Practical methods for de Bruijn sequences generation using non-linear feedback shift registers

Miroschnyk, Maryna; Korytchinko, Tetyana; Demihev, Olexandr; Krylova, Viktoriia; Karaman, Dmytro; Filippenko, Inna

doi:10.1109/tcset.2018.8336400

Cited by 5 publications

(6 citation statements)

References 3 publications

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“…Аналіз відношень між ймовірністю помилки на біт, функцією кратності помилок і вектором топології помилок для різних значень n дозволив виявити ряд закономірностей [10,11]. Перше твердження полягає в тому, що при визначеному значенні довжини кодової послідовності одному і тому ж значенню ймовірності помилки на біт на виході дискретного каналу відповідають різні топології помилок на множині n-послідовностей помилок.…”

Section: мета роботиunclassified

Estimation of Probabilistic and Statistical Characteristics of the Informational State of a Communication Channel

Кrylova,

Kotko

2023

Вісник НТУ "ХПІ"

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The methods for determining the informational state of a communication channel based on the assessment of probabilistic and statistical characteristics of errors at the channel output are presented. Adaptive information protection methods in digital communication systems, where encoder parameters change depending on the channel state, require the use of network quality control methods based on determining the statistical characteristics of the channel. It is shown that the bit error probability in the channel is constant for the presented error generation process and is independent of the method of dividing information into code blocks. The methods for assessing the statistical characteristics of the channel are based on the topological representation of error generation processes over the length of code blocks. It is demonstrated that, with a fixed code sequence length and a constant bit error probability at the output of the information channel, different error distributions correspond to sets of n-sequences. With a known number of states in the likelihood transition matrix, calculation of observation intervals for counting erroneous blocks is proposed. The presented method of researching statistical characteristics, based on the assumption of error independence, allows for the development of algorithms and procedures for assessing the state of discrete communication channels. The evaluation of potential bounds and statistical characteristics for the decoding error probability enables establishing a connection between the topological characteristics of error sequence partitioning and code parameters. The work confirms that the proposed method allows the synthesis of algorithms for determining code parameters, whose numerical values are determined based on minimizing potential decoding error probabilities.

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Section: мета роботиunclassified

Estimation of Probabilistic and Statistical Characteristics of the Informational State of a Communication Channel

Кrylova,

Kotko

2023

Вісник НТУ "ХПІ"

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“…The complexity of constructing a testing experiment with an finite state machine is determined by the properties of its diagram. To easily tested finite state machine [6][7][8][9][10], we will assign finite state machine, for which the tasks of test diagnostics are solved as simply as possible within the established costs. Before discussing the design of checking experiments, it is appropriate to recall several definition relating to experiments performed on sequential circuits or finite state machines.…”

Section: Mcandfpga-2019mentioning

confidence: 99%

“…a way to describe of the models of the control FSM, the specification of which is specified by the state table or by the state diagram. This is a special structure of the HDL-model, in which the functions of transitions and outputs are isolated into separate processes (process), and the assignment of the new state is carried out in a special process associated with synchronization [9][10][11]. One of ways to describe DD models in the form of FSM using VHDL language is the FSM template, i.e.…”

Section: Realization Of Easy Tested Finite State Machinementioning

confidence: 99%

Testability Increasing Method by Introducing Hardware Redundancy in the Easy-tested Finite State Machines

Miroshnyk¹,

Galkin²,

Zaichenko³

et al. 2019

I International Scientific and Practical Conference

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Testability increasing methods by introducing hardware redundancy into the circuit implementation are sufficiently developed and widely used in the design. Since the construction of the testing sequence is based on the use of automaton diagrams, it eliminates the need to analyze the circuit implementation of the remote control when building a diagnostic experiment. This approach allows us to extend the class of detectable faults, which in structural-analytical test generation methods is limited, as a rule, to a multitude of single constant faults. The use of automaton models in the construction of tests allows to detect any malfunction that changes the automaton diagram of a serviceable remote control and does not increase the number of states of remote control memory elements. There was described finite state machine using hardware description language. The method of computer-aided design of the easytested control FSM by introducing the hardware redundancy is presented in the paper. The FSM model is represented in VHDL in the form of the FSM template. The solution way is to add additional fragments of the VHDL code, which ensure the forced setting of the FSM into an arbitrary state without the use of synchronizing sequences. The use of the shift register in the memory part of the control FSM for organizing the path scanning was considered. The method of FSM state table expansion, which ensures the mode of bypassing all nodes of the FSM' state diagram in the diagnostic mode was proposed.

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“…This applies also for the last and first words in the ordering. DB sequences admit applications in various fields including cryptography [3,4,13,39,43], electrical engineering (mainly since they correspond to feedback-shift-registers) [7,10,11,30,31,32,36], molecular biology [33], and neuroscience [1], to name a few.…”

Section: Introductionmentioning

confidence: 99%

“…Clearly, DB sequences are the Hamiltonian cycles in the DB graph. Hence, generating Hamiltonian cycles in a DB graph forms a construction technique for DB sequences [4,9,33,36,43]. Second, some DB sequences are proved to be equal to a concatenating of certain words [14,22].…”

Section: Introductionmentioning

confidence: 99%

A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence

Amram,

Rubin,

Weiss

2021

Preprint

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We propose a novel construction for the well-known prefer-max De Bruijn sequence, based on the cycle joining technique. We further show that the construction implies known results from the literature in a straightforward manner. First, it implies the correctness of the onion theorem, stating that, effectively, the reverse of prefer-max is in fact an infinite De Bruijn sequence. Second, it implies the correctness of recently discovered shift rules for prefer-max, prefer-min, and their reversals. Lastly, it forms an alternative proof for the seminal FKM-theorem.

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Practical methods for de Bruijn sequences generation using non-linear feedback shift registers

Cited by 5 publications

References 3 publications

Estimation of Probabilistic and Statistical Characteristics of the Informational State of a Communication Channel

Estimation of Probabilistic and Statistical Characteristics of the Informational State of a Communication Channel

Testability Increasing Method by Introducing Hardware Redundancy in the Easy-tested Finite State Machines

A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence

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