On the equivalence between graph isomorphism testing and function approximation with GNNs

Graph neural networks (GNNs) have achieved lots of success on graph-structured data. In the light of this, there has been increasing interest in studying their representation power. One line of work focuses on the universal approximation of permutation-invariant functions by certain classes of GNNs, and another demonstrates the limitation of GNNs via graph isomorphism tests. Our work connects these two perspectives and proves their equivalence. We further develop a framework of the representation power of GNNs with the language of sigma-algebra, which incorporates both viewpoints. Using this framework, we compare the expressive power of different classes of GNNs as well as other methods on graphs. In particular, we prove that order-2 Graph G-invariant networks fail to distinguish non-isomorphic regular graphs with the same degree. We then extend them to a new architecture, Ring-GNNs, which succeeds on distinguishing these graphs and provides improvements on real-world social network datasets

A Novel Uplink Data Transmission Scheme For Small Packets In Massive MIMO System

Intelligent terminals often produce a large number of data packets of small lengths. For these packets, it is inefficient to follow the conventional medium access control (MAC) protocols because they lead to poor utilization of service resources. We propose a novel multiple access scheme that targets massive multiple-input multiple-output (MIMO) systems based on compressive sensing (CS). We employ block precoding in the time domain to enable the simultaneous transmissions of many users, which could be even more than the number of receive antennas at the base station. We develop a block-sparse system model and adopt the block orthogonal matching pursuit (BOMP) algorithm to recover the transmitted signals. Conditions for data recovery guarantees are identified and numerical results demonstrate that our scheme is efficient for uplink small packet transmission.Comment: IEEE/CIC ICCC 2014 Symposium on Signal Processing for Communication

Multiple Access for Small Packets Based on Precoding and Sparsity-Aware Detection

Modern mobile terminals often produce a large number of small data packets. For these packets, it is inefficient to follow the conventional medium access control protocols because of poor utilization of service resources. We propose a novel multiple access scheme that employs block-spreading based precoding at the transmitters and sparsity-aware detection schemes at the base station. The proposed scheme is well suited for the emerging massive multiple-input multiple-output (MIMO) systems, as well as conventional cellular systems with a small number of base-station antennas. The transmitters employ precoding in time domain to enable the simultaneous transmissions of many users, which could be even more than the number of receive antennas at the base station. The system is modeled as a linear system of equations with block-sparse unknowns. We first adopt the block orthogonal matching pursuit (BOMP) algorithm to recover the transmitted signals. We then develop an improved algorithm, named interference cancellation BOMP (ICBOMP), which takes advantage of error correction and detection coding to perform perfect interference cancellation during each iteration of BOMP algorithm. Conditions for guaranteed data recovery are identified. The simulation results demonstrate that the proposed scheme can accommodate more simultaneous transmissions than conventional schemes in typical small-packet transmission scenarios.Comment: submitted to IEEE Transactions on Wireless Communication