## 1 Introduction  
Network on chip (NoC) has emerged as a promising solution for multicore system on chip communication design [1; 2], which overcomes the complexity of wire delay and flexibility in chip architectures [3; 4; 5; 6]. NoC is a packet-based, on-chip communication switching network designed for communication among the intellectual property (IP) cores of SoC systems [7]. NoCs use packets to exchange data between processing elements (PEs) via network fabric that consists of resource network interfaces (RNI), routers and interconnecting links. Among these, interconnection links are the most affected by crosstalk [8].  
Crosstalk is a type of noise which is introduced by an unwanted coupling between a node and its neighboring wire or between two neighboring wires [9]. As technology scales down, the dimensions of interconnects also scale down. This reduces the spacing among interconnects [10]. With the high signal frequency and small spacing between interconnects, the coupling between the lines has become well known [11; 12]. Coupling between signal lines can cause logic failures and timing degradation in digital systems [13]. Crosstalk has become the most critical concern in modern sub-10 nm integrated circuits [14]. This coupling causes problems that can be addressed by various methods like shielding [15; 16; 17; 18; 19; 20], inserting repeaters [21; 22; 23; 24; 25] or buffers [26; 27; 28; 29; 30; 31], duplication [32] and crosstalk avoidance code (CAC) [33; 34; 35; 36]. Insertion of buffers and shielding has more area cost when compared to duplication or CAC [37].  
Various error correction code (ECC) schemes have been proposed to protect communication between IP cores [38; 39; 40; 41]. In [38; 39], the authors focus on weighing the performance and design cost of ECC. In [40; 41], which address improving the transient fault tolerance, have shown that implementing complex ECC schemes incurs high area overhead and high energy dissipation and may adversely affect the performance of the NoC. They use assumed crosstalk error injection to verify their schemes. The error rate caused by crosstalk is relevant to the spacing between interconnects and the frequency of NoC. Bandwidth is mainly determined by spacing between interconnects and working frequency. Hence, a crosstalk error model and corresponding reliable system with ECC are required to make NoC communication reliable.  
In this paper, a reliability system evaluation model of NoC communication with analysis from backend to frontend has been presented (BFRS). In the backend, with a three-wire RLC coupling model, an error rate model considering timing constraints (SSTC) is proposed to establish functional relations between interconnect spacing, length and signal frequency. With different nodes' dimensions, the SSTC calculates out error rates modeled with the physical size of interconnects and the working environment, which can be used to test the system's reliability. In the frontend, effective bandwidth can be modeled with route spacing, working frequency, encode cost on code length and automatic repeat-request (ARQ) cost with error injection rates. The reliability system performance model (RSP) can be modeled with bandwidth and effective bandwidth. BFRS summarizes the frontend to backend model. In order to verify BFRS model, we propose a reliability system with a hybrid automatic repeat request technique (RSHARQ). RSHARQ uses Hamming code as ECC and a cyclic redundancy check (CRC) with the proposed code transmission scheme as ARQ. Finally, simulation results are shown.