Cascade Code Research Articles

Method for changing the redundancy of sequential concatenated code

During the operation of information transmission systems errors occur in the transmitted data due to the influence of various negative factors. To correct errors the codes are currently used that can withstand both single and multiple errors. From the point of view of the ability to correct multiple errors, concatenated codes are highly efficient. When constructing a sequential concatenated code, coding is carried out first by the external, then by the internal code. A significant disadvantage of such coding is a significant increase in redundancy. It is proposed to regulate redundancy by encoding with the internal code only a certain part of the bits from the output of the external code encoder. The study showed the effectiveness of this method, which made it possible to change the parameters of the cascade code within a wide range. A method was proposed and tested to increase the corrective ability of selective coding by multiplying symbols decoded by an external code by coefficients that are different for symbols that have and have not been encoded by an internal code. Decoding of the external code was carried out according to the Viterbi algorithm. The performance of the proposed method has been confirmed experimentally.

Antiproton at rest and in-flight within Intra-Nuclear Cascade Liege model (INCL)

Antiproton-nucleus reaction is a versatile tool. It can be used to study fundamental behavior of antimatter (e.g., at CERN AD facility), neutron halo and skin of atomic nuclei (e.g., PUMA project), hyperon-antihyperon interaction (project at GSI FAIR), to name but a few. Since final state interactions are also important in such reactions and that the intranuclear cascade code INCL is known to do it well, it is naturally that its developers have been asked to add this new projectile to the list. Therefore, recent results of the new INCL version with antiproton as projectile are presented with comparisons to experimental data in wide energy range. The new version will be made available also in GEANT4, allowing to simulate future complex experiments involving p.

Improved forward error correction technology of RS-LDPC cascade code in optical transport network

Improved forward error correction technology of RS-LDPC cascade code in optical transport network

Method of adaptation of cascade codes to ensure reliability of information transmission of wireless data transmission systems

The article proposes a method of structural adaptation of cascade codes, designed to ensure the specified reliability of information transmission of wireless data transmission systems in the event of interference, due to the dynamic synthesis of combined structures of cascade codes under conditions of a priori uncertainty. The essence of the method is to identify the internal structure of the code, due to which the structure of the component codes of the turbo code is determined. It was developed using the gradient method due to the implementation of a multi-step iterative procedure for finding optimal system parameters. Implementation of the method allows to ensure the reliability of information transmission of wireless data transmission systems. To check the effectiveness of the method of structural adaptation of cascade codes, a simulation model was developed in the C++ programming language in the Visual Studio 2019 software environment, and wireless data transmission systems were simulated. The simulation results show that the combined structure of building cascade codes together with OFDM technology allows you to independently adapt the coding rate of each of the coding stages depending on the results of the analysis of the reliability of information in this cascade, which leads to the provision of the specified reliability of information transmission, while the BSPD bandwidth is reduced by 4–12% against 20–35% of known results. The use of Reed-Solomon codes in a sequential cascade scheme with turbo codes due to the adaptation of the coding rate of this cascade design allows obtaining an energy gain of 0.5–0.7 dB without increasing the bandwidth of the transmission system compared to systems that use only turbo codes. The obtained results are of significant relevance and can be implemented in the development of information transmission systems to ensure the reliability of data transmission, both in peacetime and in conditions of armed aggression of the Russian Federation against Ukraine.

SIMULATION AND ANALYSIS OF ENCODERS OF INTERFERENCE-RESISTANT CASCADE CODES FOR DYNAMIC SYSTEMS

For various channels of information transmission that can be used in local control systems of a wide range of processes, affordable, scalable, and inexpensive transmission methods are needed that allow the necessary information to be transmitted reliably without errors. Errors that occur in discrete, continuous communication channels are the main obstacle to the reliability of transmitted data. The main causes of errors are signal attenuation, noise and various interferences. As a result of the analysis of error statistics in discrete data transmission channels, it was concluded that single and double errors occur in the absolute majority of cases. It is proposed to combat errors by using tamper-resistant coding. Among the interference-resistant codes, redundant block-separated systematic codes are highlighted, among which is the Hamming code. The basis of the interference-resistant coding model is proposed to be the use of a systematic Hamming code followed by cascade coding by adding a parity check bit. The used model made it possible to deal with all the most likely cases of errors. Since this coding model must be flexibly used in different systems, a necessary criterion of the model is its universality. Therefore, the model was tested on a sample with code combinations of different numbers of bits. The purpose of this article is to analyze the dependence of the coding procedure execution time for encoders of different levels: a separate first-stage encoder, as well as a first-stage encoder with the addition of a second-stage encoder. Experiments were conducted with a large sample, which were subsequently analyzed and interpreted. Since the model proved to be flexible, simple, stable and effective as a result of experiments, and the process of combating interference by using cascade codes has proven itself well in world practice, it is recommended for use in various information management systems. The implementation of the coder for interference-resistant data transmission is given.

