This paper presents the implementation and experimental evaluation of a short-packet physical-layer network coding (PNC) system. Implementation of short-packet PNC systems is challenging. First, short packets may have only a few pilot symbols for synchronization and channel estimation purposes. Increasing the number of pilots increases the overhead; decreasing the number of pilots, on the other hand, degrades the packet error rate performance. Second, many short-packet systems are meant for applications with very stringent delay requirements. Employing advanced but complex PNC channel decoding may result in unacceptable delay due to the processing delay. This work presents a low-complexity and low-overhead physical-layer design of OFDM-based short-packet PNC systems, implemented over the software-defined radio platform. Our design makes use of only a small number of pilots (without separate OFDM preamble symbols) to address issues such as slot synchronization, packet detection, carrier frequency offsets, and mismatched channel state information. Our design employs reduced-complexity XOR channel decoding based code-aided parameter estimation (that includes synchronization and channel estimation) to compensate for the limitations imposed by having a small number of pilots. This is the first demonstration that provides a practical framework for applying PNC to short-packet communications.

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 10-4within 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.

This paper derives the maximum achievable sum-rate and presents the optimal encoding/decoding framework for rate-diverse wireless network coding (RD-WNC) over broadband channels consisting of multiple parallel subchannels. RD-WNC applies to a communication scenario in which a base station wants to deliver two different messages with different rates to two users. The base station combines the two separate messages into one network-coded message and broadcasts the network-coded message to both users. Each user then extracts its desired message from the network-coded message by subtracting from it the other message, which we assume to be side information available to the user. Deriving the maximum achievable sum-rate for RD-WNC is challenging when the channel consists of multiple parallel subchannels with different channel coefficients (e.g., the subcarrier channels of OFDM systems), since apart from the rate allocation between the two users, optimal power allocation among multiple subchannels needs to be identified. The first contribution of this paper is a new “mountain-leveling” power allocation algorithm to achieve the maximum sum-rate. With the resulting power allocation, we can then achieve the corresponding optimal sum-rate by having a separate encoding/decoding mechanism for each subchannels, but doing so is cumbersome and complex when the number of subchannels is large. The second contribution of this paper is a practical encoding/decoding framework using only one encoder-decoder mechanism for all subchannels without sacrificing sum-rate optimality. We provide numerical results to corroborate our theoretical findings and to demonstrate the benefits of our encoding/decoding framework.

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 Eb/No. 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 Eb/N0and achieves a target PER of 10-3with minimum Eb/No.

In this work, we derive the random coding error exponent for the uplink phase of a two-way relay system where physical layer network coding (PNC) is employed. The error exponent is derived for the practical (yet sub-optimum) XOR channel decoding setting. We show that the random coding error exponent under optimum (i.e., maximum likelihood) PNC channel decoding can be achieved even under the sub-optimal XOR channel decoding. The derived achievability bounds provide us with valuable insight and can be used as a benchmark for the performance of practical channel-coded PNC systems employing low complexity decoders when finite-length codewords are used.

Physical-layer network coding (PNC) channel decoding at the relay is of key importance for good performance in PNC systems. However, PNC channel decoders can have prohibitive computation complexity. Low complexity non-iterative PNC channel decoders are desired in practice. For such PNC decoders, decoding performance may degrade significantly when there is a relative phase offset between the simultaneous signals of multiple nodes received at the relay, particularly when bit-likelihood-based decoding is adopted. In this paper, we thoroughly investigate and numerically quantify the impact of relative phase offset on decoding performance. To maintain good decoding performance under relative phase offset, we introduce and experimentally evaluate symbol-likelihood-based decoding (in contrast to bit-likelihood-based decoding) for PNC systems. Our experimental results show that symbol-likelihood-based decoding improves the packet throughput over bit-likelihood-based decoding by 100% to 400% at SNR of 15 dBs. Moreover, we study the computational complexity under both these decoding methods. We find that a reduced-complexity decoder with symbol-likelihood-based decoding provides the best performance-complexity tradeoff for practical PNC systems.

Physical-layer network coding (PNC) can potentially boost the throughput of a two-way relay network by 100% compared with conventional packet forwarding schemes. However, the complexity of PNC channel decoders can be considerably higher than the complexity of channel decoders for point-to-point communication systems. Although many PNC channel decoders proposed to date have good decoding performance, they may not be feasibly implemented in practical systems due to their high computation complexities. This paper presents a reduced-complexity decoder (RCD), a PNC decoder with adjustable decoding complexity that is amenable to real-time implementation. We experimentally evaluate the performance-complexity trade-off of RCD. Our experimental results show that RCD can achieve substantial throughput gain over state-of-the-art decoders proposed for real-time PNC systems.