1,165 research outputs found

    Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes

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    We study the approximate message-passing decoder for sparse superposition coding on the additive white Gaussian noise channel and extend our preliminary work [1]. We use heuristic statistical-physics-based tools such as the cavity and the replica methods for the statistical analysis of the scheme. While superposition codes asymptotically reach the Shannon capacity, we show that our iterative decoder is limited by a phase transition similar to the one that happens in Low Density Parity check codes. We consider two solutions to this problem, that both allow to reach the Shannon capacity: i) a power allocation strategy and ii) the use of spatial coupling, a novelty for these codes that appears to be promising. We present in particular simulations suggesting that spatial coupling is more robust and allows for better reconstruction at finite code lengths. Finally, we show empirically that the use of a fast Hadamard-based operator allows for an efficient reconstruction, both in terms of computational time and memory, and the ability to deal with very large messages.Comment: 40 pages, 18 figure

    Inference of the sparse kinetic Ising model using the decimation method

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    In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the â„“1\ell_1-optimization based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done automatically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudo-likelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that on various topologies and with different distribution of couplings, the decimation method outperforms the widely-used â„“1\ell _1-optimization based methods.Comment: 11 pages, 5 figure

    Graph Neural Network-Enhanced Expectation Propagation Algorithm for MIMO Turbo Receivers

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    Deep neural networks (NNs) are considered a powerful tool for balancing the performance and complexity of multiple-input multiple-output (MIMO) receivers due to their accurate feature extraction, high parallelism, and excellent inference ability. Graph NNs (GNNs) have recently demonstrated outstanding capability in learning enhanced message passing rules and have shown success in overcoming the drawback of inaccurate Gaussian approximation of expectation propagation (EP)-based MIMO detectors. However, the application of the GNN-enhanced EP detector to MIMO turbo receivers is underexplored and non-trivial due to the requirement of extrinsic information for iterative processing. This paper proposes a GNN-enhanced EP algorithm for MIMO turbo receivers, which realizes the turbo principle of generating extrinsic information from the MIMO detector through a specially designed training procedure. Additionally, an edge pruning strategy is designed to eliminate redundant connections in the original fully connected model of the GNN utilizing the correlation information inherently from the EP algorithm. Edge pruning reduces the computational cost dramatically and enables the network to focus more attention on the weights that are vital for performance. Simulation results and complexity analysis indicate that the proposed MIMO turbo receiver outperforms the EP turbo approaches by over 1 dB at the bit error rate of 10−510^{-5}, exhibits performance equivalent to state-of-the-art receivers with 2.5 times shorter running time, and adapts to various scenarios.Comment: 15 pages, 12 figures, 2 tables. This paper has been accepted for publication by the IEEE Transactions on Signal Processing. Copyright may be transferred without notice, after which this version may no longer be accessibl

    Massive Unsourced Random Access: Exploiting Angular Domain Sparsity

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    This paper investigates the unsourced random access (URA) scheme to accommodate numerous machine-type users communicating to a base station equipped with multiple antennas. Existing works adopt a slotted transmission strategy to reduce system complexity; they operate under the framework of coupled compressed sensing (CCS) which concatenates an outer tree code to an inner compressed sensing code for slot-wise message stitching. We suggest that by exploiting the MIMO channel information in the angular domain, redundancies required by the tree encoder/decoder in CCS can be removed to improve spectral efficiency, thereby an uncoupled transmission protocol is devised. To perform activity detection and channel estimation, we propose an expectation-maximization-aided generalized approximate message passing algorithm with a Markov random field support structure, which captures the inherent clustered sparsity structure of the angular domain channel. Then, message reconstruction in the form of a clustering decoder is performed by recognizing slot-distributed channels of each active user based on similarity. We put forward the slot-balanced K-means algorithm as the kernel of the clustering decoder, resolving constraints and collisions specific to the application scene. Extensive simulations reveal that the proposed scheme achieves a better error performance at high spectral efficiency compared to the CCS-based URA schemes
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