Binary codes in the block-fading channel

We study coding for the non-ergodic block-fading channel. In particular, we analyze the error probability of full-diversity binary codes, and we elaborate on how to approach the outage probability limit. In so doing, we introduce the concept outage boundary region, which is a graphical way to illustrate failures in the decoding process. We show that outage achieving codes have a frame error probability which is independent of the block length. Conversely, we show that codes that do not approach the outage probability have an error probability that grows logarithmically with the block length.