Short-Packet Physical-Layer Network Coding

This paper explores the application of physical-layer network coding (PNC) for short-packet transmissions. PNC can potentially reduce the communication delay in relay-assisted wireless networks and can thus be instrumental in realizing short-packet communication systems with stringent delay requirements. In this work, first, we first derive an achievability bound for channel-coded short-packet PNC systems. Based on the random-coding error-exponent, the bound serves as a benchmark for short-packet PNC operating with traditional preamble-aided channel estimation and XOR channel decoding. Second, we design a blind channel estimation algorithm and a code-aided channel estimation algorithm for short-packet PNC systems. Both outperform the traditional preamble-aided channel estimation for PNC systems operating with mismatched channel-state-information. As a case study, we compare the three algorithms for packets of 128 symbols over a two-way relay channel. The results show that the blind algorithm outperforms the code-aided algorithm and preamble-aided algorithm by almost 0.2 and 1.5 dB respectively. Furthermore, the blind algorithm achieves the target packet error rate of 10 ⁻⁴ within 0.5 dB of the random coding bound of an imaginary system in which perfect channel-state-information is available at the relay at no cost (i.e., channel estimation is not required in the imaginary system). The bound and the algorithms give us a fundamental framework for applying PNC to short-packet transmissions.