A Compressed Sensing-Based Low-Density Parity-Check Real-Number Code

In this paper, we propose a novel low-density parity-check real-number code, based on compressed sensing. A real-valued message is encoded by a coding matrix (with more rows than columns) and transmitted over an erroneous channel, where sparse errors (impulsive noise) corrupt the codeword. In the decoding procedure, we apply a structured sparse (low-density) parity-check matrix, the Permuted Block Diagonal matrix, to the corrupted output, and the errors can be corrected by solving a compressed sensing problem. A compressed sensing algorithm, Cross Low-dimensional Pursuit, is used to decode the code by solving this compressed sensing problem. The proposed code has high error correction performance and decoding efficiency. The comparative experimental results demonstrate both advantages of our code. We also apply our code to cryptography.