This paper addresses the achievable rate of single cell and sum rate of multi-cell orthogonal frequency division multiplexing (OFDM) index modulation (IM). The single cell achievable rate of OFDM-IM with Gaussian input is calculated using a multi-ary symmetric channel. Then, the cumulative distribution function (CDF) of multi-cell OFDM-IM is investigated by stochastic geometry. Furthermore, it is proved in this paper that the probability density function (PDF) of noise plus intercell-interference (ICI) in multi-cell OFDM-IM with quadrature amplitude modulation (QAM) follows a mixture of Gaussians (MoG) distribution. Next, parameters of the MoG distribution are estimated using a simplified expectation maximization (EM) algorithm. Upper bound of sum rates of multi-cell OFDM-IM is derived. Furthermore, analytic and simulated results are compared and discussed.