Statistical mechanics of CDMA multiuser detector implemented in coherent Ising machine

The scalability and computational ability of the coherent Ising machine (CIM) have made it attract attention as one of the most effective Ising computing architectures for solving large-scale optimization problems. However, the theory and techniques of equilibrium classical thermodynamics cannot be directly applied to the CIM because it is an open-dissipative system. In an attempt to adapt the theory and techniques to the CIM, we have used a canonical frustrated model of Ising computation called the CDMA (Code Division Multiple Access) multiuser detector. Here, we derive a macroscopic equation to estimate the critical value of the spreading factor for achieving a low bit error rate as a function of the normalized pump rate in the CIM-implemented CDMA multiuser detector.