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IEEE Information Theory Workshop (ITW)

Fast Weighted Bit-Flipping Decoding of Finite-Geometry LDPC Codes

Xiaofu Wu, Ming Jiang, Chunming Zhao, Xiaohu You

Published Oct 1, 2006• 7 citations
Publisher

Abstract

In this letter, we establish a natural relationship between the improved modified-weighted-bit-flipping (IMWBF) decoding and min-sum decoding. This insight helps us to develop a fast weighted bit-flipping (FWBF) decoding algorithm. For decoding of finite-geometry low-density parity-check codes, we demonstrate through examples that the FWBF decoding can provide a further improvement to the IMWBF decoding on both convergence and performance

DOI
10.1109/itw2.2006.323772

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In this letter, we establish a natural relationship between the improved modified-weighted-bit-flipping (IMWBF) decoding and min-sum decoding. This insight helps us to develop a fast weighted bit-flipping (FWBF) decoding algorithm. For decoding of finite-geometry low-density parity-check codes, we demonstrate through examples that the FWBF decoding can provide a further improvement to the IMWBF decoding on both convergence and performance
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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 seek a decoding scheme with good performance, low complexity and fast convergence, we present an improved parallel weighted bit flipping (IPWBF) algorithm for finite geometry low-density parity-check codes whose parity check matrix is of heavy row and column weights. In the IPWBF, a bit flipping (BF) function and two parallel BF criteria, all of which scatter in the literature, are exploited jointly to serve our purpose. Meanwhile, differential evolution is used to optimize the involved parameters. Simulation results show that the proposed algorithm achieves an observable performance gain over its counterparts without any complexity penalty. Furthermore, with respect to other known low complexity decodings such as normalized BP-based, the IPWBF yields a new performance versus complexity tradeoff, that is, higher throughput at the expense of moderate performance loss.
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.
A novel self-normalized weighted bit-flipping (SNWBF) decoding algorithm for low-density parity-check (LDPC) codes is proposed. Compared to the best known weighted bit-flipping decoding, the SNWBF algorithm converges significantly faster but with little performance penalty. For decoding of LDPC codes, the proposed SNWBF algorithm considers not only the reliability of the neighboring check nodes, but also the reliability of each variable node. Compared to the IMWBF algorithm, the proposed algorithm does not require multiplicative normalization and performs even better.