LDPC Research Articles

Novel Approach towards a Fully Deep Learning-Based IoT Receiver Architecture: From Estimation to Decoding

As the Internet of Things (IoT) continues to expand, wireless communication is increasingly widespread across diverse industries and remote devices. This includes domains such as Operational Technology in the Smart Grid. Notably, there is a surge in resource-constrained devices leveraging wireless communication, especially with the advances of 5G/6G technology. Nevertheless, the transmission of wireless communications demands substantial power and computational resources, presenting a significant challenge to these devices and their operations. In this work, we propose the use of deep learning to improve the Bit Error Rate (BER) performance of Orthogonal Frequency Division Multiplexing (OFDM) wireless receivers. By improving the BER performance of these receivers, devices can transmit with less power, thereby improving IoT devices’ battery life. The architecture presented in this paper utilizes a depthwise Convolutional Neural Network (CNN) for channel estimation and demodulation, whereas a Graph Neural Network (GNN) is utilized for Low-Density Parity Check (LDPC) decoding, tested against a proposed (1998, 1512) LDPC code. Our results show higher performance than traditional receivers in both isolated tests for the CNN and GNN, and a combined end-to-end test with lower computational complexity than other proposed deep learning models. For BER improvement, our proposed approach showed a 1 dB improvement for eliminating BER in QPSK models. Additionally, it improved 16-QAM Rician BER by five decades, 16-QAM LOS model BER by four decades, 64-QAM Rician BER by 2.5 decades, and 64-QAM LOS model BER by three decades.

Cross layered adaptive rate optimized irregular LDPC for WSN

This paper proposes a cross layered adaptive rate optimized technique that uses irregular low-density parity-check (LDPC) codes over an additive white Gaussian noise (AWGN) channel in wireless sensor networks (WSNs). Irregular LDPC is used as error control code. Cross layer design along with error control code gives the energy balance in the network. This new algorithm uses the physical layer parameters such as coherence time of the channel, BER and SNR and the routing layer parameter such as demanded data rate to determine the rate of the LDPC coder. The algorithm adaptively changes the code rates as ¾, ½, and 1/3. We have conducted the simulations to verify our methods using MATLAB and find that the proposed scheme increases the network performance in terms of energy balance and quality of data by using irregular LDPC codes in the cross-layer environment.

On a class of column‐weight 3 decomposable LDPC codes with the analysis of elementary trapping sets

AbstractA column‐weight LDPC code with the parity‐check matrix is called decomposable if there exists a permutation on the rows of , such that can be decomposed into column‐weight one matrix. In this paper, some variations of edge coloring of graphs are used to construct some column‐weight three decomposable LDPC codes with girths at least six and eight. Applying the presented method on several known classes of bipartite graphs, some classes of column‐weight three decomposable LDPC codes are derived having flexibility in length and rate. Interestingly, the constructed parity‐check matrices based on the proper edge coloring of graphs can be considered as the base matrix of some high rate column‐weight three quasi‐cyclic (QC) LDPC codes with maximum‐achievable girth 20. The paper also leads to a simple characterization of elementary trapping sets of the decomposable codes based on the chromatic index of the corresponding normal graphs. This characterization corresponds to a simple search algorithm finds all possible existing elementary trapping sets in a girth‐6 or girth‐8 column‐weight 3 LDPC code which are layered super set of a short cycle in the Tanner graph of the code. Simulation results indicate that the QC‐LDPC codes with large girths lifted from the constructed base matrices have good performances over AWGN channel.

Experimental demonstration of flexible information rate PON beyond 100 Gb/s with rate-compatible LDPC codes

The applications of rate-compatible low-density parity-check (RC-LDPC) codes are investigated for a 16 quadrature amplitude modulation (16QAM) signal and coherent detection system. With rate-compatible signals, we can provide the flexible net data rate between 135.5 Gb/s and 169.7 Gb/s in a passive optical network (PON) link. Based on the LDPC codes defined in the IEEE 802.3ca standard, we construct two sets of RC-LDPC codes with a fixed and variable information bit length. Since the puncturing operation may degrade the performance of LDPC codes, we apply the protograph-based extrinsic information transfer (PEXIT) technique to optimize the puncturing positions to mitigate the degradation. Additionally, we explore four low-complexity LDPC decoding algorithms (min sum, offset min sum, variable weight min sum, and relaxed min sum with 2 nd min emulation) to investigate the relationship between the computational complexity and decoding performance. Simulation results indicate that the constructed codewords exhibit good performance in the waterfall region across a range of code rates. Finally, we conduct an experimental setup in a dual-polarization 25 GBaud 16QAM coherent PON to verify the effectiveness of the constructed LDPC codes with four decoding algorithms. The experimental results show maximal 4.8 dB receiver sensitivity differences, which demonstrate the feasibility of the method for constructing RC-LDPC codes in future high-speed flexible coherent PON.

