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

arXiv: https://arxiv.org/abs/2604.05890 · HTML: https://mlsanity.com/paper/2604.05890/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 49 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation](https://mlsanity.com/paper/2403.03545/) (2024)
- [TTOpt: A Maximum Volume Quantized Tensor Train-based Optimization and its Application to Reinforcement Learning](https://mlsanity.com/paper/2205.00293/) (2022)
- [Blind Equalization and Channel Estimation in Coherent Optical Communications Using Variational Autoencoders](https://mlsanity.com/paper/2204.11776/) (2022)

## Abstract (arXiv)

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.