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.

翻译：在高维离散输入加性噪声模型中进行贝叶斯推断是通信系统中的一个基本挑战，因为所需联合后验概率质量函数的支撑集随未知变量数量呈指数增长。本文提出了一种基于张量列车框架的方法，以实现离散输入加性噪声模型中易处理且近乎最优的贝叶斯推断。核心洞察在于：联合对数后验概率质量函数在张量列车格式下具有精确的低秩表示，从而支持紧凑存储和高效计算。为恢复符号级后验边缘概率，我们开发了一种实用推断流程，该流程利用截断泰勒级数初始化的张量列车交叉算法来近似后验对数指数的指数。为展示该方法的普适性，我们针对两个经典通信问题推导了显式低秩张量列车构造：加性高斯白噪声下的线性观测模型（应用于多输入多输出检测）以及双输入加性高斯白噪声信道上二进制线性分组纠错码的软判决译码。数值结果表明，在广泛信噪比范围内，该方法仅需适中的张量列车秩即可实现近乎最优的误码率性能。这些结果凸显了张量网络方法在通信系统高效贝叶斯推断中的应用潜力。