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Systems engineering and electronics

Sum of the magnitude based weighted bit-flipping decoding algorithms for LDPC codes

Zhang Gao-yua

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Two simple and efficient weighted bit flipping(WBF)decoding algorithms for low density paritycheck(LDPC)codes are proposed,in which the sum of the variable nodes' magnitude is introduced to compute the reliability of the parity checks.Simulation results shows that the performance of one of the improved scheme is better than that of traditional WBF and modified WBF(MWBF)algorithms about 1.65dB and 1.31dB at BER of 10-5 over an additive white Gaussian noise channel,respectively,while the average number of decoding iterations is significantly reduced.

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Two simple and efficient weighted bit flipping(WBF)decoding algorithms for low density paritycheck(LDPC)codes are proposed,in which the sum of the variable nodes' magnitude is introduced to compute the reliability of the parity checks.Simulation results shows that the performance of one of the improved scheme is better than that of traditional WBF and modified WBF(MWBF)algorithms about 1.65dB and 1.31dB at BER of 10-5 over an additive white Gaussian noise channel,respectively,while the average number of decoding iterations is significantly reduced.
Extensive simulations show that for some low density parity-check(LDPC)codes of low row/colum weight,the modified sum of the magnitude based weighted bit flipping(MSMWBF)decoding algorithm performs extraordinarily well.However,this dose not hold when it comes to large row/colum weight finite-geometry LDPC codes,which is first theoretically analyzed.Secondly,improvement in performance is observed for large row/colum weight LDPC codes by considering an additive offset term for the parity-check-equation reliability of the above algorithm.Simulation results show that the performance of the improved scheme is better than that of the MSMWBF algorithm about 0.63 dB at bit-error rate of 10-5 over the additive white Gaussian noise channel with only a modest increase in computational complexity.
To improve the decoding speed and performance of Weighted Bit Flipping (WBF) decoding algorithm for Low Density Parity Check (LDPC) codes, a two-stage WBF algorithm with a multi-/single-bit switching mechanism is proposed. It first performs multi-bit flipping decoding in the first-stage decoder. When cyclic flipping is detected or the maximum flipping function value is less than zero, it switches to the second-stage decoder. Simulation results show that the proposed algorithm obtains gains both in average decoding iteration number and in decoding performance compared with the Sum of the Magnitude based WBF (SMWBF) and the Variable node updating based SMWBF (VSMWBF).
In this paper, a modified weighted bit-flipping (WBF) algorithm is proposed for finite geometry low-density parity-check (FG-LDPC) codes. The calculation for the flipping function in the new method includes all the elements in sum product algorithm (SPA) instead of the minimum one in most existing methods. Simulation results show that the proposed method exhibits better performance than the best method available in the literature so far. The performances of different algorithms are also considered in random constructed LDPC codes. The reliability ratio based WBF (RRWBF) method performs the best in this kind of codes and the proposed method performs very closely to the RRWBF method. The decoding complexities for both FG-LDPC and random constructed LDPC are also analyzed.
In order to improve the bit-flipping (BF) decoding algorithms, a weighted hard-decision based BF decoding algorithm for low-density parity-check (LDPC) codes is presented, in which the weights of variable-nodes are employed. A new metric is defined for the weight of candidate bits not only in unsatisfied parity check equations but also in satisfied ones. The connection between min-sum decoding algorithm and the proposed algorithm is presented. Simulation results show that the new decoding algorithm can provide better FER performance and faster convergence speed than the original candidate bit based bit-flipping (CBBF) algorithm.
Abstract We propose a method to substantially reduce the computational complexity of iterative decoders of low-density parity-check (LDPC) codes which are based on the weighted bit-flipping (WBF) algorithm. In this method, the WBF-based decoders are modified so that the flipping function is calculated only over a reduced set of variable nodes. An explicit expression for the achieved complexity gain is provided and it is shown that for a code of block length N, the decoding complexity is reduced from O(N2) to O(N). Moreover, we derive an upper bound for the difference in the frame error rate of the reduced-set decoders and the original WBF-based decoders, and it is shown that the error performances of the two decoders are essentially the same.