This thesis presents a study of soft-output equlization algorithms for application in coded equalization, where the data is error-protected by an error-correction code. Two algorithms based on an approximation of the a posteriori probability are proposed. The first algorithm computes its recursion at only M states per trellis stage. The second algorithm computes only at states with values below a certain threshold. Beacuse of their low demands on computation time as well as the amount of memor used, these algorithms are suitable for channels with long impulse responses. Simulation results on the performance of a convolution-coded communications system are presented. The results show that the performances of the proposed algorithms are almost identical to the optimum al high signal-to-noise ratio (SNR) and are the same as that of the SSA (suboptimum soft output algorithm), while their computational complexities are much lower than that of the SSA.