# Optimizing Crosstalk in Optical NoC through Heuristic Fusion Mapping
## 1 Introduction  
The improvement in the degree of chip crowding promotes the generation of network on chip [1; 2]. However, as the number of cores grows, the common electrical network-on-chip cannot meet the requirements of advanced systems due to their low bandwidth and high power consumption [3]. Instead of the traditional network-on-chip (NoC) based on electrical interconnects, the optical NoC (ONoC) [4; 5; 6; 7; 8] provides higher communication bandwidth, as well as lower transmission delay and power costs. Optical NoC has many advantages, but it also has some disadvantages that cannot be ignored. Crosstalk noise is the inherent characteristic of photonic devices [9; 10]. Although the crosstalk noise is very small [11; 12], it is a factor that cannot be ignored in the highly integrated on-chip system. Crosstalk noise is critical to the design of a photonic NoC architecture, as high crosstalk noise may easily result in an inoperable architecture [7; 13; 14]. According to [15], application-specific mapping optimization provides an important means for facing the crosstalk problem in application-specific multicore systems-on-chip (SoCs). [16] summarizes the task mapping strategy of the network on chip, including particle swarm optimization (PSO) [17; 18; 19; 20], genetic algorithm (GA) [21], ant colony algorithm (ACO) [22], binomial mapping strategy (BMAP) [23], chain mapping strategy (CHMAP) [24] and so on. In [25], a mapping algorithm based on genetic algorithm is proposed to optimize the crosstalk performance of optical network-on-chip. The purpose of designing an optimization mapping algorithm is to map each task in the application program to each node in the topology, and to find the optimal network performance. In the application, the communication between tasks can be transformed into a communication graph CG = G(C,E), which is a directed graph, in which each vertex \(c_{i}\in C\) is a task, \(e_{ij}\in E\) is the edge between task \(c_{i}\) and \(c_{j}\), representing the communication between them. Similarly, the NoC architecture of opticalinterconnection can be represented by the connectivity topological graph X(T, L) described by the topology, routing algorithm and optical router mechanism, which represents the connection mode between the topological nodes, where t\({}_{i}\in\) T represents the topological nodes in the network on the optical chip, and l\({}_{ij}\in\) L is the physical link connecting the topological nodes t\({}_{i}\) and t\({}_{j}\). The mapping from communication graph CG = G(C,E) to topology graph X(T, L) can be defined by one-to-one mapping function on the premise of \(|\)C\(|\leq|\)T\(|\):  
\[\Omega\text{: C}\rightarrow\text{T, s.t. }\Omega(\text{c}_{i})=\text{t}_{i}, \forall\text{c}_{i}\in\text{C, }\exists\text{t}_{i}\in\text{T} \tag{1}\]  
This definition means that each task in an application should be mapped to a topology node, and each topology node only corresponds to one task. Figure 1 shows the mapping of an application with eight tasks in mesh topology. Because the task communication relationship in an application is fixed, when the task is mapped to the on-chip network by mapping algorithm, the relative position of tasks will be determined. The crosstalk in the on-chip network is largely from the communication intersection, and the relative position of tasks will greatly affect the communication intersection of tasks. Therefore, the crosstalk in the on-chip network can be reduced by optimizing the mapping algorithm. When the mapping algorithm is used to optimize the crosstalk in the optical network, the evaluation value of the mapping algorithm needs to correspond to the crosstalk performance of the network, so as to improve the evaluation value as the standard to find the optimal mapping method. In this paper, we design a heuristic fusion mapping algorithm PSO_SA to optimize crosstalk. The optimal mapping scheme is determined by two steps.