Generalized Memory Approximate Message Passing

Tian, Feiyan; Liu, Lei; Chen, Xiaoming

doi:10.48550/arxiv.2110.06069

Cited by 3 publications

(7 citation statements)

References 25 publications

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“…In addition, the CSI acquisition can be further jointly considered in the receiver. Last but not least, in order to achieve the lower implementation complexity, CAMP [28] and MAMP [37], [38] can be redesigned for the coded GMU-MIMO systems instead of MU-OAMP/VAMP. APPENDIX APPENDIX A PROOF OF (13) IN LEMMA 2 In this appendix, we first review the OAMP/VAMP in uncoded linear vector system.…”

Section: Discussionmentioning

confidence: 99%

“…2) Other related low-complexity AMP-type algorithms: Recently, to avoid the high complexity LMMSE in OAMP/VAMP/EP, low-complexity Bayes-optimal convolutional AMP (CAMP) [36], memory AMP (MAMP) [37], and generalized MAMP (GMAMP) [38] were proposed for unitarily-invariant matrices with arbitrary input distributions. Therefore, CAMP, MAMP, and GMAMP may be good candidates with lower complexity for the proposed framework in this paper.…”

Section: E Connection To Existing Workmentioning

confidence: 99%

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Capacity Optimal Generalized Multi-User MIMO: A Theoretical and Practical Framework

Chi¹,

Liu²,

Song³

et al. 2021

Preprint

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Conventional multi-user multiple-input multipleoutput (MU-MIMO) mainly focused on Gaussian signaling, independent and identically distributed (IID) channels, and a limited number of users. It will be laborious to cope with the heterogeneous requirements in next-generation wireless communications, such as various transmission data, complicated communication scenarios, and unprecedented massive user access. Therefore, this paper studies a generalized MU-MIMO (GMU-MIMO) system with more practical constraints, i.e., non-Gaussian signaling, non-IID channel, and massive users and antennas. These generalized assumptions bring new challenges in theory and practice. For example, there is no accurate capacity analysis for GMU-MIMO. In addition, it is unclear how to achieve the capacity optimal performance with practical complexity.To address these challenges, a unified framework is proposed to derive the GMU-MIMO capacity and design a capacity optimal transceiver, which jointly considers encoding, modulation, detection, and decoding. Group asymmetry is developed to make a tradeoff between user rate allocation and implementation complexity. Specifically, the capacity region of group asymmetric GMU-MIMO is characterized by using the celebrated mutual information and minimum mean-square error (MMSE) lemma and the MMSE optimality of orthogonal approximate message passing (OAMP)/vector AMP (VAMP). Furthermore, a theoretically optimal multi-user OAMP/VAMP receiver and practical multi-user low-density parity-check (MU-LDPC) codes are proposed to achieve the capacity region of group asymmetric GMU-MIMO. Numerical results demonstrate that the gaps between theoretical detection thresholds of the proposed framework with optimized MU-LDPC codes and quadrature phase-shift keying (QPSK) modulation and the sum capacity of GMU-MIMO are about 0.2 dB. Moreover, their finite-length performances are about 1∼2 dB away from the associated sum capacity.

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Section: Discussionmentioning

confidence: 99%

Section: E Connection To Existing Workmentioning

confidence: 99%

Capacity Optimal Generalized Multi-User MIMO: A Theoretical and Practical Framework

Chi¹,

Liu²,

Song³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Similar to OAMP/VAMP, GVAMP has a high computational complexity. To this end, a generalized MAMP (GMAMP) was proposed for GLM [27]. The complexity of GMAMP is comparable to GAMP.…”

Section: A Backgroundmentioning

confidence: 99%

“…First, the CAMP [19], long-memory AMP [20], [21] and RI-AMP [28] were consisted of NLEs and an MF with Onsager correction terms, whose structure is similar to that of AMP [3] or GAMP [24]. Second, the MAMP [22], [23] and GMAMP [27] were consisted of orthogonal NLEs and an orthogonal long-memory MF, whose structure is similar to that of OAMP/VAMP [12], [13] or GVAMP [25].…”

