Raptor Codes Research Articles

Raptor Codes with LT-LDPC Precoding Performance Analysis and FPGA Optimization

Raptor codes are designed to effectively handle packet loss and erasures as a type of fountain code, capable of generating an unlimited number of encoded symbols from source informations, which is particularly useful in scenarios where the number of transmissions is unknown or variable. Luby Transform (LT) codes, a kind of fountain code encoding method, exhibit linear complexity, and Low-Density Parity-Check (LDPC) codes can be constructed by the generator matrix and the parity-check matrix. The LT-LDPC pre-coding method combines the advantages of both, enhancing encoding and decoding efficiency. Deploying code on Field-Programmable Gate Arrays (FPGAs) involves several steps: synthesis, place and route, and bitstream generation, followed by loading the bitstream onto the FPGA to configure its internal logic according to the coding methods. This paper introduces a method of encoding and decoding Raptor codes, utilizing the intimal LT codes and the peripheral LDPC codes constructed by PEG. It employs a lop-BP decoding method over noise channels based on the Tanner graph for decoding and deploys the optimized algorithm on FPGA to enhance performance.

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.

Inter-discharge optimization for fast, reliable access to ASDEX Upgrade advanced tokamak scenario

Rapid inter-discharge simulation and optimization using the RAPTOR code have allowed the development of a reliable and reproducible early heating strategy for an advanced tokamak (AT) scenario on ASDEX Upgrade. Solving for electron heat and current diffusion in RAPTOR with ad-hoc formulas for heat transport and electron cyclotron current drive (ECCD) efficiency is found to robustly recover the coupled dynamics of Te and q, while maintaining model parameters fixed for all discharges. The pedestal top boundary condition in pre-shot simulations is set by a newly derived scaling law for the electron pressure at ρ = 0.8, using a data set of previous AT discharges. RAPTOR simulations have allowed to develop an understanding of the onset of 3/2 tearing modes, which were observed to have a detrimental impact on confinement when low magnetic shear conditions are present at the rational surface during the high-β phase. Delaying the NBI heating, by a specific time interval found via simulations, has led to avoiding these modes. A non-linear optimization scheme has been applied to optimize the ECCD deposition radii to reach a stationary state with qmin>1 at the beginning of the flat-top phase, while ensuring a non-zero magnetic shear at q = 1.5 throughout the high-β phase, and has been successfully tested in experiment. However, further experiments, aiming for qmin>1.5 , have highlighted limitations of the present feedforward control approach in the presence of shot-to-shot variations that are not included in the applied model. Application of real-time model-based control is proposed to overcome model-reality mismatches in future work.

Scenario optimization for the tokamak ramp-down phase in RAPTOR: Part A. Analysis and model validation on ASDEX Upgrade

We discuss how the combination of experimental observations and rapid modeling has enabled to improve understanding of the tokamak ramp-down phase in ASDEX Upgrade. A series of dedicated experiments has been performed, to disentangle the effect of individual actuators like plasma current, auxiliary heating and plasma shaping. Optimized discharge termination strategies with increased margin with respect to radiative and vertical stability limits are proposed and tested in experiment. Radiative collapse of the edge Te profile after the HL back-transition is avoided by initially maintaining auxiliary heating during L-mode, showing beneficial effects even after the auxiliary heating is turned off. The capability of the RAPTOR code to model the time evolution of the internal inductance has been validated, including the effect of a change in the Ip ramp-down rate and the HL transition timing. The reduction of caused by rapid compression of the plasma cross-section has been quantitatively recovered in simulations. Successful modeling of the time evolution is essential to optimize ramp-down scenarios for future fusion reactors, for which vertical stability and power balance control will be more challenging.

Analytical Techniques for Performance Evaluation of Fountain-Coded File Distribution in Packet Radio Networks

Convenient analytical techniques are developed for use in preliminary design of systems and protocols for the delivery of fountain-coded files from a source node to a destination node with the assistance of a relay node. Each node has a half-duplex packet radio, and the time-varying disturbance on each link is represented by a lumpable finite-state Markov chain. The analytical techniques include the use of first passage times and recurrence times in the derivation of an exact expression for the completion time of file transfer over a radio link and the application of results on Markov-correlated Bernoulli trials to obtain exact expressions for completion times of relay-aided file transfer in wireless networks. In the development of analytical techniques, we employ capacity-achieving channel codes and ideal fountain codes; however, we present simulation results for packet radios that employ practical channel codes and for which the fountain code is a standard systematic raptor code.

