  The bound of the information transmission rate of direct current biased
optical orthogonal frequency division multiplexing (DCO-OFDM) for visible light
communication (VLC) with finite-alphabet inputs is yet unknown, where the
corresponding spectral efficiency (SE) and energy efficiency (EE) stems out as
the open research problems. In this paper, we derive the exact achievable rate
of {the} DCO-OFDM system with finite-alphabet inputs for the first time.
Furthermore, we investigate SE maximization problems of {the} DCO-OFDM system
subject to both electrical and optical power constraints. By exploiting the
relationship between the mutual information and the minimum mean-squared error,
we propose a multi-level mercury-water-filling power allocation scheme to
achieve the maximum SE. Moreover, the EE maximization problems of {the}
DCO-OFDM system are studied, and the Dinkelbach-type power allocation scheme is
developed for the maximum EE. Numerical results verify the effectiveness of the
proposed theories and power allocation schemes.
