Physical-layer Network Coding Decoding Research Articles

Improving LDPC-Coded PNC Decoders via Informed Dynamic Scheduling

To decode the transmit message pairs and then obtain the exclusive OR (XOR) message, this letter proposes the double-reliability-based decoding (DRB) algorithms with informed dynamic scheduling (IDS) for low-density parity-check (LDPC) coded physical-layer network coding (PNC) systems. The proposed DRB decoding with informed stability (IS-DRB) utilizes a new stability measure to determine the update order of the check nodes. Moreover, by exploiting the principle of PNC decoding, we present an improved IS-DRB (IIS-DRB) decoding to select the check node with unsatisfied PNC mapped checksum and the large stability to update first. This is due to that message propagated from this check node can quickly correct the variable node that causes unsatisfied checksum. Simulation results show that the proposed algorithms can realize significant performance improvement of about 0.5 dB over the conventional DRB decoding with the limited increase in complexity.

Physical-Layer Network Coding Based Decoding Scheme for Random Access

In this paper, we propose an enhanced low-complexity binary physical-layer network coding (PNC) based decoding scheme for random access systems with binary phase-shift keying modulation to improve the system throughput. In the proposed scheme, the linear combinations of collided users’ messages in each time slot are first obtained by exploiting a low-complexity PNC decoding scheme. Based on the decoded linear combinations within a MAC frame, we then propose an enhanced message-level successive interference cancellation algorithm to recover more users’ messages. We propose an analytical framework for the PNC-based decoding scheme and derive a tight approximation of the system throughput for the proposed scheme. Subsequently, the number of repeated transmissions of a message, i.e., the number of replicas transmitted by each user, is optimized to further improve the system throughput and energy efficiency. Interestingly, the optimization results show that the optimal number of replicas for maximizing the energy efficiency is a constant for all offered loads. On the other hand, the optimal number of replicas that maximizes the system throughput decreases as the offered load increases. Numerical results show that the derived analytical results closely match with the simulation results. Furthermore, the proposed scheme achieves a considerable throughput improvement, compared to the CRDSA++ scheme.

Generalized Signal-Space Alignment Based Physical-Layer Network Coding for Distributed MIMO Systems

We study an uplink distributed multiple-input-multiple-output (D-MIMO) system, where multiple users are served by multiple base stations (BSs) connected to a common central unit (CU). We propose a generalized signal-space alignment (SSA)-based physical-layer network coding (PNC) scheme, termed G-SSA-PNC. In G-SSA-PNC, the multi-antenna users encode their messages by using nested lattice coding, linearly precode the nested lattice codewords for SSA, and then broadcast to the multi-antenna BSs. The BSs linearly post-process the received signals to extract signals at certain aligned directions. PNC decoding is applied to those extracted signals to generate network-coded message combinations, and the decoded message combinations are then forwarded to the CU for user messages decoding. Compared with the original SSA-PNC scheme, our scheme is different in the following three aspects. First, the G-SSA-PNC employs an individual shaping lattice for nested lattice coding at each source, as in contrast to the use of a common shaping lattice in original SSA-PNC. Second, we derive the feasibility condition of PNC decoding under the new nested lattice coding scheme and show that the SSA precoding and the nested lattice coding needs to be jointly designed to meet the feasibility condition. Third, we formulate a sum rate maximization problem and propose a suboptimal solution to the problem. The numerical results demonstrate the superiority of the G-SSA-PNC in performance over the benchmark schemes, including original SSA-PNC, compress-and-forward, and interference alignment.

Symbol Misalignment Estimation in Asynchronous Physical-Layer Network Coding

Symbol misalignment is inevitable in asynchronous physical-layer network coding (PNC) systems. It is paramount that such symbol misalignment is taken into account in PNC decoding for good performance. Thus, accurate estimation of symbol misalignment is crucial. This paper argues that, when Nyquist pulses (i.e., intersymbol-interference (ISI)-free pulses) are adopted, signal samples only need to be collected at baud rate for optimal symbol misalignment estimation. Based on this principle, we propose a highly accurate symbol misalignment estimation method with low complexity. Our method makes use of the constant amplitude zero autocorrelation sequence (Zadoff–Chu sequence (ZC sequence)). We derive a maximum-likelihood (ML) estimator for symbol misalignment based on the cross-correlation result of the ZC sequence. Unlike previous methods that employ oversampling, our estimation method requires only baud-rate sampling, thus having much lower complexity. Extensive simulations show that our method can accurately estimate both integral and fractional symbol misalignments using sinc pulse and raised-cosine (RC) pulse. The root-mean-square error (RMSE) of the estimation is below 10−2 (in unit of symbol duration) when the SNR is above 15, 18, and 21 dB for 127-, 63-, and 31-bit-length ZC sequences, respectively. Furthermore, our method, being an ML estimation method, has no error floor in the high-SNR regime, whereas the prior methods exhibit an error floor.

