In this paper, we derive a tight upper bound on the performance of a coded full-duplex multiple-input multipleoutput (MIMO)-based bidirectional transceiver. Iterative detection and decoding (IDD) are proposed to suppress the residual self-interference (SI) remaining after applying different stages of SI cancellation. IDD comprises an adaptive minimum meansquared error filter with log-likelihood ratio demapping, while the soft decoder by using soft-in soft-out decoding utilizes the maximum a posteriori algorithm. Furthermore, bit-interleaved coded modulation is considered in the presence of additive white Gaussian noise over MIMO frequency non-selective Rayleigh fading channels. Simulation results are presented to demonstrate the bit-error rate (BER) performance as a function of the signal-to-noise ratio showing a close match to the SI-free case for the proposed system. Furthermore, we validate our results by deriving a tight upper bound on the performance of the proposed system using rate-1/2 convolutional codes together with M-ary quadrature amplitude modulation, which asymptotically exhibits a close agreement with the simulated BER performance. Moreover, extrinsic information transfer chart analysis is used to investigate the convergence behavior of the proposed IDD receiver and to determine the number of iterations required for this convergence.