Finite alphabet iterative decoders robust to faulty hardware: Analysis and selection

In this paper, we analyze Finite Alphabet Iterative Decoders (FAIDs) running on faulty hardware. Under symmetric error models at the message level, we derive the noisy Density Evolution equations, and introduce a new noisy threshold phenomenon (called functional threshold), which accurately characterizes the convergence behavior of LDPC code ensembles under noisy-FAID decoding. The proposed functional threshold is then used to identify FAIDs which are particularly robust to the transient hardware noise. Finite-length simulations are drawn to verify the validity of the asymptotical study.