DEVELOPMENT OF A MODEL OF INTERFERENCE-RESISTANT DATA TRANSMISSION FOR INFORMATION TECHNOLOGY OF CONTROL OPTIMIZATION OF DYNAMIC SYSTEMS

For data transmission channels used in local control systems for various processes, simple and inexpensive methods are needed that will allow the necessary information to be transmitted without errors. Errors that occur in continuous communication channels are one of the main obstacles to the reliable transmission of information. As a result of the analysis of error statistics in discrete channels, it was concluded that single and double errors occur most often. The purpose of this article is to develop a model of interference-resistant data transmission for information technology optimization of control of dynamic systems. The analyzed causes of errors are signal attenuation, noise and various interferences. The resulting transmitted signal is determined by the combination of the useful signal and the interference signal. When considering discrete signals, several causes of errors are highlighted – edge distortions, pulse splitting, and others. Considered methods of combating obstacles: means of operational and preventive nature; means of increasing interference resistance during the transmission of single elements; use of feedback; adding redundancy to the code; tamper-proof coding. It is proposed to combat errors using tamper-resistant coding. Among the interference-resistant codes, redundant block separable systematic codes are selected, which are divided into cyclic codes and Hamming code. The basis of the interference-resistant coding model is the use of a systematic code - a cyclic code or a Hamming code followed by cascade coding. Since the coding model must be adaptively used in different systems, a necessary criterion of the model is its universality. The model should work in different systems without changing the encoding and decoding algorithms. Among the many types of interference-resistant codes, cascade codes are chosen for use. Widespread cascade codes are universal, easily scalable, work stably, have proven themselves well in world practice, therefore they are recommended for use in various information management systems. The implementation of the interference-resistant data transmission model is presented.

Optimization of the Cascade Code Parameters by the Criterion of the Boundary Value of the Interference Band and the Selection of the Decoding Algorithm

A coherent data transmission channel with pseudo-random tuning of the operating frequency (FH) is considered, a concatenated code based on an ensemble of orthogonal signals and a Reed-Solomon code, with various reception-decoding algorithms under conditions of simultaneous action on the channel of two interference – a barrage and a FH concentrated in a part of the band. The estimates of the boundary value of the part of the FH band covered by the interference, the characteristics of the optimal concatenated code, are obtained, and also the receive-decoding algorithm is selected, in which the boundary value of the part of the band covered by the interference takes the maximum value in a given interference environment

Multilinear Algebra for Distributed Storage

An $(n, k, d, \alpha, \beta, M)$-ERRC (exact-repair regenerating code) is a collection of $n$ nodes used to store a file. For a file of total size $M$, each node stores $\alpha$ symbols, any $k$ nodes recover the file, and any $d$ nodes repair any other node via sending out $\beta$ symbols. We establish a multilinear algebra foundation to assemble $(n, k, d, \alpha, \beta, M)$-ERRCs for all meaningful $(n, k, d)$ tuples. Our ERRCs tie the $\alpha/M$-versus-$\beta/M$ trade-off with cascade codes, the best known construction for this trade-off. We give directions on how these ERRCs repair multiple failures.

Cascade Codes for Distributed Storage Systems

A novel coding scheme for exact repair-regenerating codes is presented in this paper. The codes proposed in this work can trade between the repair bandwidth of nodes (number of downloaded symbols from each surviving node in a repair process) and the required storage overhead of the system. These codes work for general system parameters $(n,k,d)$, which are the total number of nodes, the number of nodes suffice for data recovery, and the number of helper nodes in a repair process, respectively. The proposed construction offers a unified scheme to develop exact-repair regenerating codes for the entire trade-off, including the MBR and MSR points. We conjecture that the new storage-vs.-bandwidth trade-off achieved by the proposed codes is optimum. Some other key features of this code include: the construction is linear; the required field size is only $\Theta(n)$; and the code parameters and in particular sub-packetization level is at most $(d-k+1)^k$; which is independent of the number of the parity nodes. Moreover, the proposed repair mechanism is \emph{helper-independent}, that is the data sent from each helper only depends on the identity of the helper and failed nodes, but independent of the identity of other helper nodes participating in the repair process.

