Pre-training has proven effective in addressing data scarcity and performance limitations in solving PDE problems with neural operators. However, challenges remain due to the heterogeneity of PDE datasets in equation types, which leads to high errors in mixed training. Additionally, dense pre-training models that scale parameters by increasing network width or depth incur significant inference costs. To tackle these challenges, we propose a novel **M**ixture-**o**f-**E**xperts **P**re-training **O**perator **T**ransformer (**MoE-POT**), a sparse-activated architecture that scales parameters efficiently while controlling inference costs. Specifically, our model adopts a layer-wise router-gating network to dynamically select 4 routed experts from 16 expert networks during inference, enabling the model to focus on equation-specific features. Meanwhile, we also integrate 2 shared experts, aiming to capture common properties of PDE and reduce redundancy among routed experts. The final output is computed as the weighted average of the results from all activated experts. We pre-train models with parameters from 30M to 0.5B on 6 public PDE datasets. Our model with 90M activated parameters achieves up to a 40\% reduction in zero-shot error compared with existing models with 120M activated parameters. Additionally, we conduct interpretability analysis, showing that dataset types can be inferred from router-gating network decisions, which validates the rationality and effectiveness of the MoE architecture.

This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that the capacity of the Gaussian two-pair TWRC is achievable to within$\frac{1}{ 2}$bit for arbitrary channel conditions. For the outer bound, we derive a genie-aided bound of the Gaussian two-pair TWRC, which is tighter than the cut-set bound. For the inner bound, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. We further present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide flexibility to fully exploit the channel randomness. We show that judicious power allocation at the users and at the relay is necessary to approach the channel capacity under various channel conditions.

This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that our scheme can achieve the capacity of the two-pair TWRC to within 1/2 bit per user. In the proof, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. Further, we present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide more flexibility to fully exploit the channel randomness. We also show that judicious power allocation among the superimposed codeword components at the relay is needed to approach the channel capacity.

This work investigates the broadcast channel with the knowledge of noncausal interference at the transmitter and side information at the receivers. The system studied involves one transmitter sending private information to two receivers. We first obtain an achievable rate region of this system by extending Gelfand and Pinsker's (GP's) random binning method, originally designed for point-to-point communications. We then apply the result to Gaussian scalar and vector channels, and consider the design of the auxiliary random variable used in GP's approach. Asymptotic analysis shows that the proposed scheme in both scalar and vector channels is asymptotically capacity-achieving at high signal-to-noise ratio (SNR). We further investigate the system optimization in the finite SNR regime. For the scalar channel, we derive the optimal auxiliary factor that maximizes the weighed sum-rate. For the vector channel, two kinds of suboptimal designing methods for the auxiliary matrix are proposed. Numerical results show that the proposed scheme can achieve a sum-rate close to the cut-set bound in the entire SNR regime, and significantly outperforms the schemes that do not exploit the knowledge of noncausal interference known at the transmitter.

This work investigates the maximum sum-rate of multi-pair MIMO two-way relay channels (TWRCs), in which a relay is responsible for forwarding information between multiple pairs of users. In this system, each pair of users forms a TWRC, and a user exchanges information only with its counterpart in the same TWRC. We focus on the multi-access channel (MAC) phase of the two-pair TWRCs. We first put forth a new interpretation of the space-division (SD) method based on the classical concept of principal angles in linear algebra. We argue that the signal spaces of the two users in a TWRC can be divided into the physical-layer network coding (PNC) signal subspace and the complete decoding (CD) signal subspace according to the principal angles between the two signal spaces of different user pairs. Based on the principal-angle framework, we then propose an extended SD method to mitigate the interference among the PNC signals and CD signals. We further derive the optimal decoding strategy and optimal precoder design principles that maximize the sum-rate of the MAC phase. The associated optimization problem, however, is non-convex. We therefore propose a suboptimal solution for precoder design and analyze the asymptotic rate gap benchmarked against the cut-set bound. Significant performance improvements have been observed for the proposed hybrid PNC-CD system compared with pure complete decoding and pure PNC decoding.

We consider a multi-pair two-way relay (TWR) network where the multi-antenna users of each pair exchange information via a multi-antenna relay. The interesting challenge is how to deal with the inter- user interference and explore the potential of multiple antennas concurrently. Beamforming methods in previous works are based on the criteria of zero forcing (ZF) and minimum mean square error (MMSE) to mitigate the inter-user interference. However, since the user already knows its own information, it is unnecessary to mitigate the intra-pair interference at the relay. In this paper, we propose a coordinated eigen beamforming (CEB) scheme, which maximizes the effective channel gain of each user in the sub-space nulling the inter-pair interference. The CEB scheme is implemented with an iterative optimization algorithm with limited iterations. Additionally, the power loading scheme is adopted after convergence to guarantee fairness among users. Simulation results indicate our scheme achieves near full diversity order within the sub-space, outperforming pervious works.

Many-to-one transport results in congestion in wireless sensor networks (WSNs). This is due to the sudden impulse of information flowing to a single destination by single branch. More attention has been paid to congestion control in WSN, but most research works in the past were apt to handle it by controlling output sending rate, and seldom sought solutions on utilizing the idle resources of non-congestion branch. In this paper, an Active Congestion Help (ACOH) mechanism is designed to find and build an auxiliary routing when congestion. For fairness and flow balancing, Adaptive Flow Allocation algorithm (AF) is designed to distribute flow as adaptive proportion between the main routing and the auxiliary. AF is considering the transmitting-receiving rate of congestive and auxiliary node, and quickly converges to a fair and efficient proportion. In ACOH, a simple backpressure is used to handle the data flow which exceeds the maximum throughput. Simulation results validate the effectiveness of our ACOH.

In this paper, we propose a novel multi-tier clustering strategy using cultural-based multiobjective particle swarm optimization (Cultural-MOPSO) for maximizing the longevity of wireless sensor networks. We take into account the distribution of surviving nodes and define three objective functions based on multi-tier cluster hierarchy to fully evaluate every clusterhead election. Simulation results demonstrate that our proposed strategy can achieve energy-efficient multi-tier cluster hierarchy and outperform two other PSO-based clustering schemes in terms of a new metric of network longevity.

Joint processing algorithm of detection and decoding for linear block coded multiple-input multiple- output (MIMO) system is investigated in this paper. Iterative detection and decoding (IDD) algorithm, which is considered as the optimal approach for convolutional coded MIMO system, yet is not processing efficient enough for linear block coded MIMO system under given computational complexity. In this case, although list-type detection and list- type decoding are separately used to generate a list of candidates (hard information), only the associated soft information is calculated and passed. Motivated by the joint ML principle and list-type process, we propose a much simpler and more efficient method, named list detection and decoding (LDD) algorithm. LDD exploits the common nature of list-type process in IDD to generate a list of candidates (hard information) for decoding- and-decision instead of iterative processing in IDD. We show that LDD can achieve near-optimal performance while enabling a performance-complexity tradeoff with different list size. Furthermore, the fixed complexity is suitable for hardware implementation. Simulation results show that LDD outperforms IDD while having a lower decoding complexity.