Protograph Extrinsic Information Transfer Research Articles

Design and Optimization of Linking Matrix for a JSCC System Based on DP-LDPC Codes.

Although extensive optimization of encoding and decoding schemes for joint source-channel coding (JSCC) systems has been conducted, efficient optimization schemes are still required for designing and optimizing the linking matrix between variable nodes of the source code and check nodes of the channel code. A scheme has been proposed for design and optimization of linking matrix with multi-edges by analyzing the performance of the JSCC system using the joint protograph extrinsic information transfer algorithm to calculate decoding thresholds. The proposed scheme incorporates structural constraints and is effective in designing and optimizing the multi-edges in linking matrix for the JSCC system. Experimental results have demonstrated that the designed and optimized linking matrix significantly improves the performance of the JSCC system. Furthermore, the proposed scheme reduces the complexity of the solution space for the optimized example.

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.

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.

Performance analysis and design of quasi-cyclic LDPC codes for underwater magnetic induction communications

Magnetic induction (MI) communication is an effective scheme for underwater wireless communication. In this paper, we aim to design an underwater MI communication system based on Quasi-cyclic LDPC (QC-LDPC) codes. Firstly, for a given QC-LDPC code used in underwater MI communication, we propose a novel algorithm to evaluate its performance, which is named as underwater magnetic induction protograph (UWMIP) extrinsic information transfer algorithm. Furthermore, we present a differential evolution UWMIP (DE-UWMIP) algorithm, which incorporates the differential evolution method and the UWMIP algorithm. By this algorithm, we search the optimized QC-LDPC codes with best distance threshold. Simulation results show that the proposed algorithm is effective and provide a good guidance to design the underwater MI communication system.

Redesign of Channel Codes for Joint Source-Channel Coding Systems over One-Dimensional Inter-Symbol-Interference Magnetic Recording Channels

Although the joint source-channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) codes has been shown to possess excellent error performance over additive white Gaussian noise (AWGN) channels, it cannot perform well over one-dimensional inter-symbol-interference (OD-ISI) magnetic recording channels. In this study, a new JSCC system with a three-stage serially concatenated framework of Turbo equalization is firstly proposed for OD-ISI magnetic recording channels. Then, a modified joint protograph extrinsic information transfer (M-JPEXIT) algorithm is put forward to analyze the convergence-performance of the proposed system. By applying the M-JPEXIT algorithm, the channel codes are redesigned for this system to improve the error performance. Both the M-JPEXIT analysis and the bit-error-rate (BER) simulation results show the performance improvement of the proposed channel codes, especially in the water-fall region.

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.

Spatially Coupled PLDPC-Hadamard Convolutional Codes

We propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard block codes. We develop an efficient decoding algorithm that combines pipeline decoding and layered scheduling for the decoding of SC-PLDPCH-CCs, and analyze the latency and complexity of the decoder. To estimate the decoding thresholds of SC-PLDPCH-CCs, we first propose a layered protograph extrinsic information transfer (PEXIT) algorithm to evaluate the thresholds of spatially coupled PLDPC-Hadamard terminated codes (SC-PLDPCH-TDCs) with a moderate coupling length. With the use of the proposed layered PEXIT method, we develop a genetic algorithm to find good SC-PLDPCH-TDCs in a systematic way. Then we extend the coupling length of these SC-PLDPCH-TDCs to form good SC-PLDPCH-CCs. Results show that our constructed SC-PLDPCH-CCs can achieve comparable thresholds to the block code counterparts. Simulations illustrate the superiority of the SC-PLDPCH-CCs over the block code counterparts and other state-of-the-art low-rate codes in terms of error performance. For the rate-0.00295 SC-PLDPCH-CC, a bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup> is achieved at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E_{b}/N_{0} = -1.465$ </tex-math></inline-formula> dB, which is only 0.125 dB from the ultimate Shannon limit.

