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IEEE/CIC International Conference on Communications in China (ICCC)

Flooding and node-wise RBP sequentially concatenated decoder for LDPC codes

Hua Ren Zhou, Li Peng, Jiao Feng, Bo Ni

Published Nov 1, 2015• 1 citation
Publisher

Abstract

A new strategy of belief propagation (BP) decoder for LDPC codes is presented by sequentially concatenating the scheduling algorithms of flooding and node-wise residual belief propagation (NW RBP) without increasing the complexity of hardware implementation. Compared to NW RBP, the concatenated BP decoder significantly decreases the decoding latency caused by computing and sorting the residual of each message in the factor graph of an LDPC code. As the signal-to-noise ratio (SNR) increases, the decoding performance of the concatenated BP decoder outperforms that of purely applying flooding or NW RBP, and the average number of decoding iterations required for the concatenated decoder decreases and tends to be approximately the same as the other two.

DOI
10.1109/iccchina.2015.7448671

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A new strategy of belief propagation (BP) decoder for LDPC codes is presented by sequentially concatenating the scheduling algorithms of flooding and node-wise residual belief propagation (NW RBP) without increasing the complexity of hardware implementation. Compared to NW RBP, the concatenated BP decoder significantly decreases the decoding latency caused by computing and sorting the residual of each message in the factor graph of an LDPC code. As the signal-to-noise ratio (SNR) increases, the decoding performance of the concatenated BP decoder outperforms that of purely applying flooding or NW RBP, and the average number of decoding iterations required for the concatenated decoder decreases and tends to be approximately the same as the other two.
A new decoding strategy of belief propagation (BP) for low‐density parity‐check codes is presented by serially concatenating the traditional simultaneous decoding (also known as flooding) and the informed dynamic decoding (IDD) (e.g. node‐wise residual belief propagation (NW RBP) or informed variable‐to‐check (IVC) RBP). The frame error rates (FER) and bit error rates (BER) of the concatenated BP decoder outperform that of the non‐concatenated single decoder. In addition, as the signal‐to‐noise ratio (SNR) increases, the average number of decoding iterations required for the concatenated BP decoder decreases, and tends to merge with that of the first sub‐decoder in the high SNR region. Moreover, since the IDD strategies concerned in this paper require extra effort for the residual computation, and the sequential updating of IDD is much more time consuming than the simultaneous updating of flooding. Therefore, compared with using a single IDD, serially concatenating flooding and IDD reduces both the approximate decoding complexity and the decoding latency because the concatenated decoder is still dominated by the sub‐decoder flooding.
We researched BP decoding algorithm based on variable-to-check information residual for LDPC code (VC-RBP) in this paper. It is a dynamic scheduling belief propagation using residuals, and has some advantages, such as fast decoding, good performance, and low complexity. It is similar to residual belief propagation (RBP),but has some difference in computing the residual message. Simulation shows that it outperforms with only a maximum of ten iterations by about 0.28 dB compared with RBP at an BER of 10-4.
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.
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.
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.
Reliability-Based-Layered Belief Propagation (RBL-BP) decoding algorithm for LDPC codes is proposed in this paper. Being an informed dynamic schedule (IDS), it measures convergence and selects iterations by the absolute value of logarithmic likelihood ratio information obtained from channel (ABS-LLR-CH). Each variable node can select its own iterations by estimating its own convergence, and finish iterative decoding. Simulation results show that the proposed RBL-BP algorithm has better performance than those of flooding schedule, layered belief propagation (LBP) and variable-to-check residual belief propagation (VC-RBP). For the convergence property of IDS, the proposed algorithm has faster speed than those of flooding schedule and LBP with a little increase in complexity while it has almost no speed decrease with much lower computational complexity than VC-RBP.