Energy-Efficient Partial LDPC Decoding for NAND Flash-Based Storage Systems

A new decoding method for low-density parity-check (LDPC) codes is presented to lower the energy consumption of LDPC decoders for NAND flash-based storage systems. Since the channel condition of NAND flash memory is reliable for most of its lifetime, it is inefficient to apply the maximum-effort decoding with the full parity-check matrix (H-matrix) from the beginning of the lifespan. As the energy consumption and the decoding latency are proportional to the size of the H-matrix used in decoding, the proposed algorithm starts the decoding with a partial H-matrix selected by considering the channel condition. In addition, the proposed partial decoding provides various error-correcting capabilities by adjusting the partial H-matrix. Based on the proposed partial decoding algorithm, a prototype decoder is implemented in a 65 nm CMOS process to decode a 4 KB LDPC code. The proposed decoder reduces energy consumption by 93% compared to the conventional LDPC decoding architecture at maximum.

An Efficient Design for the DVB-S2 Forward Link System Outer Layer Encoding Based on PCC Turbo Coding Across Fading Channel

The most significant challenges wireless broadcasting systems face are channel effects and Inter Symbol Interference (ISI). Many different kinds of channel coding are employed to get around these issues. Digital Video Broadcasting for Satellite Telecommunication Second Generation (DVB-S2) uses a serial concatenation of Bose, Ray-Chaudhuri, and Hocquenghem (BCH) code and Low-Density Parity-Check (LDPC) code as a Forward Error Correction (FEC) for error detection purpose and correction. In this work, a MATLAB code (m-files) is constructed to simulate the standard DVB-S2 Bit-Interleaved Coded Modulation (BICM) system according to the ETSI Technical Report (EN 302 307 1). Then, the traditional design is redesigned with a Parallel Concatenation Convolutional (PCC) Turbo coding in concatenation with LDPC coding to enhance the (FEC). The two approaches have been tested under the official modulation types QPSK, 8PSK, 16APSK, and 32APSK with 2/3, 3/4, 3/5, 4/5, and 5/6 code rates (RC). Over a Rayleigh Fading channel, the two models are compared. The proposed model performed better than the standard model regarding bit error rate (BER) mitigation when operating at varying signal-to-noise ratio (SNR) levels, especially in 8PSK 3/5 MODCODE. The proposed model achieved (2.6272×10-3) BER mitigation value with power gain equal to 4 dB.

Multi-Impairment Compensation for CO-OFDM System Based on Deep Learning and LDPC Code

Multi-Impairment Compensation for CO-OFDM System Based on Deep Learning and LDPC Code

Advanced hybrid algorithms for precise multipath channel estimation in next-generation wireless networks

Multipath channels continue to present challenges in wireless communication for both 5G and 6G networks. A multipath channel is a phenomenon in wireless communications where signals traverse from the sender to the receiver along various paths. This end occurs due to the reflection, diffraction, and refraction of signals of various objects and structures in the environment. Such pathways can cause symbol interference in the transmitted signal, leading to communication issues. To this end, our paper proposes the integration of three algorithms: teaching-learning-based optimization (TLBO), particle swarm optimization (PSO), and artificial neural networks (ANN). This combination effectively analyzes and stabilizes the transmission channel, minimizing symbol interference. We have developed, simulated, and evaluated this hybrid approach for multipath fading channels. We apply it to various coding schemes, including tail-biting convolutional code, turbo codes, low-density parity-check, and polar code. Additionally, we have explored various decoding methods such as Viterbi, maximum logarithmic maximum a posteriori, minimum sum, and cyclic redundancy check soft cancellation list. Our study encompasses new channel equalization schemes and coding gains derived from simulations and mathematical analysis. Our proposed method significantly enhances channel equalization, reducing interference and improving error correction in wireless communication systems.

Efficient Construction of Quasi-Cyclic LDPC Codes With Multiple Lifting Sizes

Efficient Construction of Quasi-Cyclic LDPC Codes With Multiple Lifting Sizes

On the First Separating Redundancy of Array LDPC Codes

On the First Separating Redundancy of Array LDPC Codes

A Quasi-Cyclic LDPC Based Low Complexity and Area-Efficient Communication System for IEEE 802.11n

Low-density parity-check (LDPC) code, which has an excellent error-correcting performance that is close to the Shannon limit, is the most often used error correction code (ECC) for reliable and effective communication. Despite higher performance and lower decoding complexity, the main disadvantage of LDPC codes is their high encoding complexity. A significant problem is the VLSI implementation of the LDPC encoder and decoder. In this paper, structured LDPC codes—also known as quasi-cyclic low-density parity check codes—have been used since it is good bit error ratio (BER) performance and adaptable hardware execution characteristics. The Complete (Encoder-Channel-Decoder) communication system with a 1/2 code rate, 648 bits codeward length, and sub-block size of z = 27 has been constructed for the IEEE 802.11n wireless standard.

