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

2026-04-07

AI Summary

This work addresses the intractability of Bayesian inference in high-dimensional discrete-input additive noise models, where the posterior support grows exponentially. It establishes, for the first time, that the joint log-posterior probability mass function admits an exact low-rank structure when represented in the tensor train (TT) format. Leveraging this insight, the authors develop a general low-rank TT model applicable to MIMO detection and channel decoding. Symbol-wise marginal posterior inference is efficiently realized by combining the TT-cross algorithm with a truncated Taylor series approximation of the exponential function. The proposed method achieves near-optimal bit error rate performance across a wide signal-to-noise ratio range with only modest TT ranks, substantially reducing both computational and memory costs.

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.

Problem

• Bayesian inference
• high-dimensional systems
• discrete-input additive noise models
• MIMO detection
• channel decoding

Innovation

• Tensor-Train
• Bayesian inference
• high-dimensional systems
• MIMO detection
• channel decoding