Non-binary LDPC codes for compressed sensing image reconstruction on AWGN channel

This work attempts to integrate Compressed Sensing (CS) and Low Density Parity Check (LDPC) codes as a means of transmission of sub-sampled measurements of digital images over additive white Gaussian noise channel for its reconstruction at far end. To this aim, a scheme to construct a four cycle free binary LDPC code of column weight two is proposed first. This binary code matrix is then used as a base matrix to construct a non-binary (NB)-LDPC code. Proposed NB parity check matrix configuration offers the benefits of a large girth, an irregular structure and a column weight more than two. With an aim to serve dual purposes viz sensing matrix for CS and error resiliency on communication channel, the present study shows that these new code structures offer low bit error rate performance compared to the existing codes and a comparable mutual incoherence measure with Discrete Cosine Transform sparse space. A large set of simulation results report the improved CS image reconstruction performance in terms of measurement sizes and rate of the NB-LDPC codes. Simulations over a large number of test images (natural, remote sensing and medical images) show ~28 dB for the reconstructed images with 70% measurements at 8 dB channel signal-to-noise ratio, half rate NB-LDPC code over GF(16) and iterative double reliability based hard decision decoding. The proposed NB-LDPC code construction technique is very simple and yet offers good decoding performance. The performance can be further improved using soft decision decoding algorithms.