Asynchronous Physical-Layer Network Coding With Quasi-Cyclic Codes

Communication in the presence of bounded timing asynchronism, which is known to the receiver but cannot be easily compensated, is studied. Examples of such situations include point-to-point communication over intersymbol interference (ISI) channels and asynchronous wireless networks. In these scenarios, although the receiver may know all the delays, it is often not an easy task for the receiver to compensate the delays as the signals are mixed together. A novel framework, which is called interleave/deinterleave transform (IDT), is proposed to deal with this problem. It is shown that the IDT allows one to design the delays so that quasi-cyclic (QC) codes with a proper shifting constraint can be used accordingly. When used in conjunction with QC codes, IDT provides significantly better performance than existing schemes relying solely on cyclic codes. Two instances of asynchronous physical-layer network coding, namely, the integer-forcing equalization for ISI channels and asynchronous compute-and-forward, are then studied. For integer-forcing equalization, the proposed scheme provides improved performance over using cyclic codes. For asynchronous compute-and-forward, the proposed scheme shows that there is no loss in the achievable information rates due to delays that are integer multiples of the symbol duration. Furthermore, the proposed approach shows that delays introduced by the channel can sometimes be exploited to obtain higher information rates than those obtainable in the synchronous case. The proposed IDT can be thought of as a generalization of the interleaving/deinterleaving idea proposed by Wang et al., which allows the use of QC codes, thereby substantially increasing the design space.