LDPC Research Articles

Improved OFDM System with Electromagnetic Wave Disturbances using LDPC Coding

Improved OFDM System with Electromagnetic Wave Disturbances using LDPC Coding

Low-complexity adaptive reconciliation protocol for continuous-variable quantum key distribution

In continuous-variable quantum key distribution systems, reconciliation is a crucial step that significantly affects the secret key rate (SKR). The rateless protocol based on Raptor codes can achieve high reconciliation efficiency at low signal-to-noise ratios (SNRs). However, the high complexity of low-density parity-check (LDPC) codes used for the precoding in Raptor codes limits the speed of reconciliation. In this paper, we propose an adaptive reconciliation protocol by modifying Raptor codes. The length of random binary sequences is increased because we remove the LDPC precoding that adds redundancy. The modified Raptor codes reduce the complexity of encoding with better performance. The proposed protocol gives a reconciliation efficiency higher than 98.1% in the SNR below −20 dB and maintains a certain SKR in long-distance transmission.

A study on acceleration of SP decoder using reliability of recording sequence by neural network based on parity check result in SMR system

We study signal processing methods to realize ultra-high-density hard disk drives (HDDs). Among them, we have applied the neural network to improve decoding performance in low-density parity-check (LDPC) coding and iterative decoding in the shingled magnetic recording (SMR) system. In this study, we realize acceleration of the sum-product (SP) decoding by updating the decoding reliability of the SP decoding using the reliability of the recording sequence calculated by the neural network based on the parity check results. As a result, the proposed system achieved error-free with the fewest number of iterations in the SP decoder compared to our previous studies.

Optimized Non-Surjective FAIDs for 5G LDPC Codes With Learnable Quantization

Optimized Non-Surjective FAIDs for 5G LDPC Codes With Learnable Quantization

Derived dynamic scheduling for belief propagation decoding of LDPC codes

AbstractAmong numerous dynamic scheduling strategies for low‐density parity‐check codes, many of them are of high complexity due to repetitive computation and ordering of belief residuals. To address these challenges, two novel approaches are proposed: the derived informed variable‐to‐check residual belief propagation and the derived variable‐node and variable‐to‐check‐edge residual belief propagation for low‐density parity‐check codes. Simulation results show that the derived dynamic scheduling exhibits a substantial gain of approximately 0.15 dB in signal‐to‐noise ratio over the non‐derived one with considerably lower decoding complexity when targeting a bit‐error rate of 10−4.

Jointly optimized quasi-cyclic LDPC codes for coded-cooperative wireless networks based on split labeling diversity

Jointly optimized quasi-cyclic LDPC codes for coded-cooperative wireless networks based on split labeling diversity

The Comparison of RS Codes, LDPC Codes, And Turbo Codes

Error correction codes have been widely used in various fields in recent years, including the communication field, storage field, digital media field, computer network field, and so on. In this paper, the development history of error correction codes is briefly summarized; and the principles and performance of three kinds of error correction control codes are systematically summarized starting from RS codes, LDPC codes, and Turbo codes. Three types of error correction codes are compared and analyzed in the field of wireless optical communication, and the error correction characteristics of different codes in three different weather conditions are compared and summarized for the applicable environments. The error correction codes are also compared in the field of aviation flight telemetry, and which codes are suitable for uplink and downlink telemetry in flight telemetry are summarized. At the same time, the paper provides an outlook on the future development trend of error correction codes.

Comparative Study of Erasure Code in Distributed Systems and Blockchain

As the data generated by various applications continues to grow exponentially, the need for efficient methods of storage and transmission increases. Erasure codes offer a promising solution by providing redundant information without completely recreating the data. Although erasure codes have been extensively studied, their integration and effectiveness in distributed systems and blockchain networks are still being explored. This paper explores and compares the foundations and applications of erasure codes in distributed systems and blockchain networks, and provides a comprehensive literature review of erasure code implementations and their impact on data storage and transmission. This study explores the foundations of erasure codes in distributed systems, including array and RS codes, and LDPC codes. The study also explores the use of erasure codes in distributed systems and blockchain and analyzes how these codes can improve the efficiency and scalability of decentralized storage solutions. The study examines the strengths and weaknesses of different erasure codes based on analysis and comparisons. The findings highlight the potential of erasure codes to revolutionize data storage and transmission in distributed systems and blockchain networks.

