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Few-mode fiber is a significant component of free-space optical communication at the receiver to obtain achievable high coupling efficiency. A theoretical coupling model from the free-space optical communication link to a few-mode fiber is proposed based on a scale-adapted set of Laguerre-Gaussian modes. It is found that the coupling efficiency of various modes behaves differently in the presence of atmospheric turbulence or random jitter. Based on this model, the optimal coupling geometry parameter is obtained to maximize the coupling efficiency of the selected mode of few-mode fiber. The communication performance with random jitter is investigated. It is shown that the few-mode fiber has better bit-error rate performance than single-mode fiber, especially in high signal-to-noise ratio regimes.