Asynchronous Physical-Layer Network Coding With Quasi-Cyclic Codes

Abstract

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 inter-symbol interference (ISI) channels and asynchronous wireless networks. In these scenarios, although the receiver may know all the delays, it is often not be an easy task for the receiver to compensate the delays as the signals are mixed together. A novel framework 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 due to delays which are integer multiples of the symbol duration. Further, 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. Index TermsCompute-and-forward, physical-layer network coding, and integer-forcing receiver. I. INTRODUCTION Physical-layer network coding (or compute-and-forward) [2] [3] [4]has been shown to be a way to effectively harness interference in wireless networks and to provide significantly higher throughput than conventional strategies for many wireless networking problems. However, most of the results in the literature consider the case when the time delays from the multiple transmitters to a receiver are all identical (we refer to this as the synchronous case). One of the important open problems in this area is to determine whether the information rates achieved with compute-and-forward in the synchronous case can be obtained when the time delays from the multiple transmitters are different also (we refer to this as the asynchronous case). So far, this question has not been conclusively answered and our understanding of asynchronous physical-layer network coding is not as thorough as that of synchronous one. Recently, there have been some efforts in the literature trying to address such problems for some specific models such as ISI [5] and asynchronous physical-layer network coding (and compute-and-forward as well) [6] [7] [8] [9]. In both cases, cyclic codes have been suggested for combating the time delays for these two seemingly di...

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