Coded modulation for Gaussian channels: Dispersion- and entropy-limited regimes

We study coded modulation over point-to-point Gaussian channels with discrete inputs and finite blocklength using recent tools from information theory. We show that finite-length channel coding has quite a significant effect at low SNR, and we identify SNR values below which the coded modulation is “dispersion limited”. Unlike the infinite-length case, coded PSK outperforms coded QAM in this dispersion-limited regime, based upon analysis of i.i.d. random codes. At high SNR, we show that finite blocklength coding barely affects the performance so that uncoded modulation is essentially optimal, and we quantify the SNR values beyond which the modulation is “entropy-limited”.