The effect of spatial coupling on compressive sensing


Conference Paper

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. ©2010 IEEE.

Full Text

Duke Authors

Cited Authors

  • Kudekar, S; Pfister, HD

Published Date

  • December 1, 2010

Published In

  • 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010

Start / End Page

  • 347 - 353

International Standard Book Number 13 (ISBN-13)

  • 9781424482146

Digital Object Identifier (DOI)

  • 10.1109/ALLERTON.2010.5706927

Citation Source

  • Scopus