Sparse-Graph Codes and Peeling Decoder for Compressed Sensing

Weijun ZENG  Huali WANG  Xiaofu WU  Hui TIAN  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.9   pp.1712-1716
Publication Date: 2016/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.1712
Type of Manuscript: LETTER
Category: Digital Signal Processing
Keyword: 
compressed sensing,  sparse sensing matrices,  sparse-graph codes,  peeling decoder,  

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Summary: 
In this paper, we propose a compressed sensing scheme using sparse-graph codes and peeling decoder (SGPD). By using a mix method for construction of sensing matrices proposed by Pawar and Ramchandran, it generates local sensing matrices and implements sensing and signal recovery in an adaptive manner. Then, we show how to optimize the construction of local sensing matrices using the theory of sparse-graph codes. Like the existing compressed sensing schemes based on sparse-graph codes with “good” degree profile, SGPD requires only O(k) measurements to recover a k-sparse signal of dimension n in the noiseless setting. In the presence of noise, SGPD performs better than the existing compressed sensing schemes based on sparse-graph codes, still with a similar implementation cost. Furthermore, the average variable node degree for sensing matrices is empirically minimized for SGPD among various existing CS schemes, which can reduce the sensing computational complexity.