This letter proposes a scheme for the backward transmission of the propagation-delay based three-user X channel, which is reciprocal to the forward transmission. The given scheme successfully delivers 10 expected messages in 6 time-slots by cyclic interference alignment without loss of degrees of freedom, which supports efficient bidirectional transmission between the two ends of the three-user X channel.

For the three-user X channel, its degree of freedom (DoF) 9/5 has been shown achievable theoretically through asymptotic model with infinite resources, which is impractical. In this article, we explore the propagation delay (PD) feature among different links to maximize the achievable DoF with the minimum cost. Since perfect interference alignment (IA) is impossible for 9 messages within 5 time-slots, at least one extra time-slot should be utilized. By the cyclic polynomial approach, we propose a scheme with the maximum achievable DoF of 5/3 for 10 messages within 6 time-slots. Feasibility conditions in the Euclidean space are also deduced, which demonstrates a quite wide range of node arrangements.