Generally, resource allocation for multi-carrier cooperation communication networks include subcarrier and power allocation, however, it is difficult to be solved because of the 0-1 integer programming of subcarrier allocation, which makes the problem non-convex. This paper focus on solving the non-convex problems and provides a general solution to the resource allocation for relay enhanced multi-carrier systems. An established scenario, decode-and-forward (DF) relay assisted orthogonal frequency division multiplex (OFDM) system, is considered and we formulate the resource allocation as a joint subcarrier pairing, assignment and power allocation problem, in which heterogeneous users data rate requirements are also considered. In order to make the expression of the proposed optimization approaches for the original maximization problem clear, a four-step methodology is given. Firstly, we transform the original non-convex problem into a standard convex problem by imposing a new constraint of subcarrier allocation index regardless of the convexity of the objective function. Further, we prove that the optimum resource allocation algorithm (ORAA) for the dual problem of the transformed optimization problem is equivalent to the optimization of the original function. Subsequently, the optimum solution could be obtained by golden section search method (GSSM) and iterative resource allocation algorithm. Lastly, a sub-optimal resource allocation algorithm (SRAA) that solves the primal problem in an asymptotically manner is proposed. Simulation results illustrate that our proposed SRAA achieves a comparable performance as the ORAA with a satisfied complexity.