The performance of LDPC-precoded, orbital-angular-momentum (OAM) modulation is studied over a 1-km free-space laser communication link subject to OAM modal crosstalk induced by atmospheric turbulence. The multidimensional signal constellation is designed as the Cartesian product of a one-dimensional non-negative pulse-amplitude modulation and a set of orthogonal OAM modes. We evaluate the performance of this modulation scheme by first determining conditional probability density functions (PDFs) of the modal crosstalk for each symbol, resulting from the propagation in weak turbulence using a numerical propagation model. It is observed that OAM modulation is more sensitive to atmospheric turbulence as the number of dimensions increases. However, this can be efficiently mitigated by an error-correction code. The coded OAM modulation scheme provides an energy-efficient alternative to single-mode transmission, since a larger rate can be obtained per given bandwidth.