Protograph Low-density Parity-check Codes Research Articles

P-LDPC coded image transmission with OFDM over underwater acoustic channel

Underwater environment is still an attractive area to explore and exploit by human beings. However, underwater characteristics limit communications due to harsh channel conditions, and efficient channel codes are essential to deploy. This study presents an underwater system based on protograph low-density parity check (P-LDPC) codes and orthogonal frequency division multiplexing (OFDM) for image transmission. The system proves a successful reconstruction of P-LDPC coded images with different levels of comparison. The performance of the proposed system is evaluated using nine objective measures such as bit error rate (BER) and peak signal to noise ratio (PSNR). Firstly, the proposed system performance is evaluated with different block lengths of P-LDPC code. Then, the implemented system shows a coding gain of approximately 1.75 dB for applying P-LDPC when compared to polar with cyclic redundancy check at 0.0001 BER. Additionally, image subjective assessment is obtained to demonstrate how the P-LDPC outweighs polar and turbo product codes in terms of estimated image quality. Lastly, further investigation is performed to study the effect of varying fast Fourier transform (FFT) size and cyclic prefix (CP) length on image reserved quality. The results show that the received image is better reconstructed for larger FFT sizes since that produce longer CP and symbol duration, and that in turn helps the system to combat the multipath fading introduced by the underwater channel.

A Cooperative Communication System With P-LDPC For Internet of Underwater Things

The acoustic communications are extremely challenging in underwater environments due to harsh conditions of this kind of nature. That medium's harshness affects the transmission reliability which in turn crucially requires an adoption of robust channel codes based on cooperative approaches to attain a more reliable data communication. This study proposes a cooperative communication system based on a protograph low-density parity check (P-LDPC) code. The system is elaborated in an Internet of underwater things (IoUT) scenario in which a relay node is acting as a helper that provides side information to destination. Compression and channel coding are offered by the system to cope with requirements of IoT in terms of reliable communication and compressed data between nodes. Furthermore, an algorithm for joint source channel coding is presented based on a modified version of offset min-sum. Moreover, layered decoding is Implemented in order to minimize number of iterations for the P-LDPC code. The results prove that proposed design can achieve a bit error rate (BER) of 5 × 10−6 at signal to noise ratio SNR = 8 dB for a coding rate of 1/3 and block length of 1500 bits. In addition, the proposed system shows a coding gain of 3.6 dB when compared with a non cooperative (no relay) approach. Besides, the proposed cooperative design can offer reduced computations versus the non cooperative system to achieve the same BER at a fixed SNR.

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.

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.

Lossy P-LDPC Codes for Compressing General Sources Using Neural Networks

It is challenging to design an efficient lossy compression scheme for complicated sources based on block codes, especially to approach the theoretical distortion-rate limit. In this paper, a lossy compression scheme is proposed for Gaussian and Laplacian sources. In this scheme, a new route using "transformation-quantization" was designed to replace the conventional "quantization-compression". The proposed scheme utilizes neural networks for transformation and lossy protograph low-density parity-check codes for quantization. To ensure the system's feasibility, some problems existing in the neural networks were resolved, including parameter updating and the propagation optimization. Simulation results demonstrated good distortion-rate performance.

Protograph Designing of P-LDPC Codes via M3 Method

Recently, a mesh model-based merging (M3) method and four basic graph models were proposed to construct the double protograph low-density parity-check (P-LDPC) code pair of the joint source channel coding (JSCC). Designing the protograph (mother code) of the P-LDPC code with both a good waterfall region and lower error floor is a challenge, and few works have existed until now. In this paper, the single P-LDPC code is improved to further verify the availability of the M3 method, and its structure is different from the channel code in the JSCC. This construction technique yields a family of new channel codes with lower power consumption and higher reliability. The structured design and better performance demonstrate that the proposed code is hardware-friendly.

Fully Absorbing Set Enumerators for Protograph-Based LDPC Code Ensembles

The average finite-length (elementary) fully absorbing set enumerators for binary protograph-based low-density parity-check (LDPC) code ensembles are derived. The method relies on generating functions, and it provides an efficient mean to obtain the normalized logarithmic asymptotic distribution of (elementary) fully absorbing sets. Using these results, the asymptotic distribution of (elementary) fully absorbing sets is evaluated for some protograph-based LDPC code ensembles. Numerical results show how the distributions can be used to estimate the error floor performance of protograph LDPC codes.

