Model-based compressive sensing (CS) for signal specific applications is of particular interest in communication sector. This process cast the problem of signal reconstruction and threshold estimation a one of learning a hyperplane that separates the sampling vectors. This paper presents a comprehensive study on the design and implementation of a Pi rotation-based encoder within the framework of Low-Density Parity-Check (LDPC) codes, focusing on optimizing constraints to enhance performance. Addressing the inherent complexity of the optimal Maximum A Posteriori (MAP) estimator, we propose two suboptimal solutions, including an iterative approach capable of managing large-scale problems. Leveraging interval analysis techniques allows for the rapid exclusion of inconsistent solutions concerning the signal model and quantization noise, thus improving computational efficiency. Additionally, we introduce the Binary Compressive Sensing with Unknown Threshold (BCS-UT) algorithm, which outperforms existing methods despite the lack of knowledge of the threshold. The proposed framework accommodates noisy binary measurements by incorporating slack variables to relax measurement consistency conditions. Furthermore, we introduce two modifications to the Sum-Product Algorithm (SPA) based on the tanh and tanh21 functions, which are essential for enhancing the performance of LDPC codes and reducing the error floor relative to the standard SPA.
Girish et al. (Tue,) studied this question.