Asynchronous NOMA and PLNC with iterative decoding

The article deals with single-carrier multiple access channel (MAC), where the relative delay of sources is a fraction of the symbol period. We review the channel likelihood function and test three approaches for inter-symbol interference (ISI). We remove ISI by (I) ISI tracking, (II) by a one-step marginalization of the channel likelihood, or (III) the discrete Fourier transform (DFT) precoding. For ISI tracking, we model ISI as a virtual convolutional code observed in a multipath channel. We use all three approaches to compare joint decoding (JD) of sources and hierarchical decoding (H-decoding)—specifically, decoding of the XOR frame. For a proof of concept, we apply a pair of serially concatenated convolutional codes as a channel code and BCJR (Bahl, Cocke, Jelinek, Raviv) decoding algorithm. DFT precoding “erases” arbitrary delay and makes the equivalent system model synchronous. The proposed reduced-state hierarchical finite state machine for H-decoding brings about 2 dB gain w.r.t. simple marginalization. The proposed methods are suitable for equally strong sources particularly with BPSK alphabet.