Design of Protograph LDPC Codes Using Resolvable Block Designs for Block Fading Channel

In this letter, we propose new protograph low-density parity-check (LDPC) codes of high code rates using resolvable block designs (RBDs) for block fading (BF) channels. To analyze the performance of the proposed LDPC codes, we derive an upper bound on bit error rate (BER) using the novel method, called the gamma evolution. Finally, we numerically show that the frame error rate (FER) of the proposed LDPC codes has a slope approaching the channel outage probability.

Design and Optimization of Protograph LDPC-Coded Multipulse PPM Systems Over Poisson Channels

Combining powerful error-correction codes (ECCs) with multipulse pulse-position modulation (MPPM) has great potential to realize high-throughput and high-reliability transmissions in free-space optical (FSO) communication systems. This paper conducts an insightful investigation on protograph low-density parity-check (PLDPC)-coded MPPM systems over Poisson channels. To be specific, we first put forward a novel type of constellations, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">irregular pulse-distribution (IPD) constellations</i> , for MPPM. We also conceive a bit-level rate-adaptive (RA) scheme, which can exploit the structural property of the IPD constellations to significantly improve the convergence performance at the price of transmission-rate loss. Furthermore, with the aid of a modified protograph extrinsic information transfer (PEXIT) algorithm, we construct three enhanced PLDPC codes with code rates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1/2, 2/3$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3/4$</tex-math></inline-formula> that exhibit excellent decoding thresholds over Poisson channels. The proposed PLDPC-coded MPPM systems with the use of the IPD constellations, RA scheme, and enhanced PLDPC codes are superior to the state-of-the-art counterparts.

Learning to Decode Protograph LDPC Codes

The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with the codelength, thus they can only support short to moderate codelengths. From the point view of practicality, we propose a high-performance neural min-sum (MS) decoding method that makes full use of the lifting structure of protograph low-density parity-check (LDPC) codes. By this means, the size of the parameter array of each layer in the neural decoder only equals the number of edge-types for arbitrary codelengths. In particular, for protograph LDPC codes, the proposed neural MS decoder is constructed in a special way such that identical parameters are shared by a bundle of edges derived from the same edge-type. To reduce the complexity and overcome the vanishing gradient problem in training the proposed neural MS decoder, an iteration-by-iteration (i.e., layer-by-layer in neural networks) greedy training method is proposed. With this, the proposed neural MS decoder tends to be optimized with faster convergence, which is aligned with the early termination mechanism widely used in practice. To further enhance the generalization ability of the proposed neural MS decoder, a codelength/rate compatible training method is proposed, which randomly selects samples from a set of codes lifted from the same base code. As a theoretical performance evaluation tool, a trajectory-based extrinsic information transfer (T-EXIT) chart is developed for various decoders. Both T-EXIT and simulation results show that the optimized MS decoding can provide faster convergence and up to 1dB gain compared with the plain MS decoding and its variants with only slightly increased complexity. In addition, it can even outperform the sum-product algorithm for some short codes.

Joint Coding/Decoding Optimization for DC-BICM System: Collaborative Design

Differential chaotic bit-interleaved coded modulation (DC-BICM) system can achieve coding gain from channel code without loss of bandwidth in the differential chaos shift keying (DCSK) system, but the current DC-BICM system using the belief propagation decoding algorithm has high decoding complexity, which brings burdens to resource-limited applications. In this letter, a novel collaborative design framework based on joint coding and decoding optimization is proposed for the DC-BICM system over multipath Rayleigh channels. Firstly, the column-weight-based (CWB) shuffled scheduling decoding is introduced into the DC-BICM system to lower the decoding complexity, called shuffled-based DC-BICM system. Then, a CWB extrinsic information transfer (CWB-EXIT) algorithm is developed for the theoretical analysis of this system. With the CWB-EXIT algorithm, a low-storage protograph low-density parity-check (P-LDPC) code is designed for this system, and the column-weight distribution is taken as an important constraint in the collaborative design process. In this way, the storage space used for storing the scheduling order in the CWB shuffled scheduling can be saved, whose size is proportional to code length. Theoretical analysis and simulations show that the shuffled-based DC-BICM system with the low-storage P-LDPC code can achieve lower decoding complexity, less storage requirement and better performance than the existing systems.