Simultaneous control of safety factor profile and normalized beta for JT-60SA using reinforcement learning

Plasma with an internal transport barrier (ITB) will be developed in JT-60SA as an attractive operation appropriate for a steady-state fusion reactor. To achieve the ITB plasma while avoiding magnetohydrodynamic instabilities, it is advantageous to simultaneously control the safety factor (q) profile and the normalized beta (). In this study, a control system for simultaneous control of the q profile and is studied in simulations prior to the real experiment in JT-60SA. The bootstrap current dominates the total current in the ITB region, which results in a coupling between the pressure profile and the q profile. Thus, it is crucial to control the q profile and according to the strength of the ITB. A two-stage neural network (NN)-based control system was developed to address this problem. The first stage estimates the transport properties (i.e. ITB strength) of the plasma from measurements. The second stage consists of several NNs for control of the q profile and . According to the ITB strength estimated by the NN in the first stage, the appropriate NN for control is selected from those in the second stage. Each NN in the second stage is trained to control plasmas with different ITB strengths through reinforcement learning employing RAPTOR, an integrated transport code. To validate this system, it is tested in a simulation employing another integrated transport code, TOPICS, to mimic the plasma control in JT-60SA plasmas with various ITB strengths. Stable control of the q profile and is achieved in ITB plasmas simulated by both the RAPTOR and TOPICS codes.

Performance Improvement of CDMA Wireless Sensor Networks in Low SNR Channels Based on Raptor Codes

Low signal to noise ratio (SNR) channels require careful design of communication systems in order to operate reliably in such extreme channels. Special measures and techniques must be considered when designing communication systems for such environments to counteract the effect of high noise power. Channel coding is a powerful tool to aid against adverse channel conditions including low SNR. Coupling channel coding with a spreading technique can further strengthen the performance of communication systems. Hence, we studied the performance of a system that combines Raptor codes with direct sequence code division multiple access (DS-CDMA) in low SNR scenarios. The studied design can operate in a wide range of low SNR values. Simulation results show that the system can offer satisfactory BER performance at different code rates. Also, combining Raptor codes with DS-CDMA showed an improvement of approximately 6 dB when compared with other schemes using DS-CDMA in low SNR conditions.

RESS: A Reliable and Effcient Storage Scheme for Bitcoin Blockchain Based on Raptor Code

RESS: A Reliable and Effcient Storage Scheme for Bitcoin Blockchain Based on Raptor Code

Raptor-IRSA Grant-free Random Access protocol for smart grids applications

This paper deals with the reliability of random access (RA) protocols for massive wireless smart grid communication (m-SGC). We propose and analyze an improved grant-free RA (GF-RA) protocol for critical SG applications under strict QoS m-SGC requirements. At first, we discuss the main features of the SG neighborhood area network (NAN) architecture. We explore the main features of low-rate machine-type wireless networks, and also we describe a technology characterization of wireless neighborhood area networks (WNAN) in medium-range coverage applications. We propose a new-improved irregular repetition slotted ALOHA, combining Raptor codes and irregular ALOHA, namely RapIRSA random access protocol, to better respond to critical high-reliability QoS requirements under a 5G network perspective. Then, we compare and comprehensively analyze the proposed RapIRSA protocol with two existing RA protocols, the IRSA protocol, and the classical Slotted Aloha. Finally, We summarize the potential challenges in implementing the proposed RA protocol for SG critical applications considering a massive number of smart sensors (SS).

