In this letter, we study the performance of digital communication systems considering the general and versatile <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\alpha } </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\boldsymbol {\eta } </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\boldsymbol {\kappa } </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">\boldsymbol {\mu } </tex-math></inline-formula> fading model, which was recently proposed in the literature. To this end, novel and exact expressions for the outage probability, average channel capacity, and average error rate of a variety of modulation formats are derived for arbitrary values of the fading parameters. Moreover, an asymptotic outage analysis is carried out in order to get further insight as to how the fading parameters impact system performance. Monte Carlo simulations are provided to validate the proposed analytical framework.