Research of LT Code Based on Key Information Feedback in Deep Space Communication

CCSDS LDPC code cannot effectively solve the problems of communication interruptions and high communication error rates in deep space communication. An application scheme of digital fountain code for deep space communication is thoroughly studied in this paper. First, an improved joint coding and decoding algorithm for LT code is proposed by adjusting the probability of the source symbol selection to achieve a nonuniform selection coding algorithm and by introducing the idea of real-time decoding on the basis of combining the BP and GE decoding algorithms to disperse the decoding complexity. Second, to ensure that the LT code can be reliably transmitted under different channel conditions, a feedback information extraction method and a retransmission coding method are designed, and an LT code transmission scheme based on key information feedback is proposed. Finally, the concatenation of the LDPC code with the LT code based on key information feedback is proposed. The LDPC code processing can be equivalently run on deep-space channels as erasure channels so that the advantage of the LT code being rateless can still be exploited in deep-space communication. Through simulation experiments, the performance of the cascade codes is analyzed from the two aspects of decoding efficiency and decoding overhead, and the performance of the cascade codes and CCSDS LDPC codes are compared from the perspective of the bit error rate. Simulation results show that the decoding efficiency of the cascade code increases, the decoding overhead decreases, and the communication bit error rate is lower in deep space communication compared with the CCSDS LDPC code. Therefore, the cascade code can improve the reliability of deep space communication.

РОЗПОДІЛЕНЕ ЗБЕРЕЖЕННЯ ДАНИХ З ВИКОРИСТАННЯМ ЗАВАДОСТІЙКОГО КОДУВАННЯ

Проведено огляд теоретичних відомостей з теорії інформації та кодування, аналіз сучасних завадостійких кодів на предмет їх застосовності для збереження даних. Проаналізовано доцільність створення розподіленого сховища даних, основним механізмом збереження інформації якого є завадостійке кодування Ріда-Соломона.

Analysis of transverse momentum distributions of charged particles produced in CC interactions at 4.2 A GeV/c

In this paper, the transverse momentum and maximum transverse momentum distributions of protons and pions produced in an event for CC collisions at 4.2 A GeV/c have been analyzed. This analysis is based on experimental data obtained from 2 m propane bubble chamber at Joint Institute for Nuclear Research, Dubna, Russia and simulation data obtained from Dubna cascade code. We observed three disparate zones for the transverse momentum distribution of the produced particles. The third zone where transverse momentum is greater than 0.375 GeV/c is restricted only for pions with transverse momentum approximately equal to 1 GeV/c, and for protons the restricted value of [Formula: see text] is [Formula: see text][Formula: see text]1.5 GeV/c. So contribution of pions to this region is less and decreases sharply than the contribution of protons. The results of cascade model are not fully compatible with the experimental results in the third [Formula: see text] region, as this region contains less number of particles for model data as compared with experimental data but is compatible in the case of [Formula: see text].

Spallation of 56Fe by 1.0 GeV Protons

Mass, charge and isotopic distributions observed in spallation reactions of 56Fe with 1 GeV protons are analysed in the framework of the intranuclear cascade code ISABEL coupled with the sequential binary decay code MECO. The code MECO provides a description of the equilibrated nuclear decay by the emission of gamma-rays, light-mass particles and clusters as well as intermediate mass fragments emitted in their ground, excited bound and excited unbound states (continuum) according to a generalized Weisskopf formalism. A good overall description of the experimental data is obtained with a global Fermi gas level density parameter and inverse cross sections based on the Christensen and Winther nuclear potential. Multifragmentation decay events are simulated with the code SMM and their influence on the above observables is discussed.

Utilization of harmony search algorithm to optimize a cascade for separating multicomponent mixtures

In this paper, a new code, Multicomponent Isotope Separation Cascade Code (MISCC-HS), is developed to calculate the optimal parameters of a cascade for separating multicomponent mixtures. The Harmony Search, HS, algorithm for finding the optimum solution is implemented and developed in the MISCC-HS. Minimizing the total flow rate of a cascade with the prescribed external isotope concentration has been studied. To demonstrate the MISCC-HS capability in converging to the near optimal cascade, the optimization results for the separation of xenon isotopes are compared with the results for the R-cascade that optimized by virtual component variation. MISCC-HS results represent the cascade with fewer centrifuges than the R-cascade. Furthermore, the ability of MISCC-HS is evaluated with other optimization algorithms. Suitable alignment of the results indicates that the use of the HS for this problem guarantees the calculation of the optimal parameters.

Fusion measurements for the 7Li + 51V system at energies around the Coulomb barrier

We present the experimental fusion cross sections for the 7Li + 51V system measured using the EN Tandem Van de Graaff Accelerator facility at National Institute of Nuclear Research (ININ), in Mexico. The study was focused on energies around the Coulomb barrier, B = 10.33 MeV (Blab = 11.75 MeV), in the interval from 10.0 MeV to 13.5 MeV in steps of 0.5 MeV, in the laboratory frame. In order to complement this study, the experimental results were compared with a fusion-evaporation analysis using the PACE2, LILITA and CASCADE codes, in the same interval of energies. We found that the xn and xnα are the most relevant evaporation channels, leading to 55Fe, 56Fe, 52Cr and 53Cr as residual nuclei.

