Various techniques have been proposed to address the problem of resource allocation in multi-carrier communications. These techniques, for the most part, arise from information-theoretic measures or otherwise associated with the channel behavior, which does not necessarily model the coding being employed. In this paper, an optimization technique is tailored for low density parity-check (LDPC) coded orthogonal frequency-division multiplexing (OFDM) systems, by employing the so-called general stability condition introduced by Richardson et al. The latter formulates a necessary condition for the belief-propagation decoder to perfectly decode a received vector with no errors. The general condition is re-formulated so as to model practical multi-carrier systems, such as OFDM. Consequently, a general resource-allocation framework is laid down for optimizing the transmitted power based on the characteristics of the LDPC code in use. The proposed optimization technique is utilized for power allocation in orthogonal frequency-division multiple access systems; and the transmitted power is minimized while guaranteeing reliable decoding. To validate the proposed approach, it is compared to information-theoretic-based methods that aim at optimizing the mutual information between the transmitter and the receiver. Both approaches are shown to provide almost identical performance for the scenarios addressed in this paper.