Section: A Backgroundmentioning

confidence: 99%

Sufficient Statistic Memory AMP

Liu¹,

Huang²,

Kurkoski³

2021

Preprint

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Approximate message passing (AMP) is a promising technique for unknown signal reconstruction of certain highdimensional linear systems with non-Gaussian signaling. A distinguished feature of the AMP-type algorithms is that their dynamics can be rigorously described by state evolution. However, state evolution does not necessarily guarantee the convergence of iterative algorithms. To solve the convergence problem of AMPtype algorithms in principle, this paper proposes a memory AMP (MAMP) under a sufficient statistic condition, named sufficient statistic MAMP (SS-MAMP). We show that the covariance matrices of SS-MAMP are L-banded and convergent. Given an arbitrary MAMP, we can construct an SS-MAMP by damping, which not only ensures the convergence of MAMP, but also preserves the orthogonality of MAMP, i.e., its dynamics can be rigorously described by state evolution. As a byproduct, we prove that the Bayes-optimal orthogonal/vector AMP (BO-OAMP/VAMP) is an SS-MAMP. As a result, we reveal two interesting properties of BO-OAMP/VAMP for large systems: 1) the covariance matrices are L-banded and are convergent in BO-OAMP/VAMP, and 2) damping and memory are useless (i.e., do not bring performance improvement) in BO-OAMP/VAMP. As an example, we construct a sufficient statistic Bayes-optimal MAMP (BO-MAMP), which is Bayes optimal if its state evolution has a unique fixed point and its MSE is not worse than the original BO-MAMP. Finally, simulations are provided to verify the validity and accuracy of the theoretical results.

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“…Compared to GAMP, GLM-VAMP can be applied to more general random matrices but needs to pay more computational complexity. Similar to GLM-VAMP, a generalized version of MAMP was proposed in [42]. Beyond single-layer model, some extensions of AMP in multi-layer regions can be found in [43], [44], [45], [46].…”

Section: Introductionmentioning

confidence: 99%

A Concise Tutorial on Approximate Message Passing

Zou¹,

Yang²

2022

Preprint

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High-dimensional signal recovery of standard linear regression is a key challenge in many engineering fields, such as, communications, compressed sensing, and image processing. The approximate message passing (AMP) algorithm proposed by Donoho et al is a computational efficient method to such problems, which can attain Bayes-optimal performance in independent identical distributed (IID) sub-Gaussian random matrices region. A significant feature of AMP is that the dynamical behavior of AMP can be fully predicted by a scalar equation termed station evolution (SE). Although AMP is optimal in IID sub-Gaussian random matrices, AMP may fail to converge when measurement matrix is beyond IID sub-Gaussian. To extend the region of random measurement matrix, an expectation propagation (EP)-related algorithm orthogonal AMP (OAMP) was proposed, which shares the same algorithm with EP, expectation consistent (EC), and vector AMP (VAMP). This paper aims at giving a review for those algorithms. We begin with the worst case, i.e. least absolute shrinkage and selection operator (LASSO) inference problem, and then give the detailed derivation of AMP derived from message passing. Also, in the Bayes-optimal setting, we give the Bayes-optimal AMP which has a slight difference from AMP for LASSO. In addition, we review some AMP-related algorithms: OAMP, VAMP, and Memory AMP (MAMP), which can be applied to more general random matrices.

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Generalized Memory Approximate Message Passing

Cited by 3 publications

References 25 publications

Capacity Optimal Generalized Multi-User MIMO: A Theoretical and Practical Framework

Capacity Optimal Generalized Multi-User MIMO: A Theoretical and Practical Framework

Sufficient Statistic Memory AMP

A Concise Tutorial on Approximate Message Passing

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