Noisy belief propagation decoder

This paper analyzes the fundamental performance limits of an LDPC Belief Propagation (BP) decoder implemented on noisy hardware and proposes a robust decoder implementation to improve the resilience to hardware errors. Assuming that the effects of hardware noise in various computational units, i.e., variable nodes and check nodes, can be approximated by Gaussian noise, we develop a Gaussian approximate density evolution for noisy BP decoders. By the Gaussian approximate density evolution, we find that zero residual error rate is achievable for noisy BP decoders as long as the message representations are of arbitrarily high precision. Noisy BP decoding thresholds are then derived for various regular LDPC codes. These decoding thresholds determine maximum allowable communication and computation noise for reliable communication. Next, we propose an averaging BP decoder implementation by averaging over the messages in all up-to-date iterations to cancel out the computation noise. Simulation results demonstrate that on noisy hardware, the averaging BP decoder significantly reduces the residual error rates when compared to the nominal BP decoder.