  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.
