## 1 Introduction  
In recent years, generalized multi-protocol label switching (GMPLS) networks have become mature in practical applications and deployments in metropolitan area networks (MANs) [1; 2; 3]. Much of the attention to GMPLS comes from the integration of internet protocol (IP) layers and the optical switching paradigm. By merging several layers to form a single control plane, the network provides a reliable system with reduced complexity. In the network, packets are optically switched in time, wavelength, or space domain along the paths connected by nodes. Due to the packet-based structure, GMPLS is perfectly compatible with optical packet switching (OPS) [4; 5; 6], which overcomes the processing delay in the electrical switching mechanism. The development of high-speed optical code-division multiple access (OCDMA) systems inspires researchers to implement optical codes as labels in GMPLS [7; 8; 9]. OCDMA labels are proposed to provide finer granularity in bandwidth utilization than their wavelength-division multiplexing (WDM) counterpart. Labels represented by optical codes are stacked in a common channel to make full use of the available bandwidth. In GMPLS, packets are forwarded along a label switching path (LSP) consisting of connections between nodes. Label distribution protocol (LDP) distributes the labels to all node connections and stores the assignments in a look-up table. To acquire the optimal LSP, LDP searches the look-up table and analyzes all possible paths from the packet source to destination. When OCDMA labels are adopted in the network, a small-size table can be employed to reduce the packet processing time. Spectral amplitude coding (SAC) is a remarkable way to implement OCDMA labels due to its system simplicity [10; 11; 12]. As SAC labels are encoded on the optical spectrum, the components of label generator and processor can be operated at a relatively low chip rate without processing the high-speed payload bits. Multiple access interference (MAI) is the main bottleneck in OCDMA systems, resulting from the overlapping wavelengths from different label signals. By using balanced detection and properly designed codes, SAC labels can be identified without MAI [13]. The recent development of grating components, such as fiber Bragg grating (FBG) and array waveguide grating (AWG), reduces the system cost of label implementation. In reference [10], SAC labels generated from a nonlinear effect named four-wave mixing (FWM) were experimentally demonstrated. A unique FWM wavelength was recognized as an identifier to achieve fast label processing. To remove the complex procedures of label swapping and label inserting, label stacking is presented in reference [11]. The authors of reference [12] proposed two packet formats with stacked labels, packets with isolated SAC labels and with SAC payloads. The experiment demonstrated that the packets with two stacked SAC labels were successfully switched in a two-node, 80 km-long network. As residential and industrial users develop in the metropolitan area, the MAN scale increases. The packets carry more SAC labels to travel a longer distance to reach the destinations. However, increasing the label number in the stack induces phase intensity-induced noise (PIIN), which is a dominant element limiting the performance of label recognition [14]. Optical code pattern is the main factor highly correlated with the PIIN variance. Optical codes with low-cross correlation are designed to suppress receiver noise [15]. We have previously introduced stuffed quadratic congruence (SQC) codes as SAC labels in reference [16]. Due to the ideal cross-correlation value, a large number of labels can be attached to packets to increase the transmission distance. However, constructing these codes requires complicated mathematical processes, and the code types are limited. The hybrid WDM/SAC scheme is an alternative method to improve network performance by reducing the PIIN effect [17; 18]. The related research was limited to an access network [17] and fiber sensor [18].