Hard-decision iterative decoding of LDPC codes with bounded error rate

Differently from bounded-distance decoders used for algebraic codes, iterative decoders used for low-density parity-check (LDPC) codes are not characterized by a deterministic decoding radius. Therefore, the error rates of LDPC-coded transmissions are usually estimated heuristically through simulations.This is adequate for many applications like wireless communications, where a frame error rate (FER) in the order of 10^(-6) or higher is usually targeted. However, lower values of FER can barely be assessed through simulations, and this limits the use of LDPC codes in applications requiring a lower FER, like optical communications and code-based cryptography. In this paper we introduce and study a version of the classic bit flipping (BF) decoder for which we are able to devise and develop a theoretical characterization of the FER. In addition, we consider a two-iteration hard-decision decoder for LDPC codes derived from BF, and discuss its error rate performance. Our results are validated through numerical simulations.