Novel intelligent blind information reconciliation for LDPC codes in quantum key distribution systems

Information reconciliation is an important step in quantum key distribution (QKD). As a good channel coding technology, LDPC (low-density parity-check) code perform well in information reconciliation. In this paper, we investigate a new approach, namely blind information reconciliation. In our approach, after the state distribution is carried out by Alice and the measurements are taken by Bob, Alice can select an appropriate LDPC encoder (parity-check matrix) from the predefined candidate pool according to the estimated QBER (quantum bit-error-rate). Bob can use the expectation–maximization (EM) estimator and the maximum average log-likelihood ratio (LLR) detector to blindly identify parity-check matrices associated with not only different code-rates but also different codeword-lengths Alice employed. Moreover, puncturing and shortening can also be invoked to adjust the code-rate slightly to improve the error-correction performance. Monte Carlo simulations have demonstrated that our proposed new blind information-reconciliation scheme can successfully identify the parity-check matrix even under high QBER conditions, reduce the interactive communication-rounds, and improve the reconciliation efficiency in comparison with the conventional rate-adaptive LDPC coding scheme without QBER estimation.

Friendly Attacks to Improve Channel Coding Reliability

This paper introduces a novel approach called "friendly attack" aimed at enhancing the performance of error correction channel codes. Inspired by the concept of adversarial attacks, our method leverages the idea of introducing slight perturbations to the neural network input, resulting in a substantial impact on the network's performance. By introducing small perturbations to fixed-point modulated codewords before transmission, we effectively improve the decoder's performance without violating the input power constraint. The perturbation design is accomplished by a modified iterative fast gradient method. This study investigates various decoder architectures suitable for computing gradients to obtain the desired perturbations. Specifically, we consider belief propagation (BP) for LDPC codes; the error correcting code transformer, BP and neural BP (NBP) for polar codes, and neural BCJR for convolutional codes. We demonstrate that the proposed friendly attack method can improve the reliability across different channels, modulations, codes, and decoders. This method allows us to increase the reliability of communication with a legacy receiver by simply modifying the transmitted codeword appropriately.

Method of assessing the information reliability of in 5G wireless transmission systems

The article proposes a method of assessing information transmission reliability by using the output normalized logarithmic ratio of the likelihood function (LRLF) of the decoder. Based on the evaluation, the method allows adapting system parameters with turbo codes (TC) or LDPC code. This method can be used in combination with other methods of parametric and structural adaptation using turbo codes or LDPC codes.

An inspired chaos-based estimation-theory optimization for low-density parity-check (LDPC) code decoding

Optimization techniques have emerged as powerful tools for solving complex engineering problems in real-time applications, surpassing traditional heuristic methods. This paper introduces a novel chaos optimization algorithm that integrates the bisection search method to enhance the convergence ability, solution accuracy, and search speed of conventional optimization problems. The proposed algorithm is applied to the design and analysis of a reduced complexity decoding scheme using Low-Density Parity-Check (LDPC) codes. By leveraging the Linear Minimum Mean Square Error (LMMSE) estimation criterion, the proposed method approximates the estimated parameters acquired during the message computation process. This combined approach effectively mitigates error propagation and premature convergence issues. The presented research offers a low-complexity decoding algorithm for LDPC codes, leveraging an optimized chaos bisection search method. The adoption of the LMMSE criterion overcomes data dependency and error propagation concerns during the estimation process. The modified chaos optimization technique, integrated with the bisection search, efficiently determines optimal values from perturbed observations, leading to improved convergence rates and data processing precision by reducing the observation dimension (search space). Simulation results validate the proposed approach, showcasing its ability to mitigate error propagation and premature convergence while maintaining coding gain accuracy. Experimental validation on an FPGA RF-SoC device (model XCZU27DR) demonstrates that the proposed method achieves a maximum throughput of 8.7 Gbps at a clock frequency of 386.72 MHz, with reduced hardware complexity. The experimental verification on an FPGA RF-SoC device highlights the algorithm's minimal hardware complexity, superior decoding throughput, and Bit Error Rate (BER) performance.

Optimized LNS-FAID of LDPC codes: a hybrid precision decoding approach for 50G-PON.

