of  
Figure 2: OISL-OSU protocol stacks. thirty-two, distributes these consecutive errors across thirty-two RS codewords for decoding. By comparison, OISL-MPLS employs an interleaving depth of only four. Consequently, each RS codeword in OISL-MPLS must process a greater number of error bytes, thereby increasing the likelihood of decoding failure. Table 2 presents the RS(255,223) parameters utilized in OISL-OSU. The implementation process of RS coding interleaving is shown in Figure 3. In the FEC process, one line of OISL-OTU-FEC frame data is divided into sixteen sub-lines according to the method of inter-byte interpolation, and one of the sub-lines is processed by each FEC encoding. The byte transmission sequence of the OISL-OTU-FEC frame after applying RS interleaving coding is depicted in Figure 4.  
Figure 4: Interleaving of RS-encoded symbols. Figure 3: Schematic diagram of 16-sub-row RS coding. \begin{table}
\begin{tabular}{l l} \hline
**Item** & **Explanation** \\ \hline Coding scheme & System code \((n,k)\), where: \\  & - Code length: \(n=255\) symbols \\  & - Code payload: \(k=n-r=223\) symbols \\  & - Overhead: \(r=32\) symbols \\ Error correction capability & 16 RS symbols \\ Primitive polynomial & \(F(x)=x^{8}+x^{7}+x^{2}+x+1\), belonging to the Galois Field \(GF(2^{8})\) \\ Generating polynomial & \(g(x)=\prod_{j=112}^{143}\left(x-\alpha^{11j}\right)=\sum_{i=0}^{32}G_{i}x^{i}\), where \(F(\alpha)=0\), with \(\alpha^{11}\) as primitive element \\ \hline \end{tabular}
\end{table} 
Table 2: RS(255,223) parameters. The uncorrectable bit error rate (effective bit error rate) after interleaving and RS(255,223) encoding is given by [22]  
\[p_{eff}=\sum_{i=t+1}^{D}\binom{D}{i}p_{b}^{i}(1-p_{b})^{D-i} \tag{1}\]  
where \(t\) denotes the maximum number of errors that the RS code can correct (error correction capability), \(D\) represents the interleaving depth, and \(p_{b}\) is the bit error rate of the original channel (before error correction). The binomial term \(\binom{l}{l}p_{b}^{i}(1-p_{b})^{D-i}\) represents the probability of exactly \(i\) errors occurring in an interleaved block (containing \(D\) symbols). Each symbol of RS is an element of \(GF(2^{8})\), and a specific basis can be chosen to represent each symbol. Specifically, the following hold@  
1. The first basis is \(\{1,\alpha^{1},\alpha^{2},\ldots,\alpha^{7}\}\), such that any symbol can be expressed as \[u_{0}\alpha^{0}+u_{1}\alpha^{1}+\ldots+u_{7}\alpha^{7},\quad u_{i}\in\{0,1\}\] (2)
2. The second basis is \(\{1,\beta^{1},\beta^{2},\ldots,\beta^{7}\}\), where \(\beta=\alpha^{117}\). On this basis, there exists a dual basis \(\{l^{0},l^{1},\ldots,l^{7}\}\) with the following characteristics: \[T_{r}(l_{i}\beta^{j})= \begin{cases}1,&\text{if $i=j$}\\ 0,&\text{otherwise}\end{cases}