On CS image reconstruction by high rate non-binary low density parity check code over GF(q)

Abstract

This paper explores the scope of integration of compressed sensing (CS) and low density parity check (LDPC) codes for 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 non-binary (NB) LDPC code is proposed first. The NB-LDPC code is designed using the base matrix of the LDPC code present in IEEE 802.16 standard. The proposed NB-LDPC code matrices are quasi-cyclic in nature with a large girth and an irregular structure. The code matrices are so designed that they can act as the sensing matrix for CS applications and also provide a means of protection from channel errors. This study shows that the proposed LDPC codes can act as CS sensing matrices and also offer a low bit error rate performance as compared to the existing codes. A large set of simulation results report the improved CS image reconstruction performance as variation in measurement sizes and rate of the NB-LDPC codes. Simulations over a large number of test images (natural, remote sensing and medical images) show structural similarity index $${\sim }$$ 0.7512, for the reconstructed images using $$60\%$$ measurements at 8 dB channel signal to noise ratio, half rate NB-LDPC code over GF(4) and iterative double reliability based hard decision decoding.