A Stopping Criterion for Low-Density Parity-Check Codes

Low-density parity-check (LDPC) codes have an inherent stopping criterion, parity-check constraints (equations). By testing the parity-check constraints, an LDPC decoder can detect successful decoding and stop their decoding, which is, however, not possible with turbo codes. In this paper, we propose a stopping criterion to predict decoding failure of LDPC codes, instead of detecting successful decoding. If the decoder predicts the decoding failure in advance, the receiver can more rapidly response to the transmitter and request for additional parity bits with an automatic repeat request (ARQ) protocol, which reduces overall system latency. The receiver can also save power consumption by avoiding unnecessary decoder iterations. The proposed stopping criterion makes use of the variations of the number of satisfied parity-check constraints in the belief-propagation (BP) decoding which is always tested in the conventional BP decoding to detect successful decoding. Thus, the proposed stopping criterion does not require any additional complexity. The counting of satisfied parity-check constraints shows behaviors of the BP decoding, which comes, otherwise, from the observations of changes of log-likelihood ratio (LLR) values in multi-bit resolution with additional complexity.