Counter Random Gradient Descent Bit-Flipping Decoder for LDPC Codes

Tabu-list random-penalty gradient descent bit-flipping (TRGDBF) is a hard-decision algorithm for decoding low-density parity-check (LDPC) codes, which offers a significant improvement in error correction. However, compared to the current gradient descent bit-flipping (GDBF) variants, it converges slower and has no obvious performance advantage unless enough iterations are allowed. To accelerate the convergence speed, this paper presents a counter random GDBF (CRGDBF) algorithm in which a bit is forbidden to flip in the next iteration after being flipped several times. Incorporating the random operation, the forbidden-mechanism shows a dynamic property, facilitating the decoder more efficiently to break trapping sets. Simulation results show that the CRGDBF can achieve up to 5 times better decoding performance than the TRGDBF algorithm within finite iterations. Additionally, an architecture is presented for implementing the CRGDBF algorithm, demonstrating it only brings limited hardware overhead compared to the TRGDBF.