Optimal SNR Exponent for Discrete-Input MIMO ARQ Block-Fading Channels

In this paper, we consider an automatic-repeat- request (ARQ) retransmission protocol signaling over a block-fading multiple-input, multiple-output (MIMO) channel. In particular, we consider fixed rate codes constructed over discrete complex signal constellations. We show that the optimal signal- to-noise ratio (SNR) exponent is given by a modified singleton bound, relating all the system parameters. To demonstrate the practical significance of the theoretical analysis, we present numerical results showing that practical singleton-bound-achieving maximum distance separable codes achieve the optimal SNR exponent.