On the Performance of Turbo Signal Recovery with Partial DFT Sensing Matrices

This letter is on the performance of the turbo signal recovery (TSR) algorithm for partial discrete Fourier transform (DFT) matrices based compressed sensing. Based on state evolution analysis, we prove that TSR with a partial DFT sensing matrix outperforms the well-known approximate message passing (AMP) algorithm with an independent identically distributed (IID) sensing matrix.Comment: to appear in IEEE Signal Processing Letter

The dynamics of message passing on dense graphs, with applications to compressed sensing

Approximate message passing algorithms proved to be extremely effective in reconstructing sparse signals from a small number of incoherent linear measurements. Extensive numerical experiments further showed that their dynamics is accurately tracked by a simple one-dimensional iteration termed state evolution. In this paper we provide the first rigorous foundation to state evolution. We prove that indeed it holds asymptotically in the large system limit for sensing matrices with independent and identically distributed gaussian entries. While our focus is on message passing algorithms for compressed sensing, the analysis extends beyond this setting, to a general class of algorithms on dense graphs. In this context, state evolution plays the role that density evolution has for sparse graphs. The proof technique is fundamentally different from the standard approach to density evolution, in that it copes with large number of short loops in the underlying factor graph. It relies instead on a conditioning technique recently developed by Erwin Bolthausen in the context of spin glass theory.Comment: 41 page

Massive Unsourced Random Access: Exploiting Angular Domain Sparsity

This paper investigates the unsourced random access (URA) scheme to accommodate numerous machine-type users communicating to a base station equipped with multiple antennas. Existing works adopt a slotted transmission strategy to reduce system complexity; they operate under the framework of coupled compressed sensing (CCS) which concatenates an outer tree code to an inner compressed sensing code for slot-wise message stitching. We suggest that by exploiting the MIMO channel information in the angular domain, redundancies required by the tree encoder/decoder in CCS can be removed to improve spectral efficiency, thereby an uncoupled transmission protocol is devised. To perform activity detection and channel estimation, we propose an expectation-maximization-aided generalized approximate message passing algorithm with a Markov random field support structure, which captures the inherent clustered sparsity structure of the angular domain channel. Then, message reconstruction in the form of a clustering decoder is performed by recognizing slot-distributed channels of each active user based on similarity. We put forward the slot-balanced K-means algorithm as the kernel of the clustering decoder, resolving constraints and collisions specific to the application scene. Extensive simulations reveal that the proposed scheme achieves a better error performance at high spectral efficiency compared to the CCS-based URA schemes

An Overview of Multi-Processor Approximate Message Passing

Approximate message passing (AMP) is an algorithmic framework for solving linear inverse problems from noisy measurements, with exciting applications such as reconstructing images, audio, hyper spectral images, and various other signals, including those acquired in compressive signal acquisiton systems. The growing prevalence of big data systems has increased interest in large-scale problems, which may involve huge measurement matrices that are unsuitable for conventional computing systems. To address the challenge of large-scale processing, multiprocessor (MP) versions of AMP have been developed. We provide an overview of two such MP-AMP variants. In row-MP-AMP, each computing node stores a subset of the rows of the matrix and processes corresponding measurements. In column- MP-AMP, each node stores a subset of columns, and is solely responsible for reconstructing a portion of the signal. We will discuss pros and cons of both approaches, summarize recent research results for each, and explain when each one may be a viable approach. Aspects that are highlighted include some recent results on state evolution for both MP-AMP algorithms, and the use of data compression to reduce communication in the MP network

Replica Analysis and Approximate Message Passing Decoder for Superposition Codes

Superposition codes are efficient for the Additive White Gaussian Noise channel. We provide here a replica analysis of the performances of these codes for large signals. We also consider a Bayesian Approximate Message Passing decoder based on a belief-propagation approach, and discuss its performance using the density evolution technic. Our main findings are 1) for the sizes we can access, the message-passing decoder outperforms other decoders studied in the literature 2) its performance is limited by a sharp phase transition and 3) while these codes reach capacity as $B$ (a crucial parameter in the code) increases, the performance of the message passing decoder worsen as the phase transition goes to lower rates.Comment: 5 pages, 5 figures, To be presented at the 2014 IEEE International Symposium on Information Theor