  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.