Performance and Capacity Analysis of MDCSK-BICM for Impulsive Noise in PLC

To further mitigate the BER error floor of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -ary differential chaos shift keying (MDCSK) modulation for impulsive noise, a low-cost high-reliability coded modulation scheme without equalizations is desirable for impulsive noise. In this paper, a protograph-based low-density parity-check coded MDCSK-based bit-interleaved coded modulation (MDCSK-BICM) scheme is proposed for the scenario with impulsive noise obeying Bernoulli-Laplace distribution. Considering the Gaussian distribution of protograph extrinsic information transfer (PEXIT) and the benchmark of coding design, the U-shaped non-coherent capacity is derived with optimal code rate for square MDCSK, showing that the code rates are stable with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$E_b/N_0$</tex-math></inline-formula> increasing but still much lower than that of DS-16DQAM at code rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;\!0.145$</tex-math></inline-formula> . The derived joint probability density function can be considered as approximately a Gaussian distribution, which is used to improve the impulsive noise fitted PEXIT. Finally, a new code under a novel principle is designed for better bit error rate performance based on the improved PEXIT analysis. Both PEXIT analysis and simulation results demonstrate that the proposed scheme achieves a better BER than that with a traditional scheme, and suggesting a research approach based on simple methods. This basic research work provides a guide to establish a framework and optimize the performance of transmission systems over practical power line communication.

Joint Code Rate Compatible Design of DP-LDPC Code Pairs for Joint Source Channel Coding Over Implant-to-External Channel

A CM2-S3 transmission link in wireless body area networks (WBAN) is implemented with a joint source channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) code pairs with high reliability and low power consumption. For the practicality and suitability considerations, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary differential chaos shift keying scheme is introduced to modulate the CM2-S3 channel with better performance than the standard modulations in WBAN. Due to the non-Gaussian-like distribution of the CM2-S3 channel model, the initial joint protograph extrinsic information transfer (JPEXIT) algorithm does not work as a coding analysis tool. To solve this problem, a numerical Gaussian approximation is employed to modify the iterative mutual information function of the JPEXIT for achieving more precise output. Then, a joint code rate compatible (JCRC) method, designed with compatibility in resisting variable channel variances and adapting different source statistics, is proposed for optimizing the DP-LDPC code pairs. Based on the JCRC method, the code searching algorithm is simplified with lower complexity because of the reduced cycle-index. The simulation results show that optimized code pairs have better bit-error ratio performances compared to existing codes, which provides a strong technical support to promote high-quality data transmission in eHealthcare on the physical layer.

Construction of Protograph-Based Partially Doped Generalized LDPC Codes

In this paper, we propose a new code design technique, called partial doping, for protograph-based generalized low-density parity-check (GLDPC) codes. While the conventional construction method of protograph-based GLDPC codes is to replace some single parity-check (SPC) nodes with generalized constraint (GC) nodes applying to multiple variable nodes (VNs) that are connected in the protograph, the proposed technique can select any VNs in the protograph to be protected by GC nodes. In other words, the partial doping technique facilitates finer tuning of doping, which in turn enables a sophisticated code optimization with higher degree of freedom. We construct the proposed partially doped GLDPC (PD-GLDPC) codes using the partial doping technique and optimize the PD-GLDPC codes by the protograph extrinsic information transfer (PEXIT) analysis. In addition, we propose a condition guaranteeing the linear minimum distance growth of the PD-GLDPC codes and use the condition for the optimization. Experimental results show that the optimized PD-GLDPC codes outperform the conventional GLDPC codes and have competitive performance compared to the state-of-the-art protograph-based LDPC codes without the error floor phenomenon over the binary erasure channel (BEC).

Design of Code Pair for Protograph-LDPC Codes-Based JSCC System With Joint Shuffled Scheduling Decoding Algorithm

Although there are many studies on code optimization of the joint source-channel coding (JSCC) system based on double protograph low-density parity-check codes with the joint belief propagation (JBP) algorithm, but it is still unknown whether the source code and channel code (as a code pair) can perform well when the joint shuffled scheduling decoding (JSSD) algorithm is adopted. In this letter, two decoding threshold analysis algorithms, including joint shuffled protograph extrinsic information transfer (PEXIT) and source shuffled PEXIT algorithm, are proposed to calculate joint/source decoding thresholds for this system with the JSSD algorithm. With the proposed algorithms, it is found that the optimized code pairs for this system with the JBP algorithm may not perform well with the JSSD algorithm, implying that code pair with the JSSD algorithm needs to be redesigned. Then, a two-stage optimized framework is proposed to design the code pair for this system with the JSSD algorithm. Simulations and decoding threshold analysis both show that the proposed code pair for this system with the JSSD algorithm can obtain lower error floor and better waterfall performance than the existing code pairs.

