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IEEE/CIC International Conference on Communications in China (ICCC)

Gradient descent bit-flipping based on penalty factor for decoding LDPC codes over symmetric alpha-stable noise channels

Chenyu Gao, Rongke Liu, Bin Dai

Published Oct 1, 2017• 2 citations
Publisher

Abstract

A modified gradient descent bit-flipping (GDBF) algorithm is proposed for decoding low-density parity-check (LDPC) codes over the symmetric alpha-stable (SaS) impulsive noise channel. To simplify the log-likelihood rate (LLR) computational implement, this paper introduces a linear approximation of the LLR for the SaS impulsive noise. Combined with the linear approximation, the new algorithm introduces a penalty factor into the syndrome components of the inversion function. Simulation results show that the GDBF algorithm based on the penalty factor performs better than GDBF algorithm.

DOI
10.1109/iccchina.2017.8330404

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A modified gradient descent bit-flipping (GDBF) algorithm is proposed for decoding low-density parity-check (LDPC) codes over the symmetric alpha-stable (SaS) impulsive noise channel. To simplify the log-likelihood rate (LLR) computational implement, this paper introduces a linear approximation of the LLR for the SaS impulsive noise. Combined with the linear approximation, the new algorithm introduces a penalty factor into the syndrome components of the inversion function. Simulation results show that the GDBF algorithm based on the penalty factor performs better than GDBF algorithm.
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.
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.
Low-Density Parity-Check (LDPC) codes have capacity-approaching error-correction performance which makes them popular in communication system. Gradient descent bit flipping (GDBF) algorithms show an error correction capability superior to most known BF algorithms. In this paper, we propose an improved gradient descent bit flipping (IGDBF) algorithm for LDPC codes on BSC channel. Compared to GDBF algorithm, the proposed algorithm reconstructs the composition of energy function, and adds a penalty term to help it converge. Simulations show that the proposed algorithm has good performance and fast convergence rate.
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.