Protograph LDPC Codes Research Articles

Protograph LDPC Code and Shaped Index Modulation Design for Multi-Mode OAM Systems

Protograph LDPC Code and Shaped Index Modulation Design for Multi-Mode OAM Systems

Customized Branched Neural Network-aided Shuffled Min-Sum Decoder for Protograph LDPC Codes

Customized Branched Neural Network-aided Shuffled Min-Sum Decoder for Protograph LDPC Codes

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-decoding-complexity-oriented collaborative design for joint source-channel coding system based on double protograph-LDPC codes

Joint-decoding-complexity-oriented collaborative design for joint source-channel coding system based on double protograph-LDPC codes

Rate-Compatible Protograph LDPC Codes for Source Coding in Joint Source—Channel Coded Modulation Systems

Using the source residual redundancy in a joint source and channel coded modulation (JSCCM) system to achieve a shaping gain has proven to be a good solution for probabilistic amplitude shaping. In a JSCCM system, rate-compatible source codes are essential for adapting to dynamically changing source probabilities. However, conventional rate-compatible source codes are not appropriate for JSCCM systems, since they may yield a loss in the shaping gain. Moreover, a code design that depends solely on the source decoding threshold appears to be ill suited, thus complicating the search for good source codes. In this paper, we propose a rate-compatible family of source codes for JSCCM systems based on an achievable system rate analysis and the source protograph extrinsic information transfer (PEXIT) algorithm. The proposed codes not only have good source decoding thresholds but also obtain shaping gains over the whole considered range of source probabilities. Numerical results show that the proposed rate-compatible family of source codes can significantly improve the bit-error-rate (BER) performance of the JSCCM system.

Asymmetric Dual-Mode Constellation and Protograph LDPC Code Design for Generalized Spatial MPPM Systems

To achieve reliable and efficient transmissions in free-space optical (FSO) communication, this paper designs a new protograph low-density parity-check (PLDPC) coded generalized spatial multipulse position modulation (GSMPPM) system over weak turbulence channels. Specifically, we investigate the PLDPC code, generalized space shift keying (GSSK) modulation, and MPPM constellation. First, we propose a type of novel GSMPPM constellations that intelligently integrates the GSSK into MPPM, referred to as asymmetric dual-mode (ADM) constellations, so as to improve the performance of the PLDPC-coded GSMPPM system. Furthermore, exploiting a protograph extrinsic information transfer (PEXIT) algorithm, we construct a type of improved PLDPC code, referred to as I-PLDPC code, which outperforms the existing PLDPC codes over weak turbulence channels. Analytical and simulation results show that the proposed ADM constellations and the proposed I-PLDPC code can obtain noticeable performance gains over their counterparts. Therefore, the proposed PLDPC-coded GSMPPM system with ADM constellations is competent to satisfy the high-reliability requirement for FSO applications.

Construction of protograph LDPC codes based on the convolution neural network

This paper presents an intelligent protograph construction algorithm. Protograph LDPC codes have shown excellent error correction performance and play an important role in wireless communications. Random search or manual construction are often used to obtain a good protograph, but the efficiency is not high enough and many experience and skills are needed. In this paper, a fast searching algorithm is proposed using the convolution neural network to predict the iterative decoding thresholds of protograph LDPC codes effectively. A special input data transformation rule is applied to provide stronger generalization ability. The proposed algorithm converges faster than other algorithms. The iterative decoding threshold of the constructed proto-graph surpasses greedy algorithm and random search by about 0.53 dB and 0.93 dB respectively under 100 times of density evolution. Simulation results show that quasi-cyclic LDPC (QC-LDPC) codes constructed from the proposed algorithm have competitive performance compared to other papers.

