Weighted Bit-flipping Algorithm Research Articles

Generalized weighted bit-flipping LDPC decoding for asymmetric optical channels

Efficient low-complexity and low-latency forward error correction (FEC) decoding is vital in high-speed optical receivers. The weighted bit-flipping (WBF) decoding algorithm is a low-complexity and high-performance iterative decoder for low-density parity-check (LDPC) codes, devised for symmetric Gaussian channels. In this paper, we present a generalization of the WBF algorithm and its variants to discrete and continuous asymmetric optical channels which have signal-dependent noises. We have employed a fully analytical approach to derive the generalized WBF decoders, and show that they can achieve a net coding gain within 0.5 dB of that of the soft-decision near-optimal decoding.

Cyclic switching weighted bit‐flipping decoding for low‐density parity‐check codes

A cyclic switching weighted bit-flipping (CS-WBF) decoding algorithm for low-density parity-check (LDPC) codes is proposed in this study. By carefully choosing two selection criteria of the bit to flip and cyclically switching from one criterion to the other according to some rules during decoding, the proposed scheme can effectively break decoding loops, which often appear for weighted bit-flipping (WBF) algorithms and greatly degrade decoding performance. Simulation results show that CS-WBF provides 0.7–1.3 dB coding gain over various simple improved WBF algorithms, such as reliability ratio-based WBF and improved modified WBF, with almost the same complexity for both regular and irregular LDPC codes. Compared with WBF algorithms that break decoding loops and the belief propagation-based algorithm, CS-WBF can also provide a better complexity-performance trade-off.

Mixed modified weighted bit‐flipping decoding of low‐density parity‐check codes

In this study, a new weighted bit-flipping (WBF) algorithm called mixed modified WBF (MM-WBF) decoding is proposed for low-density parity-check codes. The new algorithm is built by mixing two WBF algorithms, one acting as the main decoding algorithm and the other acting as the auxiliary. Simulation results show that the new algorithm achieves a notable performance gain over reliability ratio-based WBF, improved M-WBF and low-complexity WBF algorithms with almost the same computational complexity. Compared with some belief-propagation-based algorithms, MM-WBF also provides an appealing performance against complexity trade-off.

Modified Bit-Flipping Decoding of Low-Density Parity-Check Codes

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.

Channel-independent weighted bit-flipping decoding algorithm for low-density parity-check codes

In this study, 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 1.6 dB coding gain improvement at BER 10 -5 while reducing up to 53% iterations for decoding and maintaining low-decoding complexity, compared with the conventional weighted BF algorithm.

Gradient descent bit flipping algorithms for decoding LDPC codes

A novel class of bit-flipping (BF) algorithm for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are referred to as gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. The proposed algorithms exhibit better decoding performance than known BF algorithms, such as the weighted BF algorithm or the modified weighted BF algorithm for several LDPC codes.

New insights into weighted bit-flipping decoding

A natural relationship between weighted bit-flipping (WBF) decoding and belief-propagation-like (BP-like) decoding is explored. This understanding can help us develop WBF algorithms from BP-like algorithms. For min-sum decoding, one can find that its WBF algorithm is the algorithm proposed by Jiang et al. For BP decoding, we propose a new WBF algorithm and show its performance advantage. The proposed WBF algorithms are parallelized to achieve rapid convergence. Two efficient simulation-based procedures are proposed for the optimization of the associated thresholds.

Bootstrapped Modified Weighted Bit Flipping Decoding of Low Density Parity Check Codes

Recently, various decoding algorithms with Low Density Parity Check (LDPC) codes have been proposed. Most algorithms can be divided into a hard decision algorithm and a soft decision algorithm. The Weighted Bit Flipping (WBF) algorithm that is between a hard decision and a soft decision algorithms has been proposed. The Bootstrapped WBF and Modified WBF algorithms have been proposed to improve the error rate performance and decoding complexity of the WBF algorithm. In this letter, we apply the Bootstrap step to the Modified WBF algorithm. We show that the Bootstrapped modified WBF algorithm outperforms the WBF, Bootstrapped WBF, and Modified WBF algorithms. Moreover, we show that the Bootstrapped modified WBF algorithm has the lowest decoding complexity.

Improved weighted bit-flipping algorithm for decoding LDPC Codes

The paper presents an improvement of the weighted bit-flipping (WBF) decoding algorithm for LDPC codes proposed by Liu and Pados (2003). Simulation results show that the improved WBF algorithm provides about 0.25 dB coding gain over the Liu–Pados WBF algorithm. Also included in the paper is a simplified loop-detection algorithm, which is much easier to implement than the one proposed by Liu and Pados. The proposed WBF algorithm is particularly effective for decoding LDPC codes whose parity check matrices have large row/column weights such as finite geometry LDPC codes.