Delay optimal for reliability-guaranteed concurrent transmissions with raptor code in multi-access 6G edge network

This paper proposes RCMEN, a solution for Concurrent Multipath Transfer (CMT) of Raptor-Coded (RC) Protocol Data Units (PDU) in a Multi-Access 6G Edge Network (MEN) to provide low-latency and reliable transmission for 6G User Equipment (UE) and Data Network (DN). While 3GPP Release 16 aims to improve the reliability of a single service based on CMT, replication-based reliability causes high resource and signaling overhead, and asymmetric bandwidth and latency lead to excessive latency. RCMEN addresses these issues by distributing data across multiple PDU sessions and using a queue-aware variable-block-length Raptor encoder to optimize resource utilization under random arrivals. We analyze RCMEN’s delay-reliability performance using the Constrained Markov Decision Process (CMDP), reliability is guaranteed by the reliability function, which takes the amount of data sent as a parameter. Through Linear Programming, we obtain the optimal delay-reliability trade-off and optimize delay metrics for two classical RCMEN. Experiments show that both classical RCMEN optimize the long-tail distribution of latency while ensuring reliability, with the entire system being compatible with the current 5G network infrastructure.

DNA Computing-Based Multi-Source Data Storage Model in Digital Twins

The work aims to study the application of Deoxyribonucleic Acid (DNA) multi-source data storage in Digital Twins (DT) . Through the investigation of the research status of DT and DNA computing, the work puts forward the concept of DNA multi-source data storage for DT. Raptor code is improved from the design direction of degree distribution function, and six degree function distribution schemes are proposed in turn in the process of describing the research method. Additionally, a quaternary dynamic Huffman coding method is applied in DNA data storage, combined with the improved concatenated code as the error correction code. Considering the content of cytosine deoxynucleotide (C) and guanine deoxynucleotide Guanine (G) and the distribution of homopolymer in DNA storage, the work proposes and verifies an improved concatenated code algorithm Deoxyribonucleic Acid-Improved Concatenated code (DNA-ICC) . The results show that while the Signal-to-Noise Ratio (SNR) increases, the Bit Error Rate (BER) decreases gradually and the trend is similar. But the anti-interference ability of the degree distribution function optimized by the probability transfer method is better. The BER of DNA-ICC scheme decreases with the decrease of error probability, which is stronger than other error correction codes. Compared with the original concatenated code, it saves at least 1.65 s, and has a good control effect on homopolymer. When the size of homopolymer exceeds 4 nt, the probability of homopolymer is only 0.44%. The proposed Quaternary dynamic Huffman code and concatenated error correction code have excellent performance.

Performance enhancing of MIMO‐OFDM system utilizing different interleaving techniques with rate‐less fountain raptor code

Due to the importance of both rate-less digital fountain codes and Multi-Input Multi-Output (MIMO) schemes in Fifth and Sixth Generation (5G/6G) wireless networks, this paper investigates enhancing the performance of MIMO-Orthogonal Frequency Division Multiplexing (MIMO-OFDM) based system by employing the rate-less fountain codes. The rate-less codes, such as the Tornado codes and Raptor codes, have a flexible code rate that differs from the classical channel coding schemes. This paper uses Raptor code to study the MIMO system's performance with the rate-less codes over different wireless communications channels. The proposed MIMO-fountain code-based system has been tested over the various wireless communication channel conditions concerning the varied Frequency Doppler (FD). In the proposed rate-less wireless communication system, multiple interleaving techniques and equalizers are used to improve its performance. Computer-based simulation experiments are assigned to evaluate the MIMO-fountain code system using the different data transmission scenarios. Simulation results confirm the superiority of the presented wireless rate-less system compared to fixed-rate wireless systems in terms of Bit Error Rate (BER) and throughput.

Enhancement of code division multiple access system performance using raptor codes

Some kinds of communication systems work in very low signal-to-noise (LSNR) environments. For these systems to function reliably, <span>specific techniques and methodologies have to be used to mitigate the degrading effects of the channel. The channel coding method is the key element in most LSNR communication systems, but emphasizing the code division multiple access (CDMA) is a new transmission technique in these channels. To enhance the CDMA scheme's system capacity and reach unprecedented ranges of LSNR values in wireless sensor network. This paper suggests combining CDMA with certain types of channel coding algorithms, such as the raptor codes. The raptor channel encoding technique has improved the CDMA system's performance when using binary phase-shift keying (BPSK) modulation in additive white gaussian noise (AWGN) channels. It has achieved a low bit error rate in range of 10-7 at Eb/No value of (-3) dB and about 10-6 at shannon's limit. The Raptor-coded CDMA scheme works well for channel signal to noise ration (SNR) values of greater than -9 dB, showing an improvement of about 7 dB compared with turbo/convolutional channel coding methods used with the CDMA system bit error rate (BER) and throughput. On the other hand, it has been shown that the convolutional encoder presents the weakest performance compared to both the turbo and raptor codes.</span>

Anti error and erasure coding for water-to-air visible light communication through wavy water surface with wave height up to 0.6 meters.

