Generalized Adaptive Diversity Gradient Descent Bit-Flipping with a Finite State Machine

In this paper, we introduce a novel gradient descent bit-flipping algorithm with a finite state machine (GDBF-wSM) for iterative decoding of low-density parity-check (LDPC) codes. The algorithm utilizes a finite state machine to update variable node potentials—for each variable node, the corresponding finite state machine adjusts the update value based on whether the node was a candidate for flipping in previous iterations. We also present a learnable framework that can optimize decoder parameters using a database of uncorrectable error patterns. The performance of the proposed algorithm is illustrated for various regular LDPC codes, both in a binary symmetric channel (BSC) and the channel with additive white Gaussian noise (AWGN). The numerical results indicate a performance improvement when comparing our algorithm to previously proposed GDBF-based approaches.