Low Density Parity Research Articles

A Temporal Methodology for Assessing the Performance of Concatenated Codes in OFDM Systems for 4K-UHD Video Transmission

The communication channel is a critical part of the process of information degradation. In the 4K ultra-resolution video transmission domain, the communication channel is a crucial part where information degradation occurs, inevitably leading to errors during reception. To enhance the transmission process in terms of fidelity, advanced technologies such as digital video broadcasting terrestrial (DVB-T) and its evolutionary successor, digital video broadcasting terrestrial second generation (DVB-T2), are utilized to mitigate the effects of data transmission errors. Within this scenario, this research presents an innovative methodology for the temporal analysis of 4K ultra-resolution video quality under the influence of additive white Gaussian noise (AWGN) and Rayleigh channels. This analytical endeavor is facilitated through the application of concatenated coding schemes, specifically, the Bose–Chaudhuri–Hocquenghem concatenated low-density parity check (BCH-LDPC) and Reed–Solomon concatenated convolutional (RS-CONV) coders. A more comprehensive understanding of video quality can be attained by considering its temporal variations, a crucial aspect of the ongoing evolution of technological paradigms. In this study, the Structural Similarity Index (SSIM) serves as the main metric for quality assessment during simulations. Furthermore, the simulated Peak Signal-to-Noise Ratio (PSNR) values validate these findings, exhibiting consistent alignment with the SSIM-based evaluations. Additionally, the performance of the BCH-LDPC significantly outperforms that of RS-CONV under the 64-QAM modulation scheme, yielding superior video quality levels that approximate or surpass those achieved by RS-CONV under QPSK (Quadrature Phase Shift Keying) modulation, leading to an increase in spectral efficiency. This enhancement is evidenced by SSIM gains exceeding 78% on average. The computation of average gains between distinct technologies in video quality analysis furnishes a robust and comprehensive evaluation framework, empowering stakeholders to make informed decisions within this domain.

An LDPC-RS Concatenation and Decoding Scheme to Lower the Error Floor for FTN Signaling

Faster-than-Nyquist (FTN) signaling has attracted increasing interest in the past two decades. However, when the fifth-generation (5G) communication low-density parity check (LDPC) code is applied to FTN signaling with low Bahl–Cock–Jelinek–Raviv (BCJR) states of detection and few turbo equalization iterations, an error floor near 10−5 is found, which does not exist in the original LDPC used for orthogonal signaling. This can be eliminated through many detection and decoding iterations, but this is unacceptable considering the increase in latency and storage. To solve this problem, we propose an LDPC and Reed–Solomon (RS) concatenation code, shortening, and perturbation scheme to lower the error floor. We propose a parallel encoder architecture for RS component code and a concise algorithm to calculate its constant multiplier coefficients, leveraging a traditional serial encoder, which can also be used for other parallelisms, rates, and lengths. The simulation results show that the proposed concatenation and shortening scheme can lower the error floor to about 10−7. The proposed scheme has an error correction capability for coded FTN signaling and successfully lowers the error floor with the limitation of few turbo iterations and few BCJR states.

New quantum LDPC codes based on Euclidean Geometry

With the advancements in quantum error correction technique, quantum low density parity check (QLDPC) codes have emerged as a promising area in the field of quantum error correction. This paper focuses on the requirement of QLDPC codes based on points excluding the origin, and lines that do not pass through the origin of Euclidean Geometry. It also explores QLDPC codes based on all the points and lines. Finally, a series of simulation analyses are presented.

Hybrid Multi Kernel Polar Code Construction and Optimized Decoding Algorithm for 5G Mobile Communications

5G mobile communications faces difficulty in channel coding to satisfy user requirements. This paper evaluates flexibility, reliability and complexity for different channel coding schemes(Turbo codes, Low Density Parity check codes, mother polar codes, Multi Kernel-polar codes) on regular channel AWGN with BPSK modulation of code rate R=1/2. The proposed hybrid Multi Kernel-polar codes will have greater flexibility and reliability for short and large code words. The optimized decoding of Multi Kernel polar codes reduces the number of computations by using repeated LLR’s of sub-kernel matrices.

Non-binary codes approach on the performance of short-packet full-duplex transmissions

This paper illustrates the enhancement of the performance of short-packet full-duplex (FD) transmission by taking the approach of non-binary low density parity check (NB-LDPC) codes over higher Galois field. For the purpose of reducing the impacts of self-interference (SI), high order of modulation, complexity, and latency decoder, a blind feedback process composed of channels estimation and decoding algorithm is implemented. In particular, this method uses an iterative process to simultaneously suppress SI component of FD transmission, estimate intended channel, and decode messages. The results indicate that the proposed technique provides a better solution than both the NB-LDPC without feedback and the binary LDPC feedback algorithms. Indeed, it can significantly improve the performance of overall system in two important factors, which are bit-error-rate (BER) and <a name="_Hlk155778233"></a>mean square error (MSE), especially in high order of modulation. The suggested algorithm also shows a robustness in reliability and power consumption for both short-packet FD transmissions and high order modulation communications.