Protograph LDPC Code Design For LS-MIMO 1-bit ADC Systems

Recently, two emerging research topics are protograph low-density parity-check (P-LDPC) and large-scale multi-input multi-output (LS-MIMO) with low-resolution analog-to-digital (ADC) converters (LS-MIMO-LOW-ADC). In these directions, many research works have proposed 1-bit ADC as a good candidate for LS-MIMO systems in order to save both transmission power and circuit energy dissipation. However, we observed that previously reported P-LDPC codes might not have good performance for LS-MIMO systems with 1-bit ADC. Hence, we perform a re-design of the P-LDPC codes for the above systems in this paper. The new codes demonstrate a good coding gain from 0:3 dB at rate 1/2 to 0:5 dB at rate 2/3 in different LS-MIMO configurations with 1-bit ADC.

On The Performance Of 1-Bit ADC In Massive MIMO Communication Systems

Massive multiple-input multiple-output (MIMO) with low-resolution analog-to-digital converters is a rational solution to deal with hardware costs and accomplish optimal energy efficiency. In particular, utilizing 1-bit ADCs is one of the best choices for massive MIMO systems. This paper investigates the performance of the 1-bit ADC in the wireless coded communication systems where the robust channel coding, protograph low-density parity-check code (LDPC), is employed. The investigation reveals that the performance of the conventional 1-bit ADC with the truncation limit of 3-sigma is severely destroyed by the quantization distortion even when the number of antennas increases to 100. The optimized 1-bit ADC, though having substantial performance gain over the conventional one, is also affected by the quantization distortion at high coding rates and low MIMO configurations. Importantly, the investigation results suggest that the protograph LDPC codes should be re-designed to combat the negative effect of the quantization distortion of the 1-bit ADC.

Protograph LDPC-Coded BICM-ID With Irregular Mapping: An Emerging Transmission Technique for Massive Internet of Things

Bit-interleaved coded modulation with iterative decoding (BICM-ID) is a key technology enabling the communication systems to realize reliable and efficient data transmission. In this work, we present a study on the adaptive irregular-mapping (AIM)-aided BICM-ID systems with the use of protograph low-density parity-check (PLDPC) codes. To be specific, we first propose a three-step design strategy to generate a type of adaptive constellations, which can be combined with their corresponding initial constellations to formulate an AIM scheme for improving the BICM-ID performance. Then, we put forward a theoretical-analysis tool, called AIM-based protograph extrinsic information transfer (PEXIT) algorithm, to estimate the convergence performance of PLDPC codes in the AIM-aided BICM-ID systems. By making use of such an algorithm, we further develop a code-design method to construct a new type of PLDPC codes, called enhanced PLDPC codes, tailored for the AIM-aided BICM-ID systems. Both convergence analysis and simulations indicate that the proposed AIM-aided BICM-ID systems perform better than the existing counterparts, and their performance can be significantly improved by using the enhanced PLDPC codes. Consequently, the proposed designs have great potential to meet the high-reliability, high-throughput, and strong link-adaptation requirements of future wireless-communication scenarios, such as green Internet of Things (IoT).

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> .

Optimized Uniform Scalar Quantizers of Ternary ADCs for Large-Scale MIMO Communications

Large-scale multiple-input multiple-output (LS-MIMO), a promising technology for the future wireless networks to boost the network capacity, unavoidably faces hardware cost and power consumption issues due to a large number of high-resolution power-hungry analog-to-digital converters (ADCs) at the receiver side. The low-resolution ADCs have recently been proven to be an effective solution to cut down the system cost. This paper studies the LS-MIMO communication systems where three-level ADCs, so-called Ternary ADCs (T-ADCs), are employed to achieve better energy efficiency in some LS-MIMO configurations. The truncation limit of the uniform scalar quantizer of the T-ADCs is optimized to minimize the quantization distortion on the LS-MIMO received signal, and thus its performance approaches that of the well-known Lloyd-Max algorithm while offering lower complexity and better robustness. Furthermore, our proposed solution is independent of the number of antennas. The LS-MIMO systems' performance with the proposed T-ADCs is substantially improved over the conventional 3- σ uniform scalar quantizer in three different performance metrics - achievable rates, iterative decoding thresholds of pragmatic protograph low-density parity-check codes (LDPC), and the frame error rate (FER)/bit error rate (BER). Our energy efficiency investigation reveals that proposed T-ADCs attain better energy efficiency than that of the 1-bit ADCs and 2-bit ADCs when the ratio between the receiving antennas and the transmitting antennas is low and medium as the power consumption of ADCs and the transmission power are better balanced in comparison with one-bit ADCs and two-bit ADCs.

