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International Conference on Computer and Communications Management (ICCCM)

A Modified Method for General LDPC Bit-flipping Decoding

Ruizhen Wu, Lin Wang, Hua Feng, Wei He

Published Jul 27, 2019• 2 citations
Publisher

Abstract

A modified method for general LDPC bit-flipping decoding is proposed in this paper. The proposed method consists of two parts: multi-bit flipping judgement algorithm and multi-bit flipping compensation algorithm, the first part trying to find the maximum acceptable number of bits to flipping at the same time to accelerated convergence process, and the second part to compensates the new errors introduced by the first part. The proposed decoding method can be easily used to modify different BF algorithms which means the hardware implementation is simple. The simulation results show that the proposed method can achieve 2.75% to 36.05% of bit-flipping timing reduction, 3.0% to 18.1% of BER reduction at SNR 0.2dB to 4dB compared with classic BF, IMWBF, LCWBF, and RRWBF.

DOI
10.1145/3348445.3348460

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Introduction. In all types of digital communication, error control coding techniques are used. Many digital communication standards, such as Wi-Fi and 5G, use low density parity check (LDPC) codes. These codes are popular because they provide building encoders and decoders with low computational complexity. This work objective is to increase the error correcting capability of the well-known bit-flipping decoder (BF) of LDPC-codes. For this purpose, a modification of the decoder is built, which enables to dynamically control one of its main parameters whose choice affects significantly the quality of decoding. Materials and Methods. The well-known bit-flipping decoder of binary LDPC-codes is considered. This decoder has several parameters that are not rigidly bound with the code parameters. The dependence of the decoding quality on the selection of the output parameters of the bit-flipping decoder was investigated through simulation modeling. It is shown that the decoding results in this case are significantly affected by the input parameter of the decoder — threshold T. A modification of the BF-decoder of binary LDPC-codes has been developed, in which it is proposed to set the threshold dynamically during the execution of the algorithm depending on the error rate. A comparative analysis of the error- correcting capability of decoders is carried out by the simulation modeling method. Results. A lemma on the maximum value of the decoder threshold T is formulated and proved. Upper bounds for the number of operations are found for the original and modified decoders. A simulation model that implements a digital noise-immune communication channel has been built. In the model, the initial data is encoded with a given LDPC-code, then it is made noisy by additive uniformly distributed errors, and thereafter, it is decoded in turn by the bit-flipping algorithm with different threshold T parameters, as well as by a modified decoder. Based on the input and output data, the correction capacity of the decoders used is estimated. Experiments have shown that the error-correcting capability of the modified decoder in the range of the real error rate is higher than that of the original decoder, regardless of the selection of its parameters. Discussion and Conclusions. The lemma, proved in the paper, sets the upper bound on the threshold value in the original decoder, which simplifies its adjustment. The developed modification of the decoder has a better error- correcting capability compared to the original decoder. Nevertheless, the complexity of the modification is slightly increased compared to the original algorithm. It has been pointed out that the decoding quality of a modified decoder develops with a decrease in the number of cycles in the Tanner graph and an increase in the length of the code.

