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IEEE Transactions on Communications

Two bit-flipping decoding algorithms for low-density parity-check codes

Telex Magloire Ngatched. Nkouatchah, N. Ngatched, Martin Bossert, A. Fahrner, Fambirai Takawira

Published Mar 1, 2009• 15 citations
Publisher

Abstract

In this letter, a low complexity decoding algorithm for binary linear block codes is applied to low-density paritycheck (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performances at smaller complexity.

DOI
10.1109/tcomm.2009.03.041129

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In this letter, a low complexity decoding algorithm for binary linear block codes is applied to low-density paritycheck (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performances at smaller complexity.
In this paper, a low complexity algorithm for binary linear block codes is applied to low-density parity-check (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performance at smaller complexity.
In this paper, we introduce a new bit-flipping decoding algorithm for low-density parity-check codes based on loop detection mechanism, which is an extension to soft-decision decoding. This decoding algorithm's performance has been significantly improved by introducing a loop detection mechanism for the failed flipping bit and leading into the soft-decision about the reliability measure of the received symbols. Theoretical analysis shows that the complexity of this algorithm is lower. Some simulation results are given, which show that compared with other known kinds of bit-flipping decoding algorithms for LDPC codes, this new decoding on the additive white Gaussian noise channel offer excellent performance.
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.
An improved bit-flipping decoding algorithm is proposed for low-density parity-check(LDPC) codes in this paper.Two influences on error probabilities of code bits are considered: the influence of the number of code bits included in an unsatisfied check,and the influence of the number of unsatisfied checks of each code bit.No soft information is required for decoding.Simulation results show that improvement on performance is observed for the proposed algorithm,and it provides better performance over several soft-decision bit-flipping decoding algorithms for LDPC codes with large girth.
In this paper, a new method for improving hard-decision bit-flipping (BF) decoding is proposed for low-density parity-check codes. The flipping criterion is derived theoretically from the soft-decision belief-propagation decoding algorithm. The proposed BF decoding algorithm is channel independent and is improved by introducing a more efficient method for computing the reliability of the parity checks. Extensive simulations are provided to demonstrate the efficiency of the proposed algorithm. Simulation results show that the proposed algorithm can achieve about 1.5dB coding gain improvement at BER = 5×10−6while reducing up to 48% iterations for decoding and maintaining low decoding complexity, compared with the conventional weighted BF algorithm.
Bit-flipping (BF) algorithms for decoding low-density parity-check (LDPC) codes have attracted considerable attention due to their low complexity and high parallelism. While recent improvements have enabled certain BF decoders to approach the performance of belief-propagation (BP) decoding, many of these enhancements rely on complex mechanisms such as loop detection, decoder switching, or costly online computations. In this paper, we propose enhanced BF decoding algorithms that integrate refined checksum weighting and flipping function designs. The proposed weighting scheme jointly exploits soft-valued channel information and hard-decision consistency to better reflect the reliability of each checksum, while maintaining negligible online complexity. Additionally, we propose a flipping function design that implicitly discourages repeated flipping by incorporating the accumulated flip count into its computation, thus suppressing decoding loops without requiring explicit loop detection or decoder switching. Simulation results demonstrate that the proposed decoding strategies yield notable performance gains over existing BF decoders, with only a minor complexity increase.