An electronic state-to-state approach is developed to reproduce numerically the radiative processes in the experiments on the Electric Arc Shock Tube facility at NASA Ames Research Center. The experiments measured the spectral radiance of C-2 Swan band and CO 4th Positive band behind the strong shock wave in a Martian-like mixture. The present state-to-state approach solves the electronic states of strong radiators by integrating the collisional-radiative model into the master equations in the frame of Euler equations. Particularly, the electron impact dissociation of CO is included, and the rate coefficients are proposed for the electronic state-specific heavy-particle impact excitation and dissociation of C-2. The nonequilibrium radiation behind the shock is calculated by the line-by-line method, and it is then convoluted using the calibrated smearing function in order to compare with the experiments. The state-specific simulation results is found to agree well with both spectral and spatial measurement data. The simulated electronic state populations of CO and C-2 deviate from Boltzmann distributions significantly, which could explain the failure of previous two-temperature quasi-steady-state based simulations.