Decoding LDPC codes via Noisy Gradient Descent Bit-Flipping with Re-Decoding

In this paper, we consider the performance of the Noisy Gradient Descent Bit Flipping (NGDBF) algorithm under re-decoding of failed frames. NGDBF is a recent algorithm that uses a non-deterministic gradient descent search to decode low-density parity check (LDPC) codes. The proposed re-decode procedure obtains improved performance because the perturbations are independent at each re-decoding phase, therefore increasing the likelihood of successful decoding. We examine the benefits of re-decoding for an LDPC code from the IEEE 802.3an standard, and find that only a small fraction of re-decoded frames are needed to obtain significant performance benefits. When re-decoding is used, the NGDBF performance is very close to a benchmark offset min-sum decoder for the 802.3an code.