In this paper, we consider the bit rate maximizing problem and power minimizing problem with integer bit allocation. We will derive the duality between these two problems. We will show that if a transceiver is optimal for the power-minimizing problem, it is also optimal for the rate maxi-mizing problem, and the converse is true. For the power minimization problem with integer bit allocation, the solution has been found in the literature. However, there is no solution yet for the rate maximization problem with integer bit allocation. The duality allows us to develop an algorithm for finding the rate-maximizing transceiver with integer bit allocation using the solution of power-minimizing system. In the simulations, we will compute the optimal solution for the rate-maximizing problem using the proposed algorithm.