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IEEE Access

Residual-Decaying-Based Informed Dynamic Scheduling for Belief-Propagation Decoding of LDPC Codes

Huilian Zhang, Shaoping Chen

Published Jan 1, 2019• 19 citations
Publisher

Abstract

Belief-propagation (BP) algorithm and its variants are well-established methods for iterative decoding of LDPC codes. Among them, residual belief-propagation (RBP), which is the most primitive and representative informed dynamic scheduling (IDS) strategy, can significantly accelerate the convergence speed. However, RBP decoding suffers from a poor convergence error-rate performance due to its greedy property, which is one of the challenging issues in the design of IDS strategies. To tackle this problem, a novel IDS scheme, namely residual-decaying-based residual belief-propagation (RD-RBP) algorithm, is presented in this paper. In RD-RBP, a decaying mechanism is introduced to manipulate the residuals of those check-to-variable messages, preventing the decoding resources from being unreasonably occupied by a small group of edges in the Tanner graph. The greediness is therefore alleviated and better performance of convergence error-rate is achieved. Besides, a two-stage scheduling scheme combining prior-art variable-node and variable-to-check-edge RBP (V-VCRBP) with RD-RBP, named V-VC-RD-RBP, is proposed for achieving both fast convergence speed and a low convergence error-rate. The simulation results validate the advantages of the proposed schemes.

DOI
10.1109/access.2019.2899106

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Belief-propagation (BP) algorithm and its variants are well-established methods for iterative decoding of LDPC codes. Among them, residual belief-propagation (RBP), which is the most primitive and representative informed dynamic scheduling (IDS) strategy, can significantly accelerate the convergence speed. However, RBP decoding suffers from a poor convergence error-rate performance due to its greedy property, which is one of the challenging issues in the design of IDS strategies. To tackle this problem, a novel IDS scheme, namely residual-decaying-based residual belief-propagation (RD-RBP) algorithm, is presented in this paper. In RD-RBP, a decaying mechanism is introduced to manipulate the residuals of those check-to-variable messages, preventing the decoding resources from being unreasonably occupied by a small group of edges in the Tanner graph. The greediness is therefore alleviated and better performance of convergence error-rate is achieved. Besides, a two-stage scheduling scheme combining prior-art variable-node and variable-to-check-edge RBP (V-VCRBP) with RD-RBP, named V-VC-RD-RBP, is proposed for achieving both fast convergence speed and a low convergence error-rate. The simulation results validate the advantages of the proposed schemes.
When residual belief-propagation (RBP), which is a kind of informed dynamic scheduling (IDS), is applied to low-density parity-check (LDPC) codes, the convergence speed in error-rate performance can be significantly improved. However, the RBP decoders presented in previous literature suffer from poor convergence error-rate performance due to the two phenomena explored in this paper. The first is the greedy-group phenomenon, which results in a small part of the decoding graph occupying most of the decoding resources. By limiting the number of updates for each edge message in the decoding graph, the proposed Quota-based RBP (Q-RBP) schedule can reduce the probability of greedy groups forming. The other phenomenon is the silent-variable-nodes issue, which is a condition where some variable nodes have no chance of contributing their intrinsic messages to the decoding process. As a result, we propose the Silent-Variable-Node-Free RBP (SVNF-RBP) schedule, which can force all variable nodes to contribute their intrinsic messages to the decoding process equally. Both the Q-RBP and the SVNF-RBP provide appealing convergence speed and convergence error-rate performance compared to previous IDS decoders for both dedicated and punctured LDPC codes.
After the publication of the residual belief-propagation (RBP) algorithm, many low-density parity-check (LDPC) decoders using informed dynamic scheduling (IDS) have been investigated. In this paper, we propose the twofold-RBP (T-RBP) decoder that combines two residuals. Using T-RBP, significant improvement can be achieved in both convergence speed and convergence error-rate performance. In addition to T-RBP, the simplified-RBP (S-RBP) decoder is also proposed in order to reduce the complexity. Instead of comparing all the residuals of all edges in the code graph, as with previous IDS decoders, S-RBP only compares the residuals of the edges connected to a single check node, thus dramatically reduces the complexity without any significant degradation in performance. The proposed T-RBP and S-RBP can improve not only the performance of dedicated codes, but also that of punctured codes, especially the convergence speed. The improvement can make punctured LDPC codes more practical and becoming a competitive candidate for the rate compatible applications.
The informed dynamic scheduling (IDS) strategies for decoding of low-density parity-check codes obtained superior performance in error correction performance and convergence speed. However, there are still two problems existing in the current IDS algorithms. The first is that the current IDS algorithms only preferentially update the selected unreliable messages, but they do not guarantee the updating is performed with reliable information. In this paper, a two-step message selecting strategy is introduced. On the basis of the two reliability metrics and two types of variable node residuals, the residual belief propagation (BP) decoding algorithm, short for TRM-TVRBP, is proposed. With the algorithm, the reliability of the updating-messages can be improved. The second is the greediness problem, prevalently existed in the IDS-like algorithms. The problem arises mainly from the fact that the major computing resources are allocated to or concentrated on some nodes and edges. To overcome the problem, the reliability metric-based RBP algorithm (RM-RBP) is proposed, which can force every variable node to contribute its intrinsic information to the iterative decoding. At the same time, the algorithm can force the related variable nodes to be updated, and make every edge have an equal opportunity of being updated. The simulation results show that both the TRM-TVRBP and the RM-RBP have appealing convergence rate and error-correcting performance compared with the previous IDS decoders over the white Gaussian noise (AWGN) channel.
We present an enhanced informed dynamic scheduling (IDS) strategy to avoid propagations of unreliable messages in the residual belief-propagation (RBP) algorithm for decoding low-density parity-check (LDPC) codes. To reduce the resource needed for updating the degree-one variable nodes (VNs) in an RBP-based algorithm for decoding 5G New Radio (NR) LDPC codes, we further introduce a process consisting of several simple procedures for managing the resource consumption. Simulation results demonstrate that our RBP algorithm based on the proposed IDS strategy outperforms existing RBP-based algorithms at the early decoding iterations. By using our degree-one VN resource managing approach, the performance of both the proposed and the existing decoders is significantly improved in decoding the 5G NR codes.
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.
We propose Variable-to-Check Residual Belief Propagation (VCRBP) for LDPC decoding for faster convergence, better error correcting performance and lower complexity. It is similar to Residual Belief Propagation (RBP) that was recently applied to LDPC decoding by Vila Casado et al. because it is also a dynamic scheduling belief propagation using residuals, but it is different because its residuals are computed from variable-to-check message. Simulation shows that it out-performs with only maximum 8 iterations by about 0.3 dB compared with RBP at an FER of 10-4. Also, we propose node-wise VCRBP (N-VCRBP) for reducing complexity of VCRBP. N-VCRBP also exhibits the performance very close to VCRBP but with significantly lower decoding complexity.