Designing Protograph LDPC Codes for Differential Chaotic Bit-Interleaved Coded Modulation System for Underwater Acoustic Communications

Underwater acoustic (UWA) communications face many challenges, such as large multipath delay, severe fading and the time-varying distortions. Chaotic modulations have shown advantages in UWA communications, but the reliability of current chaotic modulations is still not guaranteed. In this paper, a short-length protograph low-density parity-check (P-LDPC) code design framework for the differential chaotic bit-interleaved coded modulation (DC-BICM) system for UWA communication is proposed. This design framework, considering the requirements of short codes in UWA communications, integrates the DC-BICM system, UWA channel and the differential evolutionary code searching algorithm. Through this design framework, the optimized short P-LDPC code can be obtained. Simulation results show that the DC-BICM system with the proposed P-LDPC code can obtain more than 0.48 dB coding gain and reduce 32.6%~69.5% of the average number of iterations compared with the counterparts. Moreover, the reconstructed underwater image with the proposed P-LDPC code is clearest with the highest peak-signal-noise ratio value when compared with counterparts.

Optimization of Protograph LDPC Codes via Surrogate Channel for Unequal Power Allocation

This paper investigates the possibilities of optimizing existing protograph low-density parity-check (PLDPC) codes and designing optimal PLDPC codes on both AWGN and Rayleigh channels under binary modulation with unequal power allocation (UPA) for nonuniform sources. While the binary UPA modulation achieves a power gain, it also results in unequal error protection on the coded bits in systematic codewords during transmission. For irregular codes, it is possible to best protect the information bits by optimizing the classification of variable nodes (VNs). Those VNs represent the coded bits in protograph that allows exploiting jointly the degree irregularity and the power differentiation. An algorithm for UPA-based protograph extrinsic information transfer (UPA-PEXIT) analysis on the Rayleigh channel is proposed with the concept of surrogate channel which circumvents the channel asymmetry problem with UPA. With the RJA code as example, it is shown that classification optimization does improve the decoding threshold when the source entropy is small. To design optimal codes, a UPA-based differential evolution (UPA-DE) algorithm is proposed in conjunction with the UPA-PEXIT analysis. A family of optimized codes are illustrated for three typical nonuniform source distributions and compared with the RJA and NND codes by simulations in error rate performance.

Global Design of Double Protograph LDPC Codes for Joint Source-Channel Coding

In this letter, a global design of double protograph low-density parity-check (DP-LDPC) codes is proposed for joint source-channel coding (JSCC) system. The maximum number of degree-2 variable nodes (VNs), which is very important for the performance of the system, is determined from a global perspective that considers the joint protograph as a whole. Based on the allocation of degree-2 VNs, the new guidelines with this more comprehensive perspective are summarized and the global optimized DP-LDPC codes are designed. The simulation results that are in consistent with the joint protograph extrinsic information transfer (P-EXIT) analysis indicate that the optimized DP-LDPC codes have better performance compared with the existing re-designed DP-LDPC codes.

The Efficient Design of Lossy P-LDPC Codes over AWGN Channels

Considering the high compression requirements of transmission, lossy block codes are particularly concerned due to their good compression performance and simple implementation. This paper investigates and analyzes the distortion rate performance of protograph LDPC (P-LDPC) codes for Bernoulli sources over AWGN channels. We first analytically establish the connection between the parity check matrix of a P-LDPC code and the extra distortion caused by the noisy channels. It was found that the additional distortion related to channel noise increases with the rising total degree of a parity check matrix. Further, two design algorithms are proposed for optimizing lossy multirate P-LDPC codes, considering the effect of noisy channels. Finally, simulation results demonstrate the robustness of the optimized P-LDPC codes over noisy channels.

On efficient designing of protograph LDPC codes

This paper designs two protograph LDPC codes with code-rate $R > 1/2$. A simple method using the protograph extrinsic information transfer (PEXIT) to design the codes with a low decoding threshold and the asymptotic weight enumerator (AWE) to evaluate the error floor of the codes is deployed. Simulation results show that the proposed codes have a better error floor than prior art protograph codes and offer higher rate protographs.