Efficient error correction in high-speed communication networks, such as the 50G passive optical network (50G-PON), is paramount. This Letter focuses on optimizing a layered non-surjective finite alphabet iterative decoder (LNS-FAID) for 50G-PON, with an emphasis on high-throughput and low-power consumption. We propose using a distinct lookup table (LUT) for each iteration to enhance decoding performance and lower error floors. Additionally, we improve the 2-bit LNS-FAID architecture by adding operational states and a sign backtracking (SBT) strategy. This paper also introduces a hybrid precision model that merges 3-bit and 2-bit LNS-FAIDs, which balances error correction with computational efficiency. Our simulation results show that these approaches significantly improve the performance of the LDPC code in 50G-PON.

Secure transmission and storage of Internet of Things data

The Internet of Everything is the ultimate level form of the Internet of Things. The result of digitizing the objects in life is a huge amount of data that needs to be stored and transmitted. This paper will briefly introduce the IoT and the current status of data processing. Different coding methodologies, Reed Solomon (RS) codes, Low-Density Parity-Check (LDPC) codes, and Low Complexity Parity Check (LCPC) codes will also be explained in detail from their encoding and decoding aspect. Then different codes are specifically analyzed for their usage scenarios in IoT data transmission and storage based on their particular characteristics. In the experimental section, different codes are compared from different perspectives. The main comparisons are made in terms of memory usage, operation time, energy consumption per bit of encoding, and error correction performance. The results of the analysis are RS code is simple but lacks error correction, the LDPC code has good error correction but is more complex, LCPC code strikes a balance between power efficiency and performance.

Efficient VLSI Implementation of Hybrid LDPC-STBC Codes for Enhanced Satellite Communication Systems

Satellite communication systems play a pivotal role in facilitating global connectivity, necessitating the development of robust error correction codes to ensure reliable data transmission. In contemporary communication systems, the demand for higher data rates and improved spectral efficiency has led to the integration of advanced error correction techniques. However, existing systems often face challenges in striking a balance between complexity, power consumption, and performance. This work addresses the limitations of current systems by proposing a hybrid approach that combines the advantages of LDPC (Low-Density Parity-Check) codes and STBC (Space-Time Block Coding) techniques. The hybrid LDPC-STBC codes aim to enhance the error correction capabilities of satellite communication systems, ensuring robust data transmission in the presence of channel impairments. Despite the advancements in error correction coding, current systems encounter drawbacks such as increased computational complexity, higher power consumption, and potential performance degradation under adverse channel conditions. The proposed hybrid LDPC-STBC codes mitigate these issues by leveraging the strengths of both coding schemes, achieving a synergistic balance between error correction performance and computational efficiency.

Feature of the forward error correction constructions for optical transport networks

Due to the rapid increase of network traffic in the last few years, many telecommunication operators have started transitions to 100G optical networks and beyond. However, high speed optical networks need more efficient Forward Error Correction (FEC) codes to deal with the optical impairments. Forward error correction is widely used in optical communications to improve error correction and extend optical transmission distance. It is also used to reduce optical transmitter power and system costs. In response to the rapid growth of optical communications, the ITU-T has started researching FEC coding and has recommended ITU-T G.709 and G.975.1. As optical transmission systems evolve towards longer transmission distance, greater capacity, and speeds of 100G and beyond a variety of unwanted effects are seriously affecting smooth evolution. In optical transport network, FEC is getting more and more important as spectral efficiency is increasing. As 100G system is commercialized, there are some trends in the evolution of FEC, for example overhead is increased from 7% to 20% or even more. High-performance FEC codes are therefore being developed so that higher net coding gain (NCG) and better error correction can be achieved. The Optical Internetworking Forum (OIF) suggests that soft-decision forward-error correction (SD-FEC) with a redundancy of 20% and beyond be used in a 100G DWDM coherent system. The use of advanced modulation formats is a promising solution for attaining such high data rates in optical networks. However, as a signal constellation grows in size, so does the optical signal to signal-to-noise ratio it requires to achieve a certain bit error rate (BER). This will degrade the error correction capability. Decoding is moving from hard to soft. Vendors are developing their own advanced codes instead of using codes recommended by ITU-T. Because different application systems have different decoding performance, latency, power and cost requirements, FEC systems with various transmission overhead, implementation complexity, burst-error correction ability and error floor are available in today’s market. Soft-decision FEC often uses turbo product codes and low density parity check (LDPC) codes. In research area, new codes such as LDPC codes and their different varieties are introduced into optical communication. Optimized codeword structure and decoding algorithm that provides low BER. LDPC codes can be very powerful, but their practical implementation for optical communications links at ultra-high data rates remains a challenge since the decoding of the code requires soft-decision bits about the received bits. A family of structured codes known as quasi-cyclic LDPC codes, whose common structural properties can be exploited by unified encoding and decoding architectures to reduce the complexity in implementation.

Hard-Decision Decoding Algorithms for LDPC Codes Based on Matching Pursuit

Hard-Decision Decoding Algorithms for LDPC Codes Based on Matching Pursuit