Advanced Engineering Research•Apr 4, 2021•0 citations
A modified method for general LDPC bit-flipping decoding is proposed in this paper. The proposed method consists of two parts: multi-bit flipping judgement algorithm and multi-bit flipping compensation algorithm, the first part trying to find the maximum acceptable number of bits to flipping at the same time to accelerated convergence process, and the second part to compensates the new errors introduced by the first part. The proposed decoding method can be easily used to modify different BF algorithms which means the hardware implementation is simple. The simulation results show that the proposed method can achieve 2.75% to 36.05% of bit-flipping timing reduction, 3.0% to 18.1% of BER reduction at SNR 0.2dB to 4dB compared with classic BF, IMWBF, LCWBF, and RRWBF.
A novel bit-flipping (BF) algorithm with low complexity for high-throughput decoding of low-density parity-check (LDPC) codes is presented. At each iteration, a novel threshold pattern is used to determine the code bits whether to be flipped or not, and the flipping error probability is effectively decreased. Compared with the weighted BF algorithm and its modifications, the modified BF algorithm has significantly lower complexity and decoding time. Through simulations the proposed BF algorithm is shown to achieve excellent performance and fast convergence speed while maintaining significantly low complexity thus facilitating high-throughput decoding.
We present two general multi-stage (MS) bit-flipping (BF) decoding algorithms for low-density parity-check (LDPC) codes. Both algorithms consist of soft-decision (SD) and hard-decision BF decoding parts. In comparison with known MS LDPC decoders, our approach is much simpler as all stages share the same BF structure. The only complexity increase is due to the use of an adaptive stage-switching (SS) mechanism which gives near-optimal SS timing. A new design issue we address is that the first-stage algorithm's parameter has to be re-tuned to achieve the optimal overall performance. The numerical results demonstrate that the proposed decoding methods can significantly improve the error-rate performance of the conventional SD BF decoders.
Low-density parity-check (LDPC) codes with column weight-4 are widely used in many commu-nication and storage systems. However, traditional hard decision decoding algorithms such as the bit-flipping (BF) algorithm suffer from error floor due to trapping sets in LDPC codes. In this paper, to lower error floor of the BF algorithm over the Binary Symmetric Channel (BSC), we design a set of decoding rules incorporated within the BF algorithm for column weight-4 LDPC codes. Given a column weight-4 LDPC code, the dominate error patterns of the BF algorithm are first specified, and according to the designed rules, additional bits at both variable nodes (VN) and check nodes (CN) provide more information for the BF algorithm to identify the dominate error patterns, so that the BF algorithm could deliberately flip some bits to break them. Simulation results show that the modified BF algorithm eliminates all 4-error patterns and lowers the Bit Error Rate (BER) for at least two orders of magnitude with a trivial increment of complexity.
An improved bit-flipping(BF) algorithm with low complexity for decoding structured low-density parity-check codes(LDPC) is proposed to improve the performance of the hard-decision BF algorithm.The hard-decision bits are divided into two groups based on the magnitudes of the received symbols,and at each iteration,the proposed algorithm can flip more than one bit with using two thresholds,and the flipping error probability is effectively decreased.The improved BF algorithm requires some real number comparisons before iterations and requires only logical operations during the iterations.Compared with the weighted bit-flipping algorithm and its modifications,the new method is with significantly lower complexity.Simulations show that the proposed algorithm is provided with very fast convergence speed and excellent performance with significantly low complexity.
Introduction. In all types of digital communication, error control coding techniques are used. Many digital communication standards, such as Wi-Fi and 5G, use low density parity check (LDPC) codes. These codes are popular because they provide building encoders and decoders with low computational complexity. This work objective is to increase the error correcting capability of the well-known bit-flipping decoder (BF) of LDPC-codes. For this purpose, a modification of the decoder is built, which enables to dynamically control one of its main parameters whose choice affects significantly the quality of decoding. Materials and Methods. The well-known bit-flipping decoder of binary LDPC-codes is considered. This decoder has several parameters that are not rigidly bound with the code parameters. The dependence of the decoding quality on the selection of the output parameters of the bit-flipping decoder was investigated through simulation modeling. It is shown that the decoding results in this case are significantly affected by the input parameter of the decoder — threshold T. A modification of the BF-decoder of binary LDPC-codes has been developed, in which it is proposed to set the threshold dynamically during the execution of the algorithm depending on the error rate. A comparative analysis of the error- correcting capability of decoders is carried out by the simulation modeling method. Results. A lemma on the maximum value of the decoder threshold T is formulated and proved. Upper bounds for the number of operations are found for the original and modified decoders. A simulation model that implements a digital noise-immune communication channel has been built. In the model, the initial data is encoded with a given LDPC-code, then it is made noisy by additive uniformly distributed errors, and thereafter, it is decoded in turn by the bit-flipping algorithm with different threshold T parameters, as well as by a modified decoder. Based on the input and output data, the correction capacity of the decoders used is estimated. Experiments have shown that the error-correcting capability of the modified decoder in the range of the real error rate is higher than that of the original decoder, regardless of the selection of its parameters. Discussion and Conclusions. The lemma, proved in the paper, sets the upper bound on the threshold value in the original decoder, which simplifies its adjustment. The developed modification of the decoder has a better error- correcting capability compared to the original decoder. Nevertheless, the complexity of the modification is slightly increased compared to the original algorithm. It has been pointed out that the decoding quality of a modified decoder develops with a decrease in the number of cycles in the Tanner graph and an increase in the length of the code.