Study of the cumulative number distribution of charged particles produced in He12C interactions at 4.2 A GeV/c

The behavior of the cumulative number distribution along with maximum values of cumulative number of all charged particles (i.e. protons, π±-mesons) produced in He12C-interactions at 4.2 A GeV/c from experimental and simulation data coming from cascade evaporation model has been analyzed in this paper. One could see four different regions in the distributions of cumulative number for protons in which the last region has cumulative number greater than one which correspond to cumulative region. Similarly one could see two different regions for negative and positive pions respectively but there is totally absence of the cumulative area for both positive and negative pions. The simulation data obtained from Cascade code could reproduced agreeably the distributions of the cumulative number for protons as well as for maximum values of cumulative number distribution.

Comparison of heavy-ion transport simulations: Collision integral in a box

Simulations by transport codes are indispensable to extract valuable physics information from heavy ion collisions. In order to understand the origins of discrepancies between different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term, i.e. we perform cascade calculations. When the Pauli blocking is artificially suppressed, the collision rates are found to be consistent for most codes (to within $1\%$ or better) with analytical results, or completely controlled results of a basic cascade code after eliminating the correlations within the same pair of colliding particles. In calculations with active Pauli blocking, the blocking probability was found to deviate from the expected reference values. The reason is found in substantial phase-space fluctuations and smearing tied to numerical algorithms and model assumptions in the representation of phase space. This results in the reduction of the blocking probability in most transport codes, so that the simulated system gradually evolves away from the Fermi-Dirac towards a Boltzmann distribution. As a result of this investigation, we are able to make judgements about the most effective strategies in transport simulations for determining the collision probabilities and the Pauli blocking. Investigation in a similar vein of other ingredients in transport calculations, like the mean field propagation or the production of nucleon resonances and mesons, will be discussed in the future publications.

Study of the Cumulative Number Distribution of Charged Particles Produced in d12C-Interactions at 4.2 A GeV/c

In this paper the behaviour of the cumulative number distribution and the maximum values of cumulative number in an event of all charged particles (protons,π±-mesons) produced in p12C-interctions at 4.2 A GeV/c from experimental and simulation data has been analysed. One could see four different regions in the cumulative number distributions for protons in which the last region has cumulative number greater than one which correspond to cumulative region. Similarly one could see two and three different regions for negative and positive pions respectively but there is totally absence of the cumulative area for negative pions but there are few positive pions in the cumulative area. The simulation data obtained from Cascade code cannot describe satisfactorily the distributions of the cumulative number for protons and positive and negative pions but in case of particles with maximum values of cumulative number cascade code can describe the behaviour of cumulative number distribution well.

Study of the pT-distributions of secondary charged particles produced in p12C interactions at 4.2 A GeV/c

The behavior of the transfer momentum pT distribution of protons, π+ and π− mesons, produced in p12C-interactions at 4.2 A GeV/c and also with maximum transfer momentum in an event have been studied. The experimental data have been obtained from the 2 m propane bubble chamber of Joint Institute for Nuclear Research, Dubna, Russia. The experimental results have been compared with ones coming from the Dubna version of the cascade model. We have got that there are three regions in the behavior of the transfer momentum pT distributions for all type of particles, the III region is pT > 0.375 GeV/c and it is limited for the π-mesons by the values of pT ~ 1 GeV/c though for the protons the limit values is approximately 1.5 GeV/c, meson contributions to this region approximately one order less than for protons and decrease sharper than for protons do. Cascade code could not describe satisfactorily the experimental results in the III region, the number of particles in this region of systematically less than ones coming from the experiment.

Багатокритеріальна оптимізація кодів Лабі на основі природних обчислень

In modern packet-switched telecommunications networks error correcting coding used at different levels of the Open Systems Interconnection model. At the physical and data link layers to correct and detect errors in packets commonly used classic code constructions with a fixed coding rate (for example, block codes). On the other hand, to restore the whole packets code expedient use codes without fixed encoding rate at the application level. This class of codes are Luby codes that can be used alone or be part of the cascade code constructions. The key feature of these codes is to use the special law of probability distribution in the coding process. Wherein optimization of this distribution according to different objectives depending on the specific application Luby codes can improve their effectiveness. These objectives are redundant, failure rate, probability of failure, computational complexity of coding (decoding). In practice, there is often the need to use Luby codes simultaneously satisfy several objectives. To solve this multi-objective optimization problem an approach based on generalized procedures of natural computing is proposed. The main stages of the proposed approach are presented.