On the second-order coding rate of non-ergodic fading channels

This paper analyzes the rate-reliability trade-off for non-ergodic fading channels with state information available at the receiver, specifically the second-order coding rate with a fixed length corresponding to one channel coherence time and a target average error probability. Achievability is developed using random coding and modified typicality decoding, and the converse is developed using generalized information spectrum methods. Although the infinite blocklength performance of such a wireless channel depends only upon the fading, our results suggest that both fading and noise affect finite blocklength performance. Furthermore, although our non-asymptotic bounds conform with those in the recent work by Yang et al., our finite blocklength approximation is more useful for numerical evaluation.