This paper introduces the equivalent discrete-time channel model (EDTCM) to the area of diffusion-based molecular communication (DBMC). Emphasis is on an absorbing receiver, which is based on the so-called first passage time concept. In the wireless communications community the EDTCM is well known. Therefore, it is anticipated that the EDTCM improves the accessibility of DBMC and supports the adaptation of classical wireless communication algorithms to the area of DBMC. Furthermore, the EDTCM has the capability to provide a remarkable reduction of computational complexity compared to random walk based DBMC simulators. Besides the exact EDTCM, three approximations thereof based on binomial, Gaussian, and Poisson approximation are proposed and analyzed in order to further reduce computational complexity. In addition, the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is adapted to all four channel models. Numerical results show the performance of the exact EDTCM, illustrate the performance of the adapted BCJR algorithm, and demonstrate the accuracy of the approximations.