On efficient designing of protograph LDPC codes

This paper designs two protograph LDPC codes with code-rate $R &gt; 1/2$. 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.

Protograph-Based LDPC Hadamard Codes

In this paper, we propose a new method to design low-density parity-check Hadamard (LDPC-Hadamard) codes — a type of ultimate-Shannon-limit approaching channel codes. The technique is based on applying Hadamard constraints to the check nodes in a generalized protograph-based LDPC code, followed by lifting the generalized protograph. We name the codes formed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">protograph-based</i> LDPC Hadamard (PLDPC-Hadamard) codes. We also propose a modified Protograph Extrinsic Information Transfer (PEXIT) algorithm for analyzing and optimizing PLDPC-Hadamard code designs. The proposed algorithm further allows the analysis of PLDPC-Hadamard codes with degree- 1 and/or punctured nodes. We find codes with decoding thresholds ranging from −1.53 dB to −1.42 dB. At a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup> , the gaps of our codes to the ultimate-Shannon-limit range from 0.40 dB (for rate = 0.0494) to 0.16 dB (for rate = 0.003). Moreover, the error performance of our codes is comparable to that of the traditional LDPC-Hadamard codes. Finally, the BER performances of our codes after puncturing are simulated and compared.

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).

Optimal Design of Joint Protomatrix for DP-LDPC Codes-Based JSCC System Over on-Body Channel

A high-quality data transmission scheme in wireless body area networks is implemented by a joint source-channel coding (JSCC) system with $M$ -ary differential chaos shift keying modulation over an on-body channel. Current DP-LDPC code pairs, which have shown good bit-error ratio performance over additive white Gaussian noise channel and Rayleigh fading channel, cannot perform well over on-body channel. In this paper, the DP-LDPC codes are redesigned for the JSCC system with new methods depending on the on-body channel characteristics. A protomatrix dimension-restrictive searching algorithm for DP-LDPC codes in the JSCC system is proposed according to the on-body channel bandwith and source statistic, which is effective to predesign the dimension of the code pair for a new JSCC system. In this way, the source-channel code rates are appropriately allocated to leave more source redundancy for improving the error floor. Moreover, the joint protomatrix is reconstructed into two kinds of compact structures by simplifying the edge linking relationships and modifying joint protograph extrinsic information transfer algorithm, which decreases the induction of searching entries to further accelerate the code searching speed. The searched code pairs show better bit-error ratio performances compared with existing DP-LDPC codes. The power consumption in the new joint coding system is lower than the separate coding system in WBAN on the physical layer.

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.

Joint Component Design for the JSCC System Based on DP-LDPC Codes

The joint base matrix ${{{{B}}_{{\mathrm{J}}}}}$ of the joint source-channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) codes consists of four components, namely, the source code ${{{{B}}_{{\mathrm{s}}}}}$ , the channel code ${{{{B}}_{{\mathrm{c}}}}}$ , the type-1 connection edge ${{{{B}}_{{ \textit {L1}}}}}$ and the type-2 connection edge ${{{{B}}_{{ \textit {L2}}}}}$ , each having a non-negligible influence on the system performance. Different from the traditional component-specific design approach, we propose a joint design and optimization algorithm based on the idea of multi-objective differential evolution (MODE). Specifically, we consider the optimization of the DP-LDPC JSCC system through joint design of three components ${{{{B}}_{{\mathrm{s}}}}}$ , ${{{{B}}_{{\mathrm{c}}}}}$ , ${{{{B}}_{{ \textit {L1}}}}}$ and all four components ${{{{B}}_{{\mathrm{s}}}}}$ , ${{{{B}}_{{\mathrm{c}}}}}$ , ${{{\mathbf{B}}_{{ \textit {L1}}}}}$ , ${{{{B}}_{{ \textit {L2}}}}}$ , respectively. The proposed algorithm has low search complexity due to the reduction in size and element value of base matrices. The joint protograph extrinsic information transfer (JPEXIT) analyses and the simulation results demonstrate that the resulting JSCC system is free from a high error floor, requires fewer number of iterations for reaching the same bit error rate (BER) and achieves significant coding gains as compared to the state-of-the-art. Our DP-LDPC JSCC system is also shown to outperform its separation-based counterpart by a wide margin.

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.