Design and Optimization of Tail-Biting Spatially Coupled Protograph LDPC Codes Under Shuffled Belief-Propagation Decoding

In this letter, we conduct a comprehensive investigation on tail-biting (TB) spatially coupled protograph (SC-P) low-density parity-check (LDPC) codes under shuffled belief-propagation (BP) decoding. We first propose a shuffled extrinsic information transfer (S-EXIT) algorithm tailored for the shuffled decoding. Exploiting the proposed algorithm, we accurately predict the convergence performance (i.e., decoding thresholds) for TB-SC-P codes under such a schedule and demonstrate that their convergence performance can be further improved. Based on the S-EXIT analysis, we develop an optimization method to generate a new type of TB-SC-P codes, called improved TB-SC double-protograph (I-TB-SC-DP) codes, which can inherit the superiorities of two mother protograph codes and possess more desirable decoding thresholds. Theoretical analyses and simulated results illustrate that the proposed I-TB-SC-DP codes exhibit better error performance than the existing counterparts.

On Design of Protograph LDPC Codes for Large-Scale MIMO Systems

Protograph low-density parity-check (LDPC) codes and large-scale multi-input multi-output (LS-MIMO) systems have achieved great interest with various practical applications. However, how to effectively evaluate and design protograph LDPC codes for LS-MIMO systems remains a challenging yet critical problem, especially for low-latency applications. To solve that design challenge, the protograph extrinsic information transfer chart (PEXIT) algorithm for LS-MIMO systems, so-called LS-MIMO-PEXIT algorithm, is first derived based on the mutual information functions of messages that are passed on the joint MIMO detection and LDPC decoding graph. The proposed LS-MIMO-PEXIT algorithm plays a vital role in the optimization process of designing new protograph LDPC codes, tailored for LS-MIMO communications systems. Experiment results demonstrate that the analytical results based on the LS-MIMO-PEXIT algorithm are in good agreement with the simulation results under various input constraints, including the coding rate, the number of decoding iterations, and the LS-MIMO configuration. On top of that, the new protograph LDPC codes designed using our LS-MIMO-PEXIT algorithm achieve a coding gain from 0.2 dB at a low coding rate to 0.4 dB at a high coding rate in comparison with the state-of-the-art protograph codes in the literature. Additionally, we incorporate the practical design experience and the theoretical analysis of mutual functions into a two-step procedure to search for protograph LDPC codes that do not have error-floor behavior at frame error rate (FER) or bit error rate (BER) as low as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> or 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> , respectively. Together with the coding gain, the error-floor-free feature of the proposed protograph LDPC codes is vitally important for future wireless networks where the ultra-reliability is one of the critical requirements.

Design of protograph codes for additive white symmetric alpha‐stable noise channels

The protograph low-density parity-check (LDPC) codes possess many attractive properties, such as the low encoding/decoding complexity and better error floor performance, and hence have been successfully applied to different types of communication and data storage channels. In this study, the authors design protograph LDPC codes for communication systems corrupted by the impulsive noise, which are modelled as additive white symmetric alpha-stable noise (AWS α SN) channels. They start by presenting a novel simulation-based protograph extrinsic information transfer analysis to derive the iterative decoding threshold of the protograph codes. By further applying the asymptotic weight distribution analysis, the authors design new protograph codes for the AWS α SN channel. Both theoretical analysis and simulation results demonstrate that the proposed protograph codes can provide better error rate performance than the prior art AR4JA code, the irregular codes optimised for the AWGN channel, as well as the irregular codes optimised for the AWS α SN channel.