Entanglement Purification with Quantum LDPC Codes and Iterative Decoding

Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is likely a challenging one. Given the practical difficulty in building a monolithic architecture for quantum systems, such as computers, based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected medium-sized quantum processors. In such a setting, all syndrome measurements and logical operations must be performed through the use of high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond the application of DQC since entanglement distribution and purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder with a sequential schedule for distilling 3-qubit GHZ states using a rate 0.118 family of lifted product QLDPC codes and obtain an input fidelity threshold of ≈0.7974 under i.i.d. single-qubit depolarizing noise. This represents the best threshold for a yield of 0.118 for any GHZ purification protocol. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of 3-qubit GHZ states to construct a scalable GHZ purification protocol.

Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation

Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits for each logical qubit. A more recent protocol using quantum analogues of low-density parity-check codes needs only a constant space overhead that does not grow with the number of logical qubits. However, the overhead in the processing time required to implement this protocol grows polynomially with the number of computational steps. To address these problems, here we introduce an alternative approach to constant-space-overhead fault-tolerant quantum computing using a concatenation of multiple small-size quantum codes rather than a single large-size quantum low-density parity-check code. We develop techniques for concatenating different quantum Hamming codes with growing size. As a result, we construct a low-overhead protocol to achieve constant space overhead and only quasi-polylogarithmic time overhead simultaneously. Our protocol is fault tolerant even if a decoder has a non-constant runtime, unlike the existing constant-space-overhead protocol. This code concatenation approach will make possible a large class of quantum speedups with feasibly bounded space overhead yet negligibly short time overhead.

Research on Low-Density Parity-Check Decoding Algorithm for Reliable Transmission in Satellite Communications

Satellite communications face difficulties such as intensified environmental attenuation, dynamic time-varying links, and diverse business scenarios, which usually require channel coding schemes with high coding gain and high throughput. Low-density parity-check (LDPC) codes are dominant in satellite communication coding schemes due to their excellent performance in approaching the Shannon limit and the characteristics of parallel computing. The traditional weighted-Algorithm B decoding algorithm ignores the channel received information and involves frequent multiplication operations and iteration, which introduces the channel received information for hard-decision and constellation mapping processing. Meanwhile, we design the correlated reliability between the extrinsic information and the mapping processing information to improve the correctness of decoding. The multiplication operation in the iterative process can be replaced by the simple sum of the Hamming distance coefficient, the correlated reliability between the extrinsic information and the mapping processing information, and the extrinsic information frequency, thereby reducing the complexity and storage load of the system. The simulation results show that the presented MRAI-LDPC algorithm can obtain about 0.4 dB performance gain, and the average number of iterations is reduced by 68% under a low SNR. The algorithm can achieve better error-correcting performance and higher throughput, providing strong support for reliable transmission of satellite communications.

An Integrated Orthogonal Frequency-Division Multiplexing Chirp Waveform Processing Method for Joint Radar and Communication Based on Low-Density Parity-Check Coding and Channel Estimation

With the advancement of information technology construction, the integration of radar and communication represents a crucial technological evolution. Driven by the research boom of integrated sensing and communications (ISACs), some scholars have proposed utilizing orthogonal frequency-division multiplexing (OFDM) to separately modulate radar and communication signals. However, the OFDM symbols in this paper incorporate a cyclic prefix (CP) and a virtual carrier (VC) instead of zero padding (ZP). This approach mitigates out-of-band power caused by ZP, in addition to reducing adjacent channel interference (ACI). In addition, we introduce low-density parity-check (LDPC) and use an improved normalized min-sum algorithm (NMSA) in decoding. The enhanced decoding efficiency and minimized system errors render the proposed waveform more suitable for complex environments. In terms of signal processing methods, this paper continues to use radar signals as a priori information to participate in channel estimation. Further, we consider the symbol timing offset (STO) and carrier frequency offset (CFO) issues. In order to obtain more reliable data, we use the minimum mean-square error (MMSE) estimation based on the discrete Fourier transform (DFT) to evaluate the channel. Simulation experiments verify that the system we propose not only realizes the transmission and detection functions but also improves the performance index of the integrated signal, such as the bit error rate (BER) of 7 × 10−5, the peak side lobe ratio (PSLR) of −13.81 dB, and the integrated side lobe ratio (ISLR) of −8.98 dB at a signal-to-noise ratio (SNR) of 10 dB.

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.

Bilayer LDPC Codes Combined with Perturbed Decoding for MLC NAND Flash Memory.

