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Journal of Tsinghua University(Science and Technology)

Flipped and augmented decoding algorithm for low-density parity-check codes

Jianhua Lü

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

A two stage belief-propagation(TSBP) decoding algorithm was developed based on trapping set state(TSS) detection to reduce the error floor of low-density parity-check(LDPC) codes.The algorithm uses belief-propagation algorithm until the TSS is detected,then iterative decoding is attempted to continue through flipping and augmenting the initial values of the possible error bits until the decoding succeeds or the maximum number of attempts is reached.Simulations show that the algorithm significantly reduces the maximum number of iterations for decoding in the error floor region,and with a few additional attempts,the error floor of LDPC codes can be reduced by nearly two orders of magnitude.

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A two stage belief-propagation(TSBP) decoding algorithm was developed based on trapping set state(TSS) detection to reduce the error floor of low-density parity-check(LDPC) codes.The algorithm uses belief-propagation algorithm until the TSS is detected,then iterative decoding is attempted to continue through flipping and augmenting the initial values of the possible error bits until the decoding succeeds or the maximum number of attempts is reached.Simulations show that the algorithm significantly reduces the maximum number of iterations for decoding in the error floor region,and with a few additional attempts,the error floor of LDPC codes can be reduced by nearly two orders of magnitude.
The performance of a belief propagation decoder for low-density parity-check codes is limited by the presence of trapping sets in the code’s graph. This leads to an error floor at higher signal-to-noise ratios. We propose the use of an augmented decoder which operates by iteratively decoding on a set of graphs which have a subset of repeated check nodes. We compare the augmented decoder to other modified belief propagation decoders that have been presented in the literature. We show that for all the codes considered, the augmented decoder yields the best frame error rate in the error floor region.
In this paper, a hybrid decoding scheme is proposed to lower the error floor of low-density parity-check codes. With the observation that some error bits' LLR values oscillate throughout iterative decoding procedure, a "feedback BP" (FBP) decoding algorithm is presented as second-stage decoding cell to reduce the phenomena of oscillations. The hybrid decoding scheme, which consists LLR-BP decoding algorithm and FBP decoding algorithm, detects errors in the codewords obtained by using the parity check equations of LDPC codes. Simulation results show that the new decoding scheme exhibits a lower error floor than that of belief propagation decoding algorithm in the moderate and high SNR region.
We propose an augmented belief-propagation (BP) decoder for low-density parity-check (LDPC) codes which can be used on memoryless or intersymbol-interference (ISI) channels. The proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the BP decoder. The augmented decoder is a multistage iterative decoder, where at each stage, the original channel messages on select symbol nodes are replaced by saturated messages. The key element of the proposed method is the symbol-selection process, which is based on the appropriately defined subgraphs of the code graph and/or the reliability of the information received from the channel. We demonstrate by examples that this decoder can be implemented to achieve substantial gains (compared with the standard locally operating BP decoder) for short LDPC codes decoded on both memoryless and ISI Gaussian channels. Using the Margulis code example, we also show that the augmented decoder reduces the error floors. Finally, we discuss types of BP decoding errors and relate them to the augmented BP decoder.
We propose an augmented belief propagation (BP) decoder for low-density parity check (LDPC) codes which can be utilized on memoryless or intersymbol interference channels. The proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the BP decoder. The augmented decoder is a multistage iterative decoder, where, at each stage, the original channel messages on select symbol nodes are replaced by saturated messages. The key element of the proposed method is the symbol selection process, which is based on the appropriately defined subgraphs of the code graph and/or the reliability of the information received from the channel. We demonstrate by examples that this decoder can be implemented to achieve substantial gains (compared to the standard locally-operating BP decoder) for short LDPC codes decoded on both memoryless and intersymbol interference Gaussian channels. Using the Margulis code example, we also show that the augmented decoder reduces the error floors. Finally, we discuss types of BP decoding errors and relate them to the augmented BP decoder.
This paper proposes a two-stage iterative decoding scheme named matrix transform belief propagation scheme (MT-BP) based on conventional belief propagation (BP) algorithm for lowdensity parity-check (LDPC) codes.By introducing information measurement, location vectors and parity check matrix transform, the proposed method can establish additional parity check equations and take more information bits of variable nodes into consideration compared with conventional BP algorithm.The simulations are performed on random regular LDPC codes and algebraic quasi-cyclic codes (QC-LDPC), the experimental results show MT-BP method can efficiently reduce the bit error rate (BER).
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.