Peeling Decoding of LDPC Codes with Applications in Compressed Sensing

Abstract

We present a new approach for the analysis of iterative peeling decoding recovery algorithms in the context of Low-Density Parity-Check (LDPC) codes and compressed sensing. The iterative recovery algorithm is particularly interesting for its low measurement cost and low computational complexity. The asymptotic analysis can track the evolution of the fraction of unrecovered signal elements in each iteration, which is similar to the well-known density evolution analysis in the context of LDPC decoding algorithm. Our analysis shows that there exists a threshold on the density factor; if under this threshold, the recovery algorithm is successful; otherwise it will fail. Simulation results are also provided for verifying the agreement between the proposed asymptotic analysis and recovery algorithm. Compared with existing works of peeling decoding algorithm, focusing on the failure probability of the recovery algorithm, our proposed approach gives accurate evolution of performance with different parameters of measurement matrices and is easy to implement. We also show that the peeling decoding algorithm performs better than other schemes based on LDPC codes.

Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

“…In recent years, many researchers have put forward many principles and methods to construct [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] and optimize [34][35][36] measurement matrices. This paper mainly studies the construction method of deterministic measurement matrices.…”