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IEEE International Conference on Computer and Communications (ICCC)

Syndrome-Aided Gradient Descent Bit Flipping Algorithm for LDPC Decoding

Yuang Huang, Haiyang Liu

Published Dec 11, 2020• 2 citations
Publisher

Abstract

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.

DOI
10.1109/iccc51575.2020.9345227

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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.
As a class of bit-flipping (BF) decoder, the noisy gradient descent bit flipping (NGDBF) algorithm outperforms the original GDBF and other BF algorithms. To increase the reliability of the inversion function, we propose a modified NGDBF algorithm by introducing an adjustment factor on the syndrome. Moreover, for the multi-bit flipping, we present an adaptive inversion threshold which depends on the numbers of negative bipolar syndromes. The simulation results show that our proposed algorithm outperforms the NGDBF algorithm for both single-bit and multi-bit flipping schemes.
The gradient descent bit-flipping (GDBF) decoding algorithm offers an attractive tradeoff between performance and complexity compared with the other bit-flipping (BF) decoding algorithms. However, the performance of GDBF decoding is seriously effected by infinite decoding loop, which always results in decoding failure when maximal iteration number is reached. To avoid the decoding loop and improve the performance, an efficient escaping scheme is proposed for the GDBF algorithm in this paper. This scheme firstly introduces syndrome weight to detect the decoding loop. If a decoding loop is detected, the escaping mechanism works, where only the bit which can decrease the syndrome weight most efficiently is selected to be flipped. In addition, the excluding set is introduced to further prevent the local maximum. Simulation results show that the GDBF algorithm can obtain about 1 dB code gain by utilizing this scheme. Compared with noise GDBF, it has 0.1dB performance loss as well as lower complexity.
Gradient descent bit-flipping (GDBF) decoding for low-density parity-check (LDPC) codes has gained great attentions because of low complexity and relatively good performance. However, the performance of the GDBF decoding is still much poorer than that of the MS algorithm. To further improve the performance, the iterative decoding process is introduced to GDBF decoding in this paper. At the end of each iteration, the latest information is used to update the reliability of the flipped bit, by which its reliability is greatly improved. Simulation results indicate that the proposed algorithm has about 0.4 dB performance gains compared to GDBF. Meanwhile, there is small computational complexity increased.
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.
Gradient descent bit-flipping (GDBF) algorithm achieves good error performance for decoding low density parity check codes. In the GDBF algorithm, a search point is apt to be trapped in a local optimum, which causes performance degradation of the GDBF algorithm. To overcome this issue, the noisy GDBF algorithm introduces random perturbation into the inversion function of each symbol, which decreases the probability of being trapped in a local optimum. In this paper, we develop the noisy GDBF algorithm by enhancing the threshold adaptation in multi-bit flipping procedure to improve the BER performance without increasing the time complexity.
It is known that the Gradient descent bit flipping (GDBF) algorithm is an effective hard-decision decoding algorithm for low-density parity-check (LDPC) codes. However, trapping in a local maximum limits its error-rate performance. This paper presents a modified GDBF scheme that can mitigate the trapping problem and hence can improve the error-rate performance. Compared to the conventional GDBF algorithm, the proposed method is able to improve the decoding performance of 0.3dB for an (18582, 16626) code. The (18582, 16626) LDPC decoder integrates 636k logic gates and achieves a throughput of 12.4 Gbps at a clock frequency of 200 MHz in a 90nm process.