Finite Blocklength Analysis of Coded Modulation for Block Fading Channels with Linear Precoding

In this paper, we consider the finite blocklength analysis for the single-user block fading channel with discrete input constellations. In particular, we derive novel achievability results on block error rate (BLER) for a given code rate and blocklength. We first consider the scalar block fading channel case for which we adopt linear precoding as a method to increase the spectral efficiency associated with full temporal diversity. Then, we extend our analysis to the multiple-input multiple-output block fading channels under space-time linear precoding. Numerical evaluations demonstrate the impact of finite blocklength and diversity in block fading channels as well as the effectiveness of linear precoding in minimizing the achievable BLER under practical modulation schemes, such as QPSK.