A Tensor-Train Framework for Bayesian Inference in High-Dimensional Systems: Applications to MIMO Detection and Channel Decoding

• URL: http://arxiv.org/abs/2604.05890v1
• Date: Tue, 07 Apr 2026 13:53:21 GMT
• Title: A Tensor-Train Framework for Bayesian Inference in High-Dimensional Systems: Applications to MIMO Detection and Channel Decoding
• Abstract summary: We propose a tensor-train (TT) framework for tractable, near-optimal Bayesian inference in additive noise models.<n>A practical inference procedure approximates the exponential of the log-posterior using a TT-cross algorithm with a truncated Taylor-series.<n> Numerical results show near-optimal error-rate performance across a wide range of signal-to-noise ratios.
• Score: 4.181178496700224
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian inference in high-dimensional discrete-input additive noise models is a fundamental challenge in communication systems, as the support of the required joint a posteriori probability (APP) mass function grows exponentially with the number of unknown variables. In this work, we propose a tensor-train (TT) framework for tractable, near-optimal Bayesian inference in discrete-input additive noise models. The central insight is that the joint log-APP mass function admits an exact low-rank representation in the TT format, enabling compact storage and efficient computations. To recover symbol-wise APP marginals, we develop a practical inference procedure that approximates the exponential of the log-posterior using a TT-cross algorithm initialized with a truncated Taylor-series. To demonstrate the generality of the approach, we derive explicit low-rank TT constructions for two canonical communication problems: the linear observation model under additive white Gaussian noise (AWGN), applied to multiple-input multiple-output (MIMO) detection, and soft-decision decoding of binary linear block error correcting codes over the binary-input AWGN channel. Numerical results show near-optimal error-rate performance across a wide range of signal-to-noise ratios while requiring only modest TT ranks. These results highlight the potential of tensor-network methods for efficient Bayesian inference in communication systems.

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