论文标题
多层双线性概括性消息传递
Multi-Layer Bilinear Generalized Approximate Message Passing
论文作者
论文摘要
在本文中，我们将双线性通用近似消息传递（大型AMP）方法扩展到最初是针对高维度的双线性回归提议的，以延长用于处理级联问题的多层案例，例如在相关通信中引起的矩阵基质化问题。假设具有已知先验的统计独立的矩阵条目，称为ML-Ligamp的新算法可以在高维极限中近似一般的总和产物回旋信念传播（LBP），从而大大降低了计算复杂性。我们证明，在很大的系统限制下，可以通过一组称为状态进化的简单一维方程（SE）来完全表征ML-Ligamp的渐近MSE性能。我们确定ML-Ligamp'SE预测的渐近MSE与复制方法预测的确切MMSE完全匹配，该方法众所周知，该方法在贝叶斯最佳时期是最佳的，但在实践中是不可行的。该一致性表明，尽管ML-ligamp的计算负担要低得多，但ML-Ligamp仍可能保留与MMSE估计器相同的贝叶斯最佳性能。作为一般ML-Ligamp的说明性示例，我们提供了一个检测器设计，该设计可以估算频道褪色和数据符号，共同具有高精度，用于两跳上的放大和前向继电器通信系统。
In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP' SE matches perfectly the exact MMSE predicted by the replica method, which is well known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMP's computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems.