Multi-Pair MIMO Two-Way Relaying: A Principal-Angle Perspective

This paper studies and analyzes a multi-pair MIMO two-way relay (TWR) system from a principal-angle perspective. In this system, users are grouped into pairs and two users in each pair exchange information through a common relay. The transmission scheme consists of two phases. In the uplink phase, the relay’s receive signal space is divided into two subspaces for each pair: in one subspace, the signals of the two users are near-parallel, and physical-layer network coding (PNC) decoding is applied to retrieve network-coded messages; in the other subspace, the two user signals are near-orthogonal, and complete decoding (CD) is applied to retrieve individual user messages. In the downlink phase, the relay’s transmit signal space is split into orthogonal subspaces for each pair, and in each subspace a common message is broadcasted to the two users. Our main contribution is to establish a critical link between the transmission scheme and the concept of principal angle in linear algebra. In particular, principal angle quantizes the degree of orthogonality between the user signals and helps determining how to partition the relay’s receive signal space into PNC decoding subspace and CD decoding subspace. Building on that, we discuss the optimal design of user/relay precoders for both uplink and downlink phases to maximize the asymptotic sum-rate of the proposed scheme at high signal-to-noise ratio (SNR). The analysis and numerical results indicate that our scheme performs close to the cut-set outer bound and significantly outperforms the existing schemes in the literature.

Bandwidth-Efficient Coded Modulation Schemes for Physical-Layer Network Coding with High-Order Modulations

This paper presents several soft decision iterative decoding schemes for physical-layer network coding (PNC) operated with coded modulation (CM) and bit-interleaved coded modulation (BICM). With respect to PNC operated with CM, we consider network coding-based channel decoding (NC-CD) and multi-user complete decoding (MUD-NC) for PNC decoding at the relay. Their BICM counterparts are XOR-based channel decoding (XOR-CD) and MUD-XOR, respectively. First, we show that, when the decoding is non-iterative, there is a gap between the BICM capacities of both XOR-CD and MUD-XOR under Gray mapping and the capacities of their CM counterparts, NC-CD, and MUD-NC. This is in contrast to the conventional point-to-point communication system, for which the BICM capacity with Gray mapping is known to be very close to the CM capacity, without the need for iterative decoding. Second, we investigate the error performance of iteratively decoded BICM XOR-CD and MUD-XOR. Extrinsic information transfer chart analysis and simulation results indicate that for these Gray-mapped BICM PNC systems, iterative decoding can achieve considerable gains over non-iterative decoding. Again, this is in contrast to the Gray-mapped BICM point-to-point communication system, for which iterative decoding provides little gain over non-iterative decoding. We further show that Gray mapping gives rise to best PNC rate for MUD-XOR and XOR-CD systems among several bits-to-symbol mappings under study. Overall, our results indicate that BICM PNC systems exhibit different decoding behavior from conventional BICM point-to-point systems. This paper serves as a first foray into the investigation of this issue.

Asynchronous Convolutional-Coded Physical-Layer Network Coding

This paper investigates the decoding process of asynchronous convolutional-coded physical-layer network coding (PNC) systems. Specifically, we put forth a layered decoding framework for convolutional-coded PNC consisting of three layers: symbol realignment layer, codeword realignment layer, and joint channel-decoding network coding (Jt-CNC) decoding layer. Our framework can deal with phase asynchrony (phase offset) and symbol arrival-time asynchrony (symbol misalignment) between the signals simultaneously transmitted by multiple sources. A salient feature of this framework is that it can handle both fractional and integral symbol misalignments. For the decoding layer, instead of Jt-CNC, previously proposed PNC decoding algorithms (e.g., XOR-CD and reduced-state Viterbi algorithms) can also be used with our framework to deal with general symbol misalignments. Our Jt-CNC algorithm, based on belief propagation, is BER-optimal for synchronous PNC and near optimal for asynchronous PNC. Extending beyond convolutional codes, we further generalize the Jt-CNC decoding algorithm for all cyclic codes. Our simulation shows that Jt-CNC outperforms the previously proposed XOR-CD algorithm and reduced-state Viterbi algorithm by 2 dB for synchronous PNC. For both phase-asynchronous and symbol-asynchronous PNC, Jt-CNC performs better than the other two algorithms. Importantly, for real wireless network experimentation, we implemented our decoding algorithm in a PNC prototype built on the USRP software radio platform. Our experiment shows that the proposed Jt-CNC decoder works well in practice.