Coding for the MIMO ARQ Block-Fading Channel with Imperfect Feedback and CSIR

We investigate the effects of imperfect channel knowledge and feedback in incremental-redundancy automatic-repeat request (INR-ARQ) coding systems over multiple-input multiple-output (MIMO) block-fading channels. We propose an ARQ decoder based on nearest neighbour decoding and evaluate the corresponding achievable rates. We then derive the optimal code diversity assuming that the feedback channel is modelled as a binary symmetric channel. Our main results show that the feedback link reliability must improve with the forward (transmission) signal-to-noise ratio (SNR) for the code to exploit the diversity offered by ARQ scheme. We also identify the conditions for achieving full diversity and for ARQ not helping in improving the system's diversity.