Joint Detection and Decoding of Mixed-ADC Large-Scale MIMO Communication Systems With Protograph LDPC Codes

Nowadays, large-scale multiple-input multiple-output (LS-MIMO) with low-resolution analog-to-digital converters (ADCs) is a favorable transmission scheme for 5G and beyond wireless networks to reduce the power consumption of the radio frequency chains and to increase the network capacity. This paper derives the joint message-passing detection and decoding algorithm based on the double-layer graph for LS-MIMO communication systems with mixed-ADCs. The new protograph extrinsic information chart (PEXIT) algorithm is developed to analytically evaluate the performance of protograph low-density parity-check code under various mixed-ADC combinations and LS-MIMO configuration scenarios. The simulation results validate the accuracy of the proposed algorithm. Furthermore, our experiments show that the mixed-ADC system can achieve a significant power gain even when only one received antenna is equipped with high-resolution ADCs. It is observed that 4-bit or 5-bit resolution is an optimal choice for the high-resolution receive antennas. Interestingly, mixed-ADC systems with Ternay-ADCs generally provide significant gains at the cost of the increase in the average resolution by a fraction of a bit. There are specific scenarios where the Ternary-ADC-based system outperforms the 1-bit-ADC based system at the same or lower average resolution. In the particular case of 16 ×16 MIMO configuration where the number of low-resolution antennas is N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> = 12 and the number of high-resolution antennas is N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> = 4, the Ternary-ADC based system can obtain a power gain of about 2 dB at the frame error rate (FER) or bit error rate (BER) level of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> .

Generalized Joint Shuffled Scheduling Decoding Algorithm for the JSCC System Based on Protograph-LDPC Codes

The joint shuffled scheduling decoding (JSSD) algorithm can reduce the decoding complexity of the joint source-channel coding system (JSCC) based on double protograph low-density parity-check (P-LDPC) codes. However, the JSSD algorithm will not work when the linking matrix between check nodes (CNs) of the source P-LDPC and variable nodes (VNs) of the channel P-LDPC is adopted in such a system, and this linking matrix has a significant influence on the system performance. In this paper, a generalized joint shuffled scheduling decoding (GJSSD) algorithm is designed to work for the system, and the JSSD algorithm can be regarded as a special case of this algorithm. Simulations show that the proposed GJSSD algorithm can reduce the decoding complexity with performance improvement when compared with the joint belief-propagation (JBP) algorithm.

Analysis and Improvement of Error-Floor Performance for JSCC Scheme Based on Double Protograph LDPC Codes

In a joint source-channel coding (JSCC) system, excessive source compression can cause an error floor. In the original JSCC scheme based on double protograph LDPC (DP-LDPC) codes, only connections exist between check nodes (CNs) of the source protograph and variable nodes (VNs) of the channel protograph, and error floors are observed. In this paper, we investigate the joint protograph that forms the basis of a DP-LDPC code. The joint protograph consists of a source protograph, a channel protograph, and connections between the two protographs. Our main focus is on the complete-source-variable-linking (CSVL) protomatrix of the joint protograph, which determines the error floor of the DP-LDPC code. We propose a generalized source protograph extrinsic information transfer (GSP-EXIT) algorithm for evaluating the source decoding thresholds of the CSVL protomatrix. Based on the proposed algorithm, we analyze CSVL protomatrices with regular or irregular source protographs. We present design criteria for connections between VNs of the source protograph and CNs of the channel protograph. Such design rules will result in a higher source decoding threshold, which implies a lower error floor. We also propose a differential evolution algorithm for optimizing the source protograph. We present/compare analytical results and/with simulation results, and conclude that they are consistent.

Protograph LDPC Code Design for Asynchronous Random Access

This work addresses the physical layer channel code design for an uncoordinated, frame- and slot-asynchronous random access protocol. Starting from the observation that collisions between two users yield very specific interference patterns, we define a surrogate channel model and propose different protograph low-density parity-check code designs. The proposed codes are both tested in a setup where the physical layer is abstracted, as well as on a more realistic channel model, where finite-length physical layer simulations of the entire asynchronous random access scheme, including decoding, are carried out. We find that the abstracted physical layer model overestimates the performance when short blocks are considered. Additionally, the optimized codes show gains in supported channel traffic, a measure of the number of terminals that can be concurrently accommodated on the channel, of around 17% at a packet loss rate of 10 − 2 w.r.t. off-the-shelf codes.

Integrated Design of JSCC Scheme Based on Double Protograph LDPC Codes System

In this letter, an integrated design of joint source-channel coding scheme based on the double protograph low-density parity-check (DP-LDPC) codes is proposed. As degree-2 variable nodes (VNs) structure plays an important role in the performance of both water-fall and error-floor regions, the maximum number of degree-2 VNs for DP-LDPC codes is determined from a global perspective. By comparing different allocation schemes for degree-2 VNs, new design principles are proposed. Several DP-LDPC codes with different numbers of degree-2 VNs are proposed. The simulated results reveal the superiority of the optimized DP-LDPC codes, which are in line with the decoding threshold analysis by a joint protograph extrinsic information transfer algorithm.

