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In this paper, we analyze and evaluate the performance of digital communication systems that operate over a composite fading channel following the η-μ/gamma distribution. More specifically, new analytical expressions for the channel capacity under different transmission schemes are derived in the form of infinite series. For the special case of integer μ values, simplified closed-form expressions are also obtained. Moreover, we deduce exact tractable formulas for the average bit error rate (BER) of various modulation schemes. In the high-power regime, simplified capacity and BER expressions are provided, revealing the implications of the model parameters on system performance. The relationship of the presented results with previously reported results on generalized- K and K fading channels is also established. We note that the theoretical results presented herein are given in analytical form, which can efficiently be evaluated.