This paper proposes a new iterative gradient descent decoding method for real number parity codes. The proposed decoder, named Gradient Descent Symbol Update (GDSU), is used for a class of low-density parity-check (LDPC) real-number codes that can be defined with parity check matrices which are similar to those of the binary LDPC from communication standards such as WiFi (IEEE 802.11), 5G. These codes have a simple and efficient two stage encoding that is especially appealing for the real number field. The Gradient optimization based decoding has been a relatively simple and fast decoding technique for codes over finite fields. We show that the GDSU decoder outperforms the gradient descent bit-flipping (GDBF) decoder for rates
1/2,
2/3, and has similar decoding performance for the
3/4 rate of the IEEE 802.11 codes standard.
Gradient descent bit flipping (GDBF) algorithm is an important low-complexity method for decoding LDPC codes. In particular, the multi-bit GDBF decoding has the best decoding performance among BF algorithms if a suitable threshold is prescribed. However, extensive computer searches are needed to find such a threshold for a specific LDPC code. In this paper, we propose a syndrome-aided GDBF (SAGDBF) algorithm to address the problem. The thresholds in our algorithm are adaptively adjusted according to the syndrome values in the iterative process. Simulation results for different LDPC codes suggest that the error performances of the proposed SAGDBF algorithm are close to and even better than the original multi-bit GDBF algorithm at a relatively small number of iterations. In addition, the complexity increased in our proposed algorithm is negligible compared with the original multi-bit GDBF algorithm. Hence, the proposed algorithm is suitable for practical purposes.
The Gradient descent bit flipping (GDBF) algorithm is a representative approach for decoding low-density parity-check (LDPC) codes, which offers a good tradeoff between decoding performance and complexity. Unfortunately, the decoding performance of GDBF algorithm degenerates dramatically for structured LDPC codes due to their large column weight. To address the above issue, we propose to improve GDBF algorithm by introducing a weighted parameter in the energy function of each bit. Specifically, this parameter compensates for the computational error of the energy function due to the large column weight of the parity-check matrices of structured LDPC codes. Moreover, the flipping number of each bit in the iterative process is included in the energy function to avoid consecutive bit flips in the decoding. Simulation results on typical structured LDPC codes indicate that the performance of the proposed algorithm is better than the standard GDBF algorithm at the cost of slight increment in the algorithmic complexity. The increase operations can be easily implemented, which indicates the proposed algorithm is suitable for practical purposes.