This paper presents a coding scheme based on bilayer low-density parity-check (LDPC) codes for multi-level cell (MLC) NAND flash memory. The main feature of the proposed scheme is that it exploits the asymmetric properties of an MLC flash channel and stores the extra parity-check bits in the lower page, which are activated only after the decoding failure of the upper page. To further improve the performance of the error correction, a perturbation process based on the genetic algorithm (GA) is incorporated into the decoding process of the proposed coding scheme, which can convert uncorrectable read sequences into error-correctable regions of the corresponding decoding space by introducing GA-trained noises. The perturbation decoding process is particularly efficient at low program-and-erase (P/E) cycle regions. The simulation results suggest that the proposed bilayer LDPC coding scheme can extend the lifetime of MLC NAND flash memory up to 10,000 P/E cycles. The proposed scheme can achieve a better balance between performance and complexity than traditional single LDPC coding schemes. All of these findings indicate that the proposed coding scheme is suitable for practical purposes in MLC NAND flash memory.

Efficient Integration of Rate-Adaptive Reconciliation with Syndrome-Based Error Estimation and Subblock Confirmation for Quantum Key Distribution.

An effective post-processing algorithm is essential for achieving high rates of secret key generation in quantum key distribution. This work introduces an approach to quantum key distribution post-processing by integrating the three main steps into a unified procedure: syndrome-based error estimation, rate-adaptive reconciliation, and subblock confirmation. The proposed scheme employs low-density parity-check codes to estimate the quantum bit error rate using the syndrome information, and to optimize the channel coding rates based on the Slepian-Wolf coding scheme for the rate-adaptive method. Additionally, this scheme incorporates polynomial-based hash verification in the subblock confirmation process. The numerical results show that the syndrome-based estimation significantly enhances the accuracy and consistency of the estimated quantum bit error rate, enabling effective code rate optimization for rate-adaptive reconciliation. The unified approach, which integrates rate-adaptive reconciliation with syndrome-based estimation and subblock confirmation, exhibits superior efficiency, minimizes practical information leakage, reduces communication rounds, and guarantees convergence to the identical key. Furthermore, the simulations indicate that the secret key throughput of this approach achieves the theoretical limit in the context of a BB84 quantum key distribution system.

Verifiable Quantum Secret Sharing Scheme Based on LDPC Codes

Verifiable Quantum Secret Sharing Scheme Based on LDPC Codes

A cyclic‐shift based method for counting cycles of quasi‐cyclic LDPC codes

AbstractM. Fossorier proposed how to determine the necessary and sufficient conditions for the existence of cycles in the Tanner graph of quasi‐cyclic LDPC (QC‐LDPC) codes, which has been widely investigated in the study of LDPC codes. This paper presents some new necessary and sufficient conditions for the existence of cycles with arbitrary lengths and proposes a simple and novel method for counting cycles of QC‐LDPC codes based on the improved conditions. Numerical results show that, compared with the existing methods, the presented method is effective and feasible and can enumerate cycles of QC‐LDPC codes in a cyclic‐shift way.

Parity-check codes from disjunct matrices

Parity-check codes from disjunct matrices

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.

Joint Learning and Channel Coding for Error-Tolerant IoT Systems Based on Machine Learning

In several machine learning (ML)-based Internet of Things (IoT) systems, data is captured by IoT devices and then transmitted over a wireless channel for remote processing. Since noise often appears on the channel (so causing data corruption and consequently an incorrect ML result), channel protection must be provided to guarantee an acceptable error rate for the transmitted data, especially in safety-critical applications. An often-used protection technique employs error correction codes (ECCs); however, even with some improved designs, the power dissipation required by an ECC implementation may still not meet the strict requirements of hardware-constrained platforms. To address this issue, a “joint learning and channel coding” (JLCC) scheme is proposed in this paper. In such a scheme, the ML model is retrained using two methods to tolerate some channel errors, such that the system requires an ECC with significantly lower protection capability. Since ML training is executed remotely, JLCC achieves a significant power reduction for ECC without introducing any additional overhead to the IoT device. An electrocardiogram (ECG) system is taken as a case study to illustrate the proposed JLCC scheme and evaluate its effectiveness. A low-density parity-check (LDPC) code is employed for protection of the system with/without JLCC; its analysis and implementation are presented. Simulation results show that, when employing JLCC with the proposed two retraining methods, an average reduction of 29.15% and 34.82% in the dissipated power is achieved for the ECG sensor when compared to the original system.