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In this paper, we propose a heterogeneous optical access networking scenario, in which communication links between source and destination nodes are heterogeneous, composed of free-space optical, plastic optical fiber (POF), and indoor infrared (IR) links. To deal with bandwidth limitations of POF and IR links, a power-variable rate-adaptive low-density parity-check (LDPC)-coded orthogonal frequency division multiplexing (OFDM) scheme is used, while to deal with atmospheric turbulence, the spatial diversity is used. The rate-adaptive LDPC codes are designed using a modified progressive edge-growth (MPEG) algorithm. We show that with the proposed heterogeneous communication systems, we can deliver a high-speed optical signal (40 Gb/s and beyond) to an end-user.