Considering large dynamic optical intensity range in a water-to-air (W2A) channel, we propose two promising channel coding schemes, namely the concatenated Reed Solomon-Low Density Parity Check (RS-LDPC) code and Raptor code, for W2A visible light communication (VLC). We establish a W2A-VLC link to verify the performance under different wavy water environments and different water depths with a green light emitting diode (LED). A wave generator is adopted to emulate the wavy water surface with wave height up to 0.6 m. The receiver is fixed 3.2 m above the water, and the transmitter varies from 2.5 m to 4.0 m under the water through a up-down-moveable platform. We test the coding schemes with different code lengths and code rates under 5 MSym/s air-interface symbol rate. Experimental results show that both schemes can reduce the bit error ratio (BER) and frame error rate (FER) of a W2A-VLC system, and thus can improve the reliability. Via comparing the two codes with the same overhead and approximately the same code length, it is demonstrated that Raptor code can generally outperform the concatenated RS-LDPC code. Our research provides promising channel coding methods without feedback for a W2A-VLC system.

Self-Adaptive Ordered Statistics Decoder for Finite Block Length Raptor Codes Toward URLLC

Rateless codes can adapt to the wireless channel conditions without accurate channel state information (CSI) at the transmitter side, avoiding CSI feedback and retransmission, and thus are a promising channel coding approach to meet the stringent requirements of ultrareliable low-latency communications (uRLLCs). This article investigates a self-adaptive ordered statistics decoder (S-OSD) scheme for finite block length nonbinary Raptor code (NBRC). Aiming at minimizing the decoding complexity, some strategies for our S-OSD scheme are designed, including the segmentation rules of most reliable basis, the generating and discarding rules of test error patterns, and the stop criteria, respectively. In addition, an upper bound of block error rates (BLERs) for the NBRC under OSD is derived, which can be used to estimate the number of NBRC symbols required to successfully decode the input information via the S-OSD. Simulation results show that the complexity of our S-OSD scheme is greatly reduced comparing to the existing OSD schemes, while achieving very low BLER in the short block length regime.

Healing plasma current ramp-up by nitrogen seeding in the full tungsten environment of WEST

Achieving a successful plasma current ramp-up in a full tungsten tokamak can be challenging due to the large core radiation (and resulting low core temperature) that can be faced with this heavy metallic impurity if its relative concentration is too high. Nitrogen injection during the plasma current ramp-up of WEST discharges greatly improves the core temperature and magnetohydrodynamic (MHD) stability. Experimental measurements and integrated simulations with the RAPTOR code, complemented with the QuaLiKiz neural network for computing turbulent transport, allow a detailed understanding of the mechanisms at play. Increased edge radiation during this transient phase is shown to improve confinement properties, driving higher core temperature and better MHD stability. This also leads to increased operation margins with respect to tungsten contamination.

Factored LT and Factored Raptor Codes for Large-Scale Distributed Matrix Multiplication

We propose two coding schemes for distributed matrix multiplication in the presence of stragglers. These coding schemes are adaptations of Luby Transform (LT) codes and Raptor codes to distributed matrix multiplication and are termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Factored LT (FLT) codes</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Factored Raptor (FRT) codes</i> . We show that all nodes in the Tanner graph of a randomly sampled code have a tree-like neighborhood with high probability. This ensures that the density evolution analysis gives a reasonable estimate of the average recovery threshold of FLT codes. The recovery threshold of the proposed FLT codes is asymptotically optimal when the output degree distribution is Soliton. Empirically, we show that FRT codes have an excellent recovery threshold while the number of worker nodes is moderately large. In addition, using Azuma–Hoeffding inequality, we derive concentration results to show that the recovery threshold of a randomly chosen FLT code is close to the ensemble average. FLT and FRT codes have better recovery thresholds when compared to Product codes and they are expected to have better numerical stability when compared to Polynomial codes, while they can also be decoded with a low-complexity decoding algorithm. Finally, the proposed codes are better matched to the practically important case of sparse matrix-matrix multiplication as compared to many previous schemes.

