Abstract-Energy-efficient wireless communication is becoming increasingly important, especially forwireless devices with a limited battery life and cannot be recharged on a frequent basis. In this paper, a bit allocation algorithm to minimize the total energy consumption for transmitting a bit successfully is proposed for a two-way orthogonal frequency-division multiplexing (OFDM) relay system, whilst considering the constraints of quality-of-service (QoS) and total transmit power. Our scenario is fit for the delay-tolerant services delivered through low-complexity devices in application areas of IoT and M2M communications. Unlike existing bit allocation schemes, which maximize the energy efficiency by measuring "bits-per-Joule" with fixed bidirectional total bit rates constraint and no power limitation, our scheme adapts the bidirectional total bit rates and their allocation on each subcarrier with a total transmit power constraint.In order to do so, we propose a new idea to decompose the optimization problem. The problem is solved in two general steps. The first step allocates the bit rates on each subcarrier when the total bit rate of each user is fixed. In the second step, the Lagrangian multipliers are used as the optimization variants, and the dimension of the variant optimization is reduced from 2N to 2, where N is the number of subcarriers. We also prove that the optimal point is on the bounds of the feasible region, thus the optimal solution could be