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IEEE Communications Letters

An efficient dynamic schedule for layered belief-propagation decoding of LDPC codes

Guojun Han, Xingcheng Liu

Published Dec 1, 2009• 29 citations
Publisher

Abstract

An efficient dynamic schedule for layered belief-propagation (LBP) decoding of low-density parity-check (LDPC) codes is presented, in which the check nodes connecting to a variable node with maximum relative message residual are chosen in each dynamic decoding iteration, and then LBP is performed for these check nodes. In this schedule we combined the features of lazy schedule and node-wise residual belief propagation (NWRBP) together while keeping the extra computational complexity very low. Simulation results show that the new schedule speeds up the convergence rate and greatly improves error performance at medium to high signal-to-noise ratio (SNR) when compared to the standard LBP decoding algorithm.

DOI
10.1109/lcomm.2009.12.091555

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An efficient dynamic schedule for layered belief-propagation (LBP) decoding of low-density parity-check (LDPC) codes is presented, in which the check nodes connecting to a variable node with maximum relative message residual are chosen in each dynamic decoding iteration, and then LBP is performed for these check nodes. In this schedule we combined the features of lazy schedule and node-wise residual belief propagation (NWRBP) together while keeping the extra computational complexity very low. Simulation results show that the new schedule speeds up the convergence rate and greatly improves error performance at medium to high signal-to-noise ratio (SNR) when compared to the standard LBP decoding algorithm.
Layered belief-propagation (LBP) with dynamic schedule for low-density parity-check (LDPC) codes using variable nodes residual is presented. The proposed schedule outperforms the conventional LBP with predetermined schedule both in terms of convergence speed and error performance. As compared with node-wised residual belief-propagation (NRBP), it has much lower extra complexity. For LDPC code constructed by PEG, simulation results show that the new schedule offers better error performance and requires much lower extra complexity.
Low-density parity-check (LDPC) codes are favorable in modern telecommunication technologies due to its superior error-correction capability especially when the codeword length is large. The commonly-used LDPC decoders are based on the belief-propagation (BP) algorithms. It is well known that the layered (serial) belief-propagation (LBP) decoding algorithms can reduce the number of iterations by half in comparison with the flooding (parallel) BP decoding algorithms. Further reduction in total number of iterations can be achieved by using the informed dynamic scheduling techniques, such as residual BP (RBP) and node-wise residual BP (NWRBP) methods. However, the incurred additional computation of residuals is far from trivial. In this paper, we propose a novel efficient dynamic scheduling scheme, called a posteriori probability RBP (APPRBP) algorithm, which offers more flexibility to leverage the performance-complexity trade-off using a threshold parameter. The simulation results demonstrate that the average iteration numbers for our proposed APPRBP algorithm can be remarkably reduced especially in the low E_b/N_0 (signal-energy-per-information-bit to noise-power-spectral-density ratio) conditions while the bit-error rate (BER) performance is subject to slight degradation.
Low-density parity-check (LDPC) codes have been chosen for the fifth-generation (5G) new radio (NR) enhanced Mobile Broad Band (eMBB) data channel. Since NR LDPC codes puncture the first two block columns of the parity-check matrix, the decoding complexity is reduced, but it slows down the convergence rate. In this letter, we propose a fixed schedule that decodes the layers with the least-punctured edges and those with the highest-degree (LPHD), which has much faster convergence speed than conventional schemes. The fixed scheduling schemes cannot take full advantage of the dynamic changes of decoding messages. As a result, the residual-based layered belief propagation (RB-LBP) is proposed to rearrange the layers dynamically among different iterations. Compared with some informed dynamic scheduling (IDS) strategies, RB-LBP reduces the decoding complexity with slight performance loss.
In this work, we investigate the decoding of Low-Density Parity-Check (LDPC) codes using informed dynamic scheduling algorithms that require a reduced number of iterations. In particular, we devise the weighted residual layered belief propagation (WR-LBP) decoding algorithm, which exploits the residual within a structured layer framework to speed the number of required decoding iterations. The proposed WR-LBP algorithm is assessed against important LDPC decoding algorithms, in terms of the number of iterations required for convergence and the bit error rates.
Low-density parity-check (LDPC) codes are favorable in modern telecommunication technologies due to its superior error-correction capability especially when the codeword length is large. The commonly-used LDPC decoders are based on the belief-propagation (BP) algorithms. It is well known that the layered (serial) belief-propagation (LBP) decoding algorithms can reduce the number of iterations by half in comparison with the flooding (parallel) BP decoding algorithms. Further reduction in total number of iterations can be achieved by using the informed dynamic scheduling techniques, such as residual BP (RBP) and node-wise residual BP (NWRBP) methods. However, the incurred additional computation of residuals is far from trivial. In this paper, we propose a novel efficient dynamic scheduling scheme, called a posteriori probability RBP (APPRBP) algorithm, which offers more flexibility to leverage the performance-complexity trade-off using a threshold parameter. The simulation results demonstrate that the average iteration numbers for our proposed APPRBP algorithm can be remarkably reduced especially in the low E_b/N_0 (signal-energy-per-information-bit to noise-power-spectral-density ratio) conditions while the bit-error rate (BER) performance is subject to slight degradation.
Four reliability-based high-efficient dynamic schedules (RHDS) for belief propagation (BP) decoding of low-density parity-check codes are proposed. The RHDS only processes one variable (or check) node, which has the maximum relative residual among all the variable (or check) nodes in each decoding iteration, thus keeping less greediness and decreasing complexity in comparison with egde-wise variable-to-check residual belief propagation (VC-RBP) algorithm. Simulation results show that RHDS's convergence rate is higher than VC-RBP while still keeping very low computational complexity.