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International Symposium on Information Theory and its Applications

Multi-bit flip type gradient descent bit flipping decoding using no thresholds

Ryoji Haga, Shogo Usami

Published Oct 1, 2012• 4 citations
OpenAlex

Abstract

Gradient Descent Bit Flipping (GDBF) decoding has one of the best decoding performances of the bit flip type decoding algorithms for low density parity check code. Multi-bit type GDBF decoding, however, achieves good error performance only with suitable thresholds. In this paper, we propose multi-bit type GDBF decoding without using thresholds. The proposed method estimates the number of bits to flip from the received soft sequence using the characteristic of the probability density distribution of the additive white Gaussian noise channel. The error performance of the proposed method is almost equal to that of the conventional method despite not using thresholds.

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arXiv:1402.2773•IEEE Transactions on Communications•Sep 9, 2014•108 citations
Gradient Descent Bit Flipping (GDBF) decoding has one of the best decoding performances of the bit flip type decoding algorithms for low density parity check code. Multi-bit type GDBF decoding, however, achieves good error performance only with suitable thresholds. In this paper, we propose multi-bit type GDBF decoding without using thresholds. The proposed method estimates the number of bits to flip from the received soft sequence using the characteristic of the probability density distribution of the additive white Gaussian noise channel. The error performance of the proposed method is almost equal to that of the conventional method despite not using thresholds.
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.
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.
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.
A key challenge for decoding irregular parity-check codes under the gradient descent bit-flipping (GDBF) algorithm is that the irregularity in column degrees reduces the accuracy of the reliability measurements obtained through a flipping function (FF). To address the challenge, we introduce a novel approach based on the gradient descent bit-flipping with momentum (GDBF-w/M). We first propose an offset GDBF-w/M (OGDBF-w/M) algorithm for decoding column-irregular codes over the additive white Gaussian noise channel, where the FF includes an offset term depending on column degrees.We then propose a diversity-based offset GDBF-w/M (D-OGDBF-w/M) algorithm which employs multiple OGDBF-w/M decoders with distinct offset values. Furthermore, we extend the proposed algorithms to the binary symmetric channel, although they are initially intended for the additive white Gaussian noise channel. Numerical results demonstrate that they achieve significant improvements in decoding performance for irregular parity-check codes, particularly for column-irregular codes.
Gradient descent bit flipping (GDBF) and its many variants have offered remarkable improvements over legacy, or modified, bit flipping decoding techniques in case of decoding low density parity check (LDPC) codes. GDBF method and its many variants, such as noisy gradient descent bit flipping (NGDBF) have been extensively studied and their performances have been assessed over multiple channels such as binary symmetric channel (BSC), binary erasure channel (BEC) and additive white Gaussian noise (AWGN) channel. However, performance of the said decoders in more realistic channels or channel conditions have not been equally studied. An improved noisy gradient descent bit flipping algorithm is proposed in this paper that optimally decodes LDPC encoded codewords over Rayleigh fading channel and under various fade rates. Comparing to NGDBF method, our proposed decoder provides substantial improvements in both error performance of the code, and in the number of iterations required to achieve the said error performance. It subsequently reduces the end-to-end latency in applications with low or ultra-low latency requirements.
A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported GDBF variant, and comes within 0.5 dB of the belief propagation algorithm for several tested codes. Unlike other previous GDBF algorithms that provide an escape from local maxima, the proposed algorithm uses only local, fully parallelizable operations and does not require computing a global objective function or a sort over symbol metrics, making it highly efficient in comparison. The proposed NGDBF algorithm requires channel state information which must be obtained from a signal to noise ratio (SNR) estimator. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.