Interleaved Block-Sparse Transform

TL;DR

The paper tackles the hardware bottleneck in achieving Bayes-optimal recovery for large-scale linear systems with right-unitarily invariant transforms. It introduces the Interleaved Block-Sparse Transform (IBS-FT), constructed from interleaved low-dimensional transforms, and couples it with the IBS-CD-MAMP estimator to perform a memory-domain MLE and a source-domain NLE, thereby reducing implementation scale. The authors develop BS-FT, W-IBS-FT, and B-IBS-FT variants, analyze their complexity (notably $\Theta_{\rm IBS} = \mathcal{O}(\log_{N} N_s)$), and demonstrate through simulations in compressed sensing and interleave frequency division multiplexing that substantial hardware savings are achievable with minimal performance loss. Overall, the IBS-FT and IBS-CD-MAMP enable scalable, low-complexity, nearly Bayes-optimal signal recovery in large-scale sensing and multicarrier systems, offering practical applicability for modern transceivers.

Abstract

Low-complexity Bayes-optimal memory approximate message passing (MAMP) is an efficient signal estimation algorithm in compressed sensing and multicarrier modulation. However, achieving replica Bayes optimality with MAMP necessitates a large-scale right-unitarily invariant transformation, which is prohibitive in practical systems due to its high computational complexity and hardware costs. To solve this difficulty, this letter proposes a low-complexity interleaved block-sparse (IBS) transform, which consists of interleaved multiple low-dimensional transform matrices, aimed at reducing the hardware implementation scale while mitigating performance loss. Furthermore, an IBS cross-domain memory approximate message passing (IBS-CD-MAMP) estimator is developed, comprising a memory linear estimator in the IBS transform domain and a non-linear estimator in the source domain. Numerical results show that the IBS-CD-MAMP offers a reduced implementation scale and lower complexity with excellent performance in IBS-based compressed sensing and interleave frequency division multiplexing systems.

Figures (5)

• Figure 1: Graphic illustration of CD-MAMP estimator.
• Figure 2: Graphic illustration for the BW-IBS-FT.
• Figure 3: Graphic illustration for BW-IBS-FT in large-scale noisy linear system.
• Figure 4: Graphic illustration for the IBS-CD-MAMP estimator.
• Figure 5: Comparisons of IBS-FT performance in compressed sensing and multicarrier modulation.