Short packet physical-layer network coding with mismatched channel state information

Future multi-terminal communication networks such as machine-to-machine, telecommand and remote control communication systems will be based on short-packet transmissions. Physical-layer network coding (PNC) in such multi-terminal communication systems can potentially enhance network throughput and reduce communication latency. For practical PNC systems, preambles are contained in transmissions for accurate estimation of the channel-state-information (CSI). Identifying good preamble-length regimes, however, is critical for good performance of short-packet PNC systems. Long preambles for short packets reduce spectral efficiency. On the other hand, short preambles compromise accuracy of estimated CSI, leading to sub-par packet error rate (PER) performance. This paper studies the impact of preamble length on the performance of short-packet PNC systems. Specifically, we use random coding bound to quantify PER of channel-coded mismatched-CSI PNC systems and identify the preamble-length regime that achieves the target PER with minimum E
_b
/N
_o
. As an example, we consider a simple yet practically relevant setup of a BPSK modulated PNC system in a two-way relay channel operating with short packets of 128 symbols. Our results show that a preamble of 20 to 30 symbols provides the minimum PER for a wide range of E
_b
/N
₀
and achieves a target PER of 10
^-3
with minimum E
_b
/N
_o
.