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Modern Electronics Technique

An Improved Multi-bit Flipping Algorithm for LDPC Decoding

Lan Tang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The bit-flipping(BF) algorithm of low density parity check(LDPC) code has low computation complexity and great practicability.On the basis of studying simple BF,WBF and RRWBF,an improved BF algorithm is proposed on considering the reliability ratio and absolute value of symbol.The proposed algorithm flips more than one bit in each iteration.Simulation results indicate that compared with RRWBF,the error rate of the proposed algorithm with 5 dB is improved from 10-3 to 10-4.

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The bit-flipping(BF) algorithm of low density parity check(LDPC) code has low computation complexity and great practicability.On the basis of studying simple BF,WBF and RRWBF,an improved BF algorithm is proposed on considering the reliability ratio and absolute value of symbol.The proposed algorithm flips more than one bit in each iteration.Simulation results indicate that compared with RRWBF,the error rate of the proposed algorithm with 5 dB is improved from 10-3 to 10-4.
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.
Compared with belief-propagation decoding algorithm which has complexity class of o(n2),bit-flipping(BF) decoding algorithm for low density parity check(LDPC) codes has only complexity class of o(n).However,the performance of BF algorithm is degraded.This paper presents a modified BF decoding algorithm,which uses reliability ratio as a weight of information node in unsatisfied parity checks so that the soft information is introduced in decoding,and the decoding performance is improved greatly with a little more computation.Analyses show the modified algorithm still has a complexity class of o(n).Simulation results indicate that the error rate with 7dB SNR is improved from 10-3 of the weighted bit-flipping decoding algorithm to 10-4 of the modified algorithm.
An improved iterative bit-flipping(BF) algorithm adapted for decoding low-density parity-check(LDPC) codes is proposed to improve the performance of the hard-decision BF decoding algorithm.The new algorithm uses an alternating threshold pattern to determine the bits whether to be flipped or not,and the flipping error probability is effectively decreased.Simulation results show that compared with BF algorithm,the improved BF algorithm improves both the error-correction performance and the convergence speed while maintaining the low computational complexity.
Several Weighted BF (WBF) algorithms are investigated in this paper, and a novel modified reliability-ratio based WBF (MRWBF) decoding algorithm for LDPC codes is proposed.WBF algorithm considers the influence of parity information on the error metric.Based on WBF, the improved WBF (IWBF) algorithm further uses the feature of message reliability on the symbol decision.The reliability-ratio based WBF (RRWBF) can eliminate the defect of requiring off-line pre-processing in IWBF.Our proposed MRWBF further removes the step of calculating normalized weighted parameters in RRWBF and achieves more reduction in decoding complexity.The results of simulations show that the proposed algorithm is feasible, effective, and can achieve good decoding performance.
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.
Based on decoding performance, complexity and latency of finite-geometry low-density parity-check (LDPC) codes, an efficient decoding algorithm is proposed. The algorithm is a hybrid bit-flipping (BF)/majority-logic (MLG) algorithm. In the algorithm, there are two stages. At the first stage, a code is decoded with bit-flipping (BF) with a small fixed number of iterations. Then the output from bit-flipping (BF) decoder is decoded by majority-logic (MLG) decoding. And in bit-flipping (BF) decoding, a new method is used to find the least reliable position. In the hybrid algorithm, there aren't real operations. Simulation results show that the algorithm provides 0.3dB coding gain over weight bit-flipping (WBF) decoding, and within 1 dB away from sum-product algorithm (SPA) decoding.