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.

저지연 LDPC 복호기의 하드웨어 구현 및 검증

In this investigation, we developed the hardware for a low-latency low-density parity check (LDPC) decoder and validated its error-correction performance. The LDPC code was chosen as the error-correction code conforming to the international portable Internet standard IEEE 802.16e. The LL-LDPC code, implemented in this study, efficiently minimizes the number of coded calculations through the utilization of a type of Structured-LDPC code defined by the physical layer description in IEEE 802.16e. The low-delay LDPC decoder employs a parallel decoding method to mitigate the decoding delay associated with repetitive decoding. Comprising four SISO modules based on four coding repetitions in the coder, the low-delay LDPC decoder significantly reduces delay times. The four SISO modules operate in parallel, enabling simultaneous decoding and thereby decreasing the delay time by 1/4 compared to alternative approaches.

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.

Huffrith Algorithm with Quasi Cyclic Low Density Parity Check in NOMA Systems

Huffrith Algorithm with Quasi Cyclic Low Density Parity Check in NOMA Systems

Window code parameters of spatially-coupled LDPC codes

In this paper, we define a window code to be the portion of a Spatially-coupled low-density parity check (SC-LDPC) code seen by a single iteration of a windowed decoder. We consider the design of SC-LDPC codes for windowed decoding via optimization of the window code. In particular, because iterative decoding is optimal on codes with cycle-free graph representations, we ask fundamental questions about the construction and parameters of cycle-free window codes. We show that it is possible to have an SC-LDPC code with cycles and with cycle-free window codes. We consider the relationship between the distance of the window code and the distance of the SC-LDPC code. Further, we show that SC-LDPC codes with MDS window codes exist, and all such codes are asymptotically bad. This work gives insight into the tradeoffs between window code parameters and performance of the SC-LDPC code.

ANALYSIS OF DEVELOPMENT TRENDS IN MODERN BUSINESS COMMUNICATIONS

Advanced communication techniques are used to organize fixed-user access to corporate communication network (CCNs) resources, with the ability to quickly change the encoding speed during network overloads. Estimating the probability of a denial of service caused by a lack of free channel resources at Access Network was one of the research's aims. IP based network enable the delivery of different services. Primary determinants of users' subjective quality evaluation of communication: data transmission: fast, without errors or failures; video communication: high-quality images, no delays; audio communication: no voice distortion, no call failures. Important to network operators to make effective use of their own resources while maintaining transmission quality standards. Control over metrics such packet loss ratio, delay variations, and latency is crucial. For certain corporate networks, the implementation of 5G mobile communication equipment holds great potential, especially in terms of enabling remote access for staff members. Simultaneously, concerns over unauthorized access to information and the risk of packet loss during transmission have become increasingly pressing. This paper discusses the effectiveness of Low-Density Parity Check (LDPC) codes and polar codes in variable length packet transmission in a 5G system. The modeling results of 5G communication system operation at a fixed value of packet loss are discussed.

Machine learning assisted adaptive LDPC coded system design and analysis

AbstractThis paper proposes a novel machine learning (ML) assisted low‐latency low density parity check (LDPC) coded adaptive modulation (AM) system, where short block‐length LDPC codes are used. Conventional adaptive modulation and coding (AMC) system includes fixed look‐up table method, which is also called inner loop link adaptation (ILLA) and outer loop link adaptation (OLLA). For ILLA, the adaptive capability is achieved by switching the modulation and coding modes based on a look‐up table using signal‐to‐noise ratio (SNR) thresholds at the target bit error rate (BER), while OLLA builds upon the ILLA method by dynamically adjusting the SNR thresholds to further optimize the system performance. Although both improve the system overall throughput by switching between different transmission modes, there is still a gap to optimal performance as the BER is comparatively far away from the target BER. Machine learning (ML) is a promising solution in solving various classification problems. In this work, the supervised learning based k‐nearest neighbours (KNN) algorithm is invoked for choosing the optimum transmission mode based on the training data and the instantaneous SNR. This work focuses on the low‐latency communications scenarios, where short block‐length LDPC codes are utilized. On the other hand, given the short block‐length constraint, we propose to artificially generate the training data to train our ML assisted AMC scheme. The simulation results show that the proposed ML‐LDPC‐AMC scheme can achieve a higher throughput than the ILLA system while maintaining the target BER. Compared with OLLA, the proposed scheme can maintain the target BER while the OLLA fails to maintain the target BER when the block length is short. In addition, when considering the channel estimation errors, the performance of the proposed ML‐LDPC‐AMC maintains the target BER, while the ILLA system's BER performance can be higher than the target BER.

