## 3 Packet Switching Strategy and Label Distribution Scenario of Extended SAC Labels  
In this section, we adopt the concept of label stacking and extended SAC labels to achieve packet switching applications in GMPLS networks. Label stacking is applied to optical networks by attaching multiple labels to a single packet. The LDP determines an LSP linked from the packet source to the destination according to the forward information. The connections along the LSP correspond to a set of extended SAC labels. When a packet arrives, the network nodes analyze the label stack to make a switching decision. Then, the node controls an optical switch to guide the packet to the correct path. Label stacking simplifies the computational complexity of packet switching as it avoids label removing and label inserting. The only required function for each node is to recognize a specific label from the stack.  
Figure 2 shows a schematic diagram of a GMPLS network with extended SAC labels. The network nodes are divided into two categories: edge node and core node. Edge nodes set up an LSP and insert  
Figure 1: Average cross-correlation value \(\lambda\) of extended SAC labels versus code length \(L\).  
the corresponding labels to a packet. Core nodes analyze the label stack and determine the switching path. There are two LSPs in this network, which are denoted as LSP 1 and LSP 2. Each connection in the LSPs corresponds to an extended SAC label. For LSP 1, packets pass through three connections, which map labels **E**(1,1), **E**(2,1), and **E**(3,2). Edge node 1 attaches these labels to packets before sending them to the network. When packets reach core nodes, the optical labels are converted to electrical signals for decoding. Except for label recognition, packets stay in the optical domain during the switching process, which solves the mismatch between electrical signals and optical components.  
Figure 2(a) shows the time waveform and power spectral density (PSD) of an optical packet traveling along LSP 1. In this example, the packet's payload, represented by four data bits (1,1,0,1), is modulated on an optical carrier with on-off keying (OOK). For bit \"1\" an optical pulse carrying stacked SAC labels is transmitted, while a zero message is sent for bit \"0.\" The label stack is a synthesizing vector {1, 2, 1, 0, 1, 0, 0, 0}, which comes from the summation of **E**(1,1), **E**(2,1), and **E**(3,2). As the SAC scheme is employed, the label stack is represented by a wavelength distribution of {\(\lambda_{1}\), 2\(\lambda_{2}\), \(\lambda_{3}\), \(\lambda_{4}\), 0, \(\lambda_{6}\), 0, 0, 0}. The simulations were conducted with _Optisystem_. The power and bandwidth of the light source are set to \(-10\) dBm and \(0.3\) THz, respectively. Two light sources centered at 193 THz and 193.4 THz are employed to generate the labels with \(j=1\) and \(j=2\). The bit rate is 10 GB/s and the chip width of the SAC labels is 0.1 THz.  
Figure 3: _Cont._  
Figure 2: Packet switching over a generalized multi-protocol label switching (GMPLS) network with extended SAC labels.  
Figure 3b shows the packet signals traveling along LSP 2. The payload energy is lower than that of Figure 3a, as only two labels, **E**(3,1) and **E**(2,2), are carried in a single bit. The labels corresponding to LSP 2 are not overlapping, due to the proper label assignment and path selection. When a label stack is constructed, the labels with distinct values of \(j\) are preferred to reduce the overlap on wavelengths. Different LSPs result in different labels in a stack. For a long LSP, a large number of labels are included in a packet, and wavelength superposition becomes inevitable. Therefore, balanced detection is adopted in the node architecture to recognize the desired label without MAI.