Abstract The residual belief propagation (RBP) algorithm, which is the most classic informed dynamic scheduling strategy, achieves outstanding performance in error correction and can drastically accelerate convergence speed. However, the greedy algorithmic property of this iterative decoding will inevitably cause loss of decoding performance. To address this, a novel algorithm called the partial average bundle residual belief propagation (PABRBP) is proposed in this paper. According to the construction characteristics of a base matrix of protograph‐LDPC codes, informed dynamic scheduling (IDS) strategies are applied to an edge bundle of base matrices for the first time. This edge bundle of the base matrix can be applied to a corresponding cyclic permutation matrix. Furthermore, the update level of each bundle is determined by the value of the Partially Average Bundle Residual (PABR). Therefore, the edge message with the maximum residual in each bundle is updated in order, and the process of iterative decoding is less likely to become trapped in a local optimum. Additionally, the generation of silent nodes is reduced as much as possible. To further improve the PABRBP decoding performance for medium and long codes over the fading channel, the adjusted compensation term is periodically introduced. Analysis and simulation results show that PABRBP demonstrates a notable convergence quality and decoding performance improvement over the fading channels compared to existing state‐of‐art IDS algorithms.
Abstract The residual belief propagation (RBP) algorithm, which is the most classic informed dynamic scheduling strategy, achieves outstanding performance in error correction and can drastically accelerate convergence speed. However, the greedy algorithmic property of this iterative decoding will inevitably cause loss of decoding performance. To address this, a novel algorithm called the partial average bundle residual belief propagation (PABRBP) is proposed in this paper. According to the construction characteristics of a base matrix of protograph‐LDPC codes, informed dynamic scheduling (IDS) strategies are applied to an edge bundle of base matrices for the first time. This edge bundle of the base matrix can be applied to a corresponding cyclic permutation matrix. Furthermore, the update level of each bundle is determined by the value of the Partially Average Bundle Residual (PABR). Therefore, the edge message with the maximum residual in each bundle is updated in order, and the process of iterative decoding is less likely to become trapped in a local optimum. Additionally, the generation of silent nodes is reduced as much as possible. To further improve the PABRBP decoding performance for medium and long codes over the fading channel, the adjusted compensation term is periodically introduced. Analysis and simulation results show that PABRBP demonstrates a notable convergence quality and decoding performance improvement over the fading channels compared to existing state‐of‐art IDS algorithms.
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.
Abstract The informed dynamic scheduling (IDS) strategies, in which the edge message with the maximum message‐residual is updated preferentially, achieve remarkable error‐correction performance when applied to low‐density parity‐check (LDPC) codes. However, the IDS strategies incur inferior convergence in iterative decoding owing to the greedy problem, which is called the update‐relayed trend here. In order to solve the greediness, two locally informed dynamic scheduling algorithms based on the law of large numbers are proposed. The proposed decoding algorithms use random select of check nodes over a predefined update range (RSPUR) which effectively suppresses the propagation of the update‐relayed trend and accordingly restrains the forming of multi‐update cycles. Moreover, the decoding algorithm is further improved based on random select of check nodes over an adjustable update range (RSCAR). The update ranges are selected based on the law of large numbers. Therefore, the computational resources can be allocated more equitably by increasing iterations. Simulation results show that both the proposed algorithms achieve excellent performance in terms of throughput and convergence with low decoding complexity over the Additive White Gaussian Noise (AWGN) and the fading channels compared to the previous IDS strategies. Hence, the proposed algorithms behave excellently over the wireless channels.
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.
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.
Low‐density parity‐check (LDPC) codes have excellent performance for a wide range of applications at reasonable complexity. LDPC codes with short blocks avoid the high latency of codes with large block lengths, making them potential candidates for ultra reliable low‐latency applications of future wireless standards. In this work, a novel informed dynamic scheduling (IDS) strategy for decoding LDPC codes, denoted reliability‐based residual belief propagation (Rel‐RBP), is developed by exploiting the reliability of the message and the residuals of the possible updates to choose the messages to be used by the decoding algorithm. A different measure for each iteration of the IDS schemes is also presented, which underlies the high cost of those algorithms in terms of computational complexity and motivates the development of the proposed strategy. Simulations show that Rel‐RBP speeds up the decoding at reduced complexity and results in error rate performance gains over prior work.