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IEEE Vehicular Technology Conference

Performance of low density parity check (LDPC) codes with bootstrap decoding algorithm on a fast fading channel

Yoichi Inaba, Tomoaki Otsuki Ohtsuki

Published Feb 22, 2005• 4 citations
Publisher

Abstract

Low density parity check (LDPC) codes can be decoded in various ways, namely the bit-flipping (BF) algorithm, the weighted BF (WBF) algorithm and the log-likelihood ratio belief propagation (LLR-BP) algorithm, and so on. These algorithms provide a wide range of tradeoffs among decoding complexity, decoding speed, and error rate performance. Recently, the bootstrapped WBF (BWBF) algorithm has been proposed to improve the error rate performance and the decoding complexity of the WBF algorithm. In this paper, we study the effects of the predetermined threshold /spl alpha/ of the bootstrap step on BER for various LDPC codes. Furthermore, we apply the bootstrap step to the LLR-BP algorithm. We evaluate the BWBF and the bootstrapped LLR-BP (B-LLR-BP) algorithms on a fast fading channel. We show that the optimal threshold depends on the row and column weights of the LDPC codes. We also show that the BWBF algorithm provides a large improvements in both the error rate performance and the decoding complexity on a fast fading channel. Moreover, we show that the LLR-BP algorithm hardly receives the effect of the bootstrap step.

DOI
10.1109/vetecs.2004.1387969

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Low density parity check (LDPC) codes can be decoded in various ways, namely the bit-flipping (BF) algorithm, the weighted BF (WBF) algorithm and the log-likelihood ratio belief propagation (LLR-BP) algorithm, and so on. These algorithms provide a wide range of tradeoffs among decoding complexity, decoding speed, and error rate performance. Recently, the bootstrapped WBF (BWBF) algorithm has been proposed to improve the error rate performance and the decoding complexity of the WBF algorithm. In this paper, we study the effects of the predetermined threshold /spl alpha/ of the bootstrap step on BER for various LDPC codes. Furthermore, we apply the bootstrap step to the LLR-BP algorithm. We evaluate the BWBF and the bootstrapped LLR-BP (B-LLR-BP) algorithms on a fast fading channel. We show that the optimal threshold depends on the row and column weights of the LDPC codes. We also show that the BWBF algorithm provides a large improvements in both the error rate performance and the decoding complexity on a fast fading channel. Moreover, we show that the LLR-BP algorithm hardly receives the effect of the bootstrap step.
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.
LDPC (Low Density Parity Check Codes) is a low -density puppet test code applied to channel codes. Among the existing LDPC decoding algorithms, the LLR-BP decoding arithmetic is too complicated to calculate the calculation due to the containing a large number of bilateral positive cut functions. Therefore, this article proposes a LDPC decoding algorithm that combines the Modified Weighted Bit Flipping Decoding Algorithm (MWBF) with the Logarithmic Likelihood Ratio Based Confidence Propagation Algorithm (LLR-BP). In the process of the LLR-BP decoding iteration, the introduction of the MWBF algorithm not only does it reduce the complexity of iteration and decoding, but also avoids the traditional weighted bit-flipping decoding algorithm (WBF). Excessive effects of code performance.
Abstract- Low Density Parity Check (LDPC) codes can be decoded in various ways, namely the Bit-Flipping (BF) algorithm, the Weighted BF algorithm (WBF) ， the Belief Propagation (BP) algorithm and so on. These algorithms provide a wide range of tradeoffs among decoding complexity, decoding speed, and error rate performance. In this paper, a novel self-reliability-based weighted bit-flipping decoding scheme for low-density parity-check codes is proposed. Improvement in performance is observed in comparison with the modified weighted bit-flipping decoding scheme, and the decoding complexity can be significantly reduced as well. Key-Words:- Low-density parity-check (LDPC) codes, decoding algorithm, bit flipping, self reliability
A Hybrid Bit Flip(HBF) decoding algorithm for Low-Density Parity-Check (LDPC) codes is proposed in this paper. The algorithm makes full use of the soft output of belief-propagation (BP) (decoding) algorithm for LDPC codes, and greatly improves the bit error rate (BER) of the classical bit-flip (BF) algorithm. The simulation results in AWGN channel show that the HBF algorithm outperforms the BP algorithm under almost the same computational complexity. Furthermore, the former can achieve much lower error floor than the latter can do.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
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.