To obtain a full picture of potential applications for propagation-delay based X channels, it is important to obtain all feasible schemes of cyclic interference alignment including the encoder, channel instance, and decoder. However, when the dimension goes larger, theoretical analysis about this issue will become tedious and even impossible. In this letter, we propose a computer-aided solution by searching the channel space and the scheduling space, which can find all feasible schemes in details. Examples are given for some typical X channels. Computational complexity is further analyzed.

In this paper, we deal with the problem of compatibility class encoding, and propose a novel algorithm for finding a good functional decomposition with application to LUT-based FPGA synthesis. Based on exploration of the design space, we concentrate on extracting a set of components, which can be merged into the minimum number of multiple-output CLBs or LUTs, such that the decomposition constructed from these components is also minimal. In particular, to explore more degrees of freedom, we introduce pliable encoding to take over the conventional rigid encoding when it fails to find a satisfactory decomposition by rigid encoding. Experimental results on a large set of MCNC91 logic synthesis benchmarks show that our method is quite promising.

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.