NDLI: The effect of spatial coupling on compressive sensing

Content Provider	IEEE Xplore Digital Library
Author	Kudekar, S. Pfister, H.D.
Copyright Year	2010
Description	Author affiliation: New Mexico Consortium and CNLS, Los Alamos National Laboratory, USA (Kudekar, S.) \|\| Department of Electrical and Computer Engineering, Texas A&M University, College Station, USA (Pfister, H.D.)
Abstract	Recently, it was observed that spatially-coupled LDPC code ensembles approach the Shannon capacity for a class of binary-input memoryless symmetric (BMS) channels. The fundamental reason for this was attributed to a threshold saturation phenomena derived in [1]. In particular, it was shown that the belief propagation (BP) threshold of the spatially coupled codes is equal to the maximum a posteriori (MAP) decoding threshold of the underlying constituent codes. In this sense, the BP threshold is saturated to its maximum value. Moreover, it has been empirically observed that the same phenomena also occurs when transmitting over more general classes of BMS channels. In this paper, we show that the effect of spatial coupling is not restricted to the realm of channel coding. The effect of coupling also manifests itself in compressed sensing. Specifically, we show that spatially-coupled measurement matrices have an improved sparsity to sampling threshold for reconstruction algorithms based on verification decoding. For BP-based reconstruction algorithms, this phenomenon is also tested empirically via simulation. At the block lengths accesible via simulation, the effect is rather small but, based on the threshold analysis, we believe this warrants further study.
Starting Page	347
Ending Page	353
File Size	557762
Page Count	7
File Format	PDF
ISBN	9781424482153
e-ISBN	9781424482160
DOI	10.1109/ALLERTON.2010.5706927
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-09-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Couplings Parity check codes Decoding Sparse matrices Noise measurement Equations Compressed sensing
Content Type	Text
Resource Type	Article

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