Residual Belief Propagation Research Articles

Derived dynamic scheduling for belief propagation decoding of LDPC codes

AbstractAmong numerous dynamic scheduling strategies for low‐density parity‐check codes, many of them are of high complexity due to repetitive computation and ordering of belief residuals. To address these challenges, two novel approaches are proposed: the derived informed variable‐to‐check residual belief propagation and the derived variable‐node and variable‐to‐check‐edge residual belief propagation for low‐density parity‐check codes. Simulation results show that the derived dynamic scheduling exhibits a substantial gain of approximately 0.15 dB in signal‐to‐noise ratio over the non‐derived one with considerably lower decoding complexity when targeting a bit‐error rate of 10−4.

Partial IDS decoding based on the base graph of protograph LDPC codes

AbstractThe 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.

Joint Channel Estimation, Activity Detection and Data Decoding Based on Dynamic Message-Scheduling Strategies for mMTC

In this work, we present a joint channel estimation, activity detection and data decoding scheme for massive machine-type communications. By including the channel and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> activity factor in the factor graph, we present the bilinear message-scheduling GAMP (BiMSGAMP), a message-passing solution that uses the channel decoder beliefs to refine the activity detection and data decoding. We include two message-scheduling strategies based on the residual belief propagation (RBP) and the activity user detection (AUD) in which messages are evaluated and scheduled in every new iteration. An analysis of the convergence of BiMSGAMP along with a study of its computational complexity is carried out. Numerical results show that BiMSGAMP outperforms state-of-the-art algorithms, highlighting the gains achieved by using the dynamic scheduling strategies and the effects of the channel decoding part in the system.

Low-Complexity LDPC Decoding Algorithm Based on Layered Vicinal Variable Node Scheduling

The informed dynamic scheduling (IDS) strategies for the low-density parity check (LDPC) decoding have shown superior performance in error correction and convergence speed, particularly those based on reliability measures and residual belief propagation (RBP). However, the search for the most unreliable variable nodes and the residual precomputation required for each iteration of the IDS-LDPC increases the complexity of the decoding process which becomes more sequential, making it hard to exploit the parallelism of signal processing algorithms available in multicore platforms. To overcome this problem, a new, low-complexity scheduling system, called layered vicinal variable nodes scheduling (LWNS) is presented in this paper. With this LWNS, each variable node is updated by exchanging intrinsic information with all its associated control and variable nodes before moving to the next variable node updating. The proposed scheduling strategy is fixed by a preprocessing step of the parity control matrix instead of calculation of the residuals values and by computation of the most influential variable node instead the most unreliable metric. It also allows the parallel processing of independent Tanner graph subbranches identified and grouped in layers. Our simulation results show that the LWNS BP have an attractive convergence rate and better error correction performance with low complexity when compared to previous IDS decoders under the white Gaussian noise channel (AWGN).

Fast Column Message-Passing Decoding of Low-Density Parity-Check Codes

A new fast column message-passing (FCMP) schedule for decoding LDPC codes is presented and investigated in this brief. FCMP converges in half the number of iterations compared to existing serial decoding schedules, has a significantly lower computational complexity than residual-belief-propagation (RBP)-based schedules, and consumes less power compared to state-of-the-art schedules. An FCMP decoder architecture supporting IEEE 802.11ad (WiGig) LDPC codes is presented. The architecture is synthesized using the TSMC 40 nm CMOS technology node and operates at a clock frequency of 200 MHz. The decoder achieves a throughput of 8.4 Gbps while consuming 72 mW of power. This results in an energy efficiency of 8.6 pJ/bit, which is the best-reported energy-efficiency in the literature for a WiGig LDPC decoder.

Dynamic Message Scheduling Based on Activity-Aware Residual Belief Propagation for Asynchronous mMTC

In this letter, we propose a joint active device detection and channel estimation framework based on factor graphs for asynchronous uplink grant-free massive multiple-antenna systems. We then develop the message-scheduling GAMP (MSGAMP) algorithm to perform joint active device detection and channel estimation. In MSGAMP we apply scheduling techniques based on the residual belief propagation (RBP) and the activity user detection (AUD) in which messages are generated using the latest available information. MSGAMP-type schemes show a good performance in terms of activity error rate and normalized mean squared error, requiring a smaller number of iterations for convergence and lower complexity than state-of-the-art techniques.

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

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.

Improved Decoding Algorithms of LDPC Codes Based on Reliability Metrics of Variable Nodes

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.

Knowledge‐aided informed dynamic scheduling for LDPC decoding of short blocks

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.

Serially concatenated belief propagation decoder for low‐density parity‐check codes

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.

Informed Scheduling by Stochastic Residual Belief Propagation in Distributed Wireless Networks

This letter devises a novel algorithm for cooperative spectrum sensing based on belief propagation (BP) for distributed wireless networks. The algorithm, called stochastic residual belief propagation (SR-BP), extends the use of residual belief propagation (R-BP) to distributed networks, improving the accuracy, convergence rate, and communication cost for cooperative spectrum sensing. We demonstrate that SR-BP converges to a unique fixed point under conditions similar to those ensuring convergence of asynchronous BP. Then, we develop a way to derive a probability distribution from the residual of each message. Finally, we provide numerical results to showcase the improvements in convergence speed, message overhead and detection accuracy of SR-BP.

Decoding for LDPC codes with enhanced residual belief-propagation

Decoding for LDPC codes with enhanced residual belief-propagation

Two Informed Dynamic Scheduling Strategies for Iterative LDPC Decoders

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.

A BP Decoding Algorithm Based on Nodes Residual for LDPC Codes and Its Hardware Implementation

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. This paper further optimized the new algorithm on DSP of TMS320dm6446, and it is good for hardware implementation.

A BP Decoding Algorithm Based on Nodes Residual for LDPC Codes and its Hardware Implementation

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. This paper further optimized the new algorithm on DSP of TMS320dm6446, and it is good for hardware implementation.

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

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.

Variable-to-check residual belief propagation for LDPC codes

Variable-to-check residual belief propagation for LDPC decoding for faster convergence, better error performance and lower complexity is proposed. 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 the residuals are computed from a variable-to-check message. Simulation shows that it outperforms with only a maximum of eight iterations by about 0.3 dB compared with RBP at an FER of 10−4.