Performance Analysis of Protograph LDPC Codes Over Large-Scale MIMO Channels With Low-Resolution ADCs

Protograph LDPC (P-LDPC) codes and large-scale multiple-input multiple-output (LS-MIMO) are cornerstones of 5G and future wireless systems, thanks to their powerful error-correcting capability and high spectral efficiency. To alleviate the high complexity in signal detection/decoding that dramatically grows with the number of antennas (in the order of tens or even hundreds), low-resolution analog-to-digital converters (ADCs) and joint detection and decoding using factor graph have recently attracted paramount interest. Unlike high-resolution ADCs, by using a small number of bits to quantize the received signal, low-resolution ADCs help reduce the hardware cost and power consumption of the RF circuit of practical LS-MIMO transceivers. Such a very much desirable reduction comes at the cost of additional quantization noise, introduced by low-resolution ADCs. This work aims to provide a unified framework to analyze the impact of the low-resolution ADCs on the performance of P-LDPC codes in practical LS-MIMO systems. It is worth noting that the previous analytical tools that have been used to evaluate the performance of P-LDPC codes do not account for the quantization noise effect of the low-resolution ADCs and the fact that the covariance of quantization noise depends on the fading channels. This article addresses this shortcoming by first leveraging the additive quantization noise model. We then derive the expression of extrinsic information for the belief-propagation LS-MIMO detector. The mutual information functions, which are the core elements of our proposed protograph extrinsic information transfer (PEXIT) algorithm, are analyzed for LS-MIMO communication systems. Our proposed PEXIT algorithm allows us to analyze and predict the impact of the low-resolution ADCs on the performance of P-LDPC codes, considering various input parameters, including the LS-MIMO configuration, the code rate, and the maximum number of decoding iterations, and the code structure. Based on our extensive analytical and simulation results, we found that the performance of 3-bit and 4-bit ADC systems only have a small gap to that of the unquantized systems. Especially when the 5-bit ADC scheme is applied, the performance loss is negligible. This finding sheds light on the practical design of LS-MIMO systems using P-LDPC codes.

Joint Optimization of Protograph LDPC Code Pair for Joint Source and Channel Coding

Double protograph low-density parity-check code has been shown to be a good solution for joint source-channel coding. Moreover, the source code and channel code (as one code pair) can be jointly optimized to achieve a good bit error rate (BER) performance. In this paper, first, an optimal design criterion of this code pair based on an extended curve-fitting algorithm is proposed. Second, a joint optimization procedure which searches for both the optimal decoding threshold and the optimal code pair is presented. In addition, for short-to-moderate-length codewords, the finite-length effect cannot be ignored and the procedure has to be modified with a new notion named length-N decoding threshold . The protograph extrinsic information transfer analysis and the BER simulation have shown that our optimized code pairs acquire lower decoding thresholds than conventional code pairs. Moreover, the optimized code pairs with short-to-moderate-length codewords can mitigate the finite-length effect and obtain low length-N decoding thresholds .

Design and Analysis of Punctured Terminated Spatially Coupled Protograph LDPC Codes With Small Coupling Lengths

Spatially coupled protograph (SC-P) low-density parity-check codes can achieve excellent performance and simple implementation when the coupling length is sufficiently large. However, in the case of small coupling lengths, terminated SC-P (TE-SC-P) codes suffer from relatively weaker decoding thresholds and lower code rates compared with the original protograph codes. To address the above issues, we propose a novel design method to enhance the performance of such TE-SC-P codes. Specifically, we develop a bus-topology-like puncturing rule so as to formulate a new family of SC-P codes, referred to as punctured TE-SC-P (P-TE-SC-P) codes. Theoretical analyses and simulation results show that the proposed P-TE-SC-P codes possess significant performance gains over conventional SC-P codes and randomly punctured TE-SC-P (called RP-TE-SC-P) codes with relatively higher computational complexity.