Post-FEC performance evaluation of optical SDM systems with mode-dependent loss

This work is focused on the bit error rate (BER) performance of spatial division multiplexing (SDM) systems over an optical channel with mode-dependent loss or gain (collectively referred to in this paper as MDL). When the latter is non-negligible, the BER has a random nature that introduces the outage probability as an important performance metric for the system design and also impacts on the selection of a forward-error correction (FEC) scheme. In MDL-impaired SDM systems, the pre-FEC BER is a random variable whose probability density function (PDF) and coding gain depend on the signal-to-noise ratio (SNR) at the receiver input. Hence, the common and simple approach of adding a coding gain factor to the pre-FEC BER to obtain the post-FEC BER is not adequate, and numerical simulations are needed. In this paper, we simulate and analyze the performance in terms of post-FEC BER for two proposals of applying low-density parity check (LDPC) FEC encoder/decoder in a SDM system MDL-impaired and an optimal linear multiple input multiple output (MIMO) receiver. In the first one, the LDPC is applied independently to each mode, and in the second one, the LDPC is applied among all SDM modes. Simulation results indicate that the first proposal outperforms the second. Simplifications in the log-likelihood ratio (LLR) computations have also been considered.

An efficient reconfigurable code rate cooperative low-density parity check codes for gigabits wide code encoder/decoder operations

In recent days, extensive digital communication process has been performed. Due to this phenomenon, a proper maintenance of authentication, communication without any overhead such as signal attenuation code rate fluctuations during digital communication process can be minimized and optimized by adopting parallel encoder and decoder operations. To overcome the above-mentioned drawbacks by using proposed reconfigurable code rate cooperative (RCRC) and low-density parity check (LDPC) method. The proposed RCRC-LDPC is capable to operate over gigabits/sec data and it effectively performs linear encoding, dual diagonal form, widens the range of code rate and optimal degree distribution of LDPC mother code. The proposed method optimize the transmission rate and it is capable to operate on 0.98 code rate. It is the highest upper bounded code rate as compared to the existing methods. The proposed method optimizes the transmission rate and is capable to operate on a 0.98 code rate. It is the highest upper bounded code rate as compared to the existing methods. the proposed method's implementation has been carried out using MATLAB and as per the simulation result, the proposed method is capable of reaching a throughput efficiency greater than 8.2 (1.9) gigabits per second with a clock frequency of 160 MHz.

Enhanced symbol capacity and loss budget employing joint channel coded modulation in DMT-WDM-PON

A joint channel coded modulation scheme based on symbol division multiplexing (SDM) is proposed and experimentally demonstrated in a 100-Gb/s discrete multi-tone wavelength division multiplexing passive optical network (DMT-WDM-PON) with enhanced symbol capacity and system power loss budget. The SDM was performed through low-density parity check (LDPC) coded quadrature amplitude modulation (QAM) following the optimized many-to-one mapping rule. By time domain multiplexing all four 6-bit/symbol 64QAM symbols together onto the same complex constellation point, the produced SDM-16QAM can achieve a 50% symbol capacity gain compared to the typical 16QAM with the same symbol rate. For low-latency intention, the fifth-generation new radio standard LDPC code with ultra-short code length and flexible code rate is structured to provide high signal transmission reliability and a robust mechanism within both intra- and inter-SDM symbols, supporting the iterative SDM de-multiplexing. The SDM significantly reduces the QAM orders and widens the constellation Euclidean distance, which can optimize the signal launch fiber power and reduce the resolution requirements for optoelectronic and electronic components, thus leading to apparent enhancement of the power loss budget to serve more optical network units. The experimental results show that a 4.11-dB power loss budget gain can be achieved including 1.25-dB superior receiver power sensitivity and 2.86-dB improvement of launch fiber power in the proposed DMT-WDM-PON over 20-km fiber transmission.

Performance Enhancement of LDPC Codes Based on Protograph Construction in 5G-NR Standard

To meet the high throughput demands, the 3rd Generation Partnership Project has specified the low-density parity check (LDPC) codes in the fifth generation-new radio 5G-NR standard with rate and length compatibility and scalability. This paper presents an extensive performance evaluation and enhancement of LPDC using the protograph-based construction defined in the 5G-NR standard. Firstly, the protograph-LDPC with layered offset min-sum (OMS) decoding, polar with successive cancellation list (SCL), and block turbo code are implemented and compared. Puncturing and shortening are applied to maintain block length at 1024 and code rate at 1/2 for all codes for comparison fairness. The results showed that P-LDPC outperforms its counterparts in terms of bit/ frame error rate (BER/ FER) behavior for given signal-to-noise ratios. Then, different P-LDPC settings were realized to study the effects of base graph selection (Graph1 or Graph2), code rate change (1/3 - 2/3), and block lengths increase (260 – 4160 bits). The simulation outcomes proved that BER performed better for lower coding rates or higher block lengths. Furthermore, P-LDPC behavior was examined over a Rayleigh flat-fading channel to achieve a 12.5 dB coding gain at 0.001 BER compared with uncoded transmission.

