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

TL;DR

This paper introduces a tensor-train framework for efficient Bayesian inference in high-dimensional communication models, enabling near-optimal performance with manageable computational complexity.

Contribution

The authors develop a low-rank tensor-train approach for exact representation and efficient computation of joint posterior probabilities in high-dimensional Bayesian models.

Findings

Achieves near-optimal error-rate performance in MIMO detection.

Requires only modest tensor ranks for accurate inference.

Provides explicit low-rank tensor constructions for key communication problems.

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.