NOREC4DNA: using near-optimal rateless erasure codes for DNA storage

BackgroundDNA is a promising storage medium for high-density long-term digital data storage. Since DNA synthesis and sequencing are still relatively expensive tasks, the coding methods used to store digital data in DNA should correct errors and avoid unstable or error-prone DNA sequences. Near-optimal rateless erasure codes, also called fountain codes, are particularly interesting codes to realize high-capacity and low-error DNA storage systems, as shown by Erlich and Zielinski in their approach based on the Luby transform (LT) code. Since LT is the most basic fountain code, there is a large untapped potential for improvement in using near-optimal erasure codes for DNA storage.ResultsWe present NOREC4DNA, a software framework to use, test, compare, and improve near-optimal rateless erasure codes (NORECs) for DNA storage systems. These codes can effectively be used to store digital information in DNA and cope with the restrictions of the DNA medium. Additionally, they can adapt to possible variable lengths of DNA strands and have nearly zero overhead. We describe the design and implementation of NOREC4DNA. Furthermore, we present experimental results demonstrating that NOREC4DNA can flexibly be used to evaluate the use of NORECs in DNA storage systems. In particular, we show that NORECs that apparently have not yet been used for DNA storage, such as Raptor and Online codes, can achieve significant improvements over LT codes that were used in previous work. NOREC4DNA is available on https://github.com/umr-ds/NOREC4DNA.ConclusionNOREC4DNA is a flexible and extensible software framework for using, evaluating, and comparing NORECs for DNA storage systems.

Reliable Random Access for Decentralized UAV Networks Based on Raptor Codes

In this paper, we propose the Raptor coded random access (RCRA) scheme to enable reliable transmission in the decentralized unmanned aerial vehicle (UAV) network. The considered network is composed of several overlapped random access systems with interference nodes, and the proposed RCRA scheme reduces bit-error ratio (BER) of the random access systems by three steps. First, we choose the number of slots based on a derived lower bound, which is necessary for reliable random access. Second, error-correcting codes are incorporated as the precode before random access, and then the access probability is optimized to achieve the minimum BER. Third, by correlating two consecutive slots, an idle-slot-filling approach is designed to further improve the efficiency of the random access systems. Numerical results show the proposed RCRA scheme reduces significantly both block-error ratio (BLER) and BER at moderate-and high-signal-to-noise ratio (SNR) region. With Es/N0 equal to 0 dB, the RCRA scheme saves 20% slots, compared with the existing frameless ALOHA scheme, to achieve a target BER of 10-4.

Rate compatible reconciliation for continuous-variable quantum key distribution using Raptor-like LDPC codes

In the practical continuous-variable quantum key distribution (CV-QKD) system, the postprocessing process, particularly the error correction part, significantly impacts the system performance. Multi-edge type low-density parity-check (MET-LDPC) codes are suitable for CV-QKD systems because of their Shannon-limit-approaching performance at a low signal-to-noise ratio (SNR). However, the process of designing a low-rate MET-LDPC code with good performance is extremely complicated. Thus, we introduce Raptor-like LDPC (RL-LDPC) codes into the CV-QKD system, exhibiting both the rate compatible property of the Raptor code and capacity-approaching performance of MET-LDPC codes. Moreover, this technique can significantly reduce the cost of constructing a new matrix. We design the RL-LDPC matrix with a code rate of 0.02 and easily and effectively adjust this rate from 0.016 to 0.034. Simulation results show that we can achieve more than 98% reconciliation efficiency in a range of code rate variation using only one RL-LDPC code that can support high-speed decoding with an SNR less than -16.45 dB. This code allows the system to maintain a high key extraction rate under various SNRs, paving the way for practical applications of CV-QKD systems with different transmission distances.