Following the great success of Machine Learning (ML), especially Deep Neural Networks (DNNs), in many research domains in 2010s, several learning-based approaches were proposed for detection in large inverse linear problems, e.g., massive MIMO systems. The main motivation behind is that the complexity of Maximum A-Posteriori (MAP) detection grows exponentially with system dimensions. Instead of using DNNs, essentially being a black-box in its most basic form, we take a slightly different approach and introduce a probabilistic Continuous relaxation of disCrete variables to MAP detection. Enabling close approximation and continuous optimization, we derive an iterative detection algorithm: ConCrete MAP Detection (CMD). Furthermore, by extending CMD to the idea of deep unfolding, we allow for (online) optimization of a small number of parameters to different working points while limiting complexity. In contrast to recent DNN-based approaches, we select the optimization criterion and output of CMD based on information theory and are thus able to learn approximate probabilities of the individual optimal detector. This is crucial for soft decoding in today's communication systems. Numerical simulation results in MIMO systems reveal CMD to feature a promising performance complexity trade-off compared to SotA. Notably, we demonstrate CMD's soft outputs to be reliable for decoders.

中文翻译：

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ConCrete MAP：学习离散变量的概率松弛以实现低复杂度的软估算

随着机器学习（ML）特别是深度神经网络（DNN）的巨大成功，在2010年代的许多研究领域中，提出了几种基于学习的方法来检测大型逆线性问题，例如大规模MIMO系统。其背后的主要动机是，最大A后验（MAP）检测的复杂性随系统尺寸呈指数增长。代替使用DNN（本质上是其最基本的形式的黑匣子），我们采用略有不同的方法，并将离散变量的概率连续松弛引入MAP检测。通过启用近似逼近和连续优化，我们得出了一种迭代检测算法：Concrete MAP Detection（CMD）。此外，通过将CMD扩展到深度展开的思想，我们允许（在线）优化少量参数以适应不同的工作点，同时限制了复杂性。与最近的基于DNN的方法相反，我们基于信息论选择了优化准则和CMD的输出，因此能够了解单个最优检测器的近似概率。这对于当今通信系统中的软解码至关重要。MIMO系统中的数值仿真结果表明，与SotA相比，CMD具有可观的性能复杂度折衷。值得注意的是，我们证明了CMD的软输出对于解码器是可靠的。我们基于信息论选择了CMD的优化准则和输出，因此能够了解各个最优检测器的近似概率。这对于当今通信系统中的软解码至关重要。MIMO系统中的数值仿真结果表明，与SotA相比，CMD具有可观的性能复杂度折衷。值得注意的是，我们证明了CMD的软输出对于解码器是可靠的。我们基于信息论选择了CMD的优化准则和输出，因此能够了解单个最优检测器的近似概率。这对于当今通信系统中的软解码至关重要。MIMO系统中的数值仿真结果表明，与SotA相比，CMD具有可观的性能复杂度折衷。值得注意的是，我们证明了CMD的软输出对于解码器是可靠的。