Partitioning qubits in hypergraph product codes to implement logical gates

The promise of high-rate low-density parity check (LDPC) codes to substantially reduce the overhead of fault-tolerant quantum computation depends on constructing efficient, fault-tolerant implementations of logical gates on such codes. Transversal gates are the simplest type of fault-tolerant gate, but the potential of transversal gates on LDPC codes has hitherto been largely neglected. We investigate the transversal gates that can be implemented in hypergraph product codes, a class of LDPC codes. Our analysis is aided by the construction of a symplectic canonical basis for the logical operators of hypergraph product codes, a result that may be of independent interest. We show that in these codes transversal gates can implement Hadamard (up to logical SWAP gates) and control-Z on all logical qubits. Moreover, we show that sequences of transversal operations, interleaved with error correction, allow implementation of entangling gates between arbitrary pairs of logical qubits in the same code block. We thereby demonstrate that transversal gates can be used as the basis for universal quantum computing on LDPC codes, when supplemented with state injection.

All-photonic one-way quantum repeaters with measurement-based error correction

Quantum repeater is the key technology enabler for long-distance quantum communication. To date, most of the existing quantum repeater protocols are designed based on specific quantum codes or graph states. In this paper, we propose a general framework for all-photonic one-way quantum repeaters based on the measurement-based error correction, which can be adapted to any Calderbank–Shor–Steane code including the recently discovered quantum low-density parity check (QLDPC) codes. We present a decoding scheme, where the error correction process is carried out at the destination based on the accumulated data from the measurements made across the network. This procedure not only outperforms the conventional protocols with independent repeaters but also simplifies the local quantum operations at repeaters. As an example, we numerically show that the [[48, 6, 8]] generalized bicycle code (as a small but efficient QLDPC code) has an equally good performance while reducing the resources by at least an order of magnitude.

Secure key distribution exploiting error rate criticality for radio frequency links.

We propose a method by which two radio frequency (RF) communication terminals exchange encryption keys or other data securely. This method draws on the approach developed for quantum key distribution (QKD) for detecting eavesdroppers but our method does not use any quantum properties at all. Instead, by exploiting the effects an eavesdropper has on channel stability, we explore a line-of-sight link radio in which data transfer rates are so high as to approach the Shannon limit. With very steep rises in bit error rate accompanying a small degradation of signal-to-noise limits for certain forward error correction codes, it becomes possible to infer the existence of an eavesdropper before they are able to obtain a complete key. We describe our method and analyse one possible implementation using low density parity check codes with quadrature phase shift keying modulation. The proposed technique is in principle far easier to implement than quantum-based approaches for RF and optical wireless links since the required hardware is readily available and the basic principles are well known and well understood. Finally, we show our method to have a higher key rate and spectral efficiency than those of QKD.

High-Precision Short-Term Lifetime Prediction in TLC 3-D NAND Flash Memory as Hot-Data Storage

3D NAND flash memory is the ubiquitous non-volatile memory (NVM) on the market because of its large storage capacities, high reliability, and low bit-cost. The reliability characteristics of 3D NAND flash memory, however, are considerably different from those of 2D NAND flash memory due to the peculiar architectures. In this paper, read disturb (RD) at various program/erase (P/E) stages is thoroughly explored. To adjust the low-density parity check (LDPC) codes dynamically and extend the lifetime of 3D NAND flash memory, short-term lifetime prediction models of RD and endurance are proposed based on in-depth studies on the correlations of fail bit count (FBC) at various lifetime stages, and their accuracy is tested experimentally. A new short-term warning system (STWS) is proposed to extend the lifetime of 3D NAND-based storages. It consists of the error-bits’ prediction module (EBPM) and the self-adjustable low-density parity check codes module (SLDPC), where EBPM predicts FBC periodically and SLDPC pre-allocates LDPC codes for future use based on the result of EBPM. The experimental result shows that our prediction models have high reliability, and STWS can effectively prolong the lifetime of NAND flash. The findings of this study provide fundamental insights into FBC degradation in 3D NAND flash, as well as a simple and practical method for building 3D NAND-based storage with high reliability.