Efficiency Meets Reliability: Enhanced Generalized Interleaved Transform for Random Multiplexing

To meet the demands of 6G wireless systems operating in high-mobility scenarios, this paper presents a design of a random multiplexing (RM) communication system that is both storage-efficient and highly reliable. In principle, RM with cross-domain memory approximate message passing (CD-MAMP) can achieve replica maximum a posteriori (MAP)-optimal performance by constructing a fully dense equivalent channel matrix. However, its practical implementation is hindered by the large storage overhead of conventional interleavers and by performance degradation in severely ill-conditioned channels, which existing related work (focusing on interleaving and transform designs) fails to address simultaneously. To overcome these issues, we develop a storage-efficient and highly reliable system that integrates RM with CD-MAMP, referred to as RM-MAMP. Specifically, we propose a Logistic chaotic mapping interleaver with a quantitative parameter-selection criterion, and a dual-stage high-order permutation polynomial interleaver, both of which achieve nearly identical bit-error-rate (BER) as fully random interleavers while reducing the interleaver storage from O(N) to O(1) and significantly lowering interleaver signaling overhead. We further propose a highly reliable interleaved transform framework, comprising an interleaved phase perturbation transform and a multi-layer interleaved coupled transform, to enhance the incoherence and diversity of the equivalent channel matrix. Simulation results show that the proposed storage-efficient interleavers maintain BER performance comparable to fully random interleavers, while the highly reliable transforms provide over 4 dB gain in severely time-varying channels, confirming the dual benefits of reduced storage overhead and improved robustness for the enhanced RM-MAMP system.

Interleaved Block-Sparse Transform

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.