DE2050604A1 - Circuit of a generator for a binomial random sequence of pulses - Google Patents

Description

PATENT ADVOCATE

H. October 1970

Anw.-Aktes 75 "262

Patent registration

Applicant; Ceskoslovenska akademie ved., Praha 1, Narodni tr. 3, CS.3.R.

Circuit of a generator for a binomial random sequence of pulses

The invention relates to a circuit of a generator for a binomial random sequence of pulses, the two different sizes, for example a ¹¹ O "and a" 1 ", corresponding to the V / ahrscheinlichkeit for the occurrence of these pulses to an improved convergence to 7 The result sequence of the pulses corresponding to the "0" and the "1" reaches the value accuracy of the probability for the occurrence of those pulses that are generated by a generator for a binomial pseudo-random sequence of pulses, but at the same time the statistical properties, that is, the randomness and the independence of the binomial sequence are preserved. So the properties remain

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receive a generator for a binomial sequence, the function of which is based on a physical principle, characterize. *

Known generators for binomial random sequences of pulses are usually designed in such a way that independent random sequences of the two variables, for example the pulses corresponding to an "O" and a "1", have the same probability of occurrence P (O) = P (I ) = 0.5 can be generated. This ideal probability value of 0.5 can - as in any technical implementation - can only be guaranteed with a certain degree of accuracy in the specific implementation. This problem, i.e. the question of accuracy, is particularly important for generators whose function is based on a physical principle. These generators are referred to as "true random" in the Anglo-Saxon specialist publications. In addition to this type of generator, there is also a type of generator, the so-called binomial pseudo-random sequence of pulses, in which the accuracy of the value of the probability of the occurrence of the ^{pulses corresponding, for example, to an 11} O "and a" 1 ", which depends on the choice of the generation program and which usually depends can be determined numerically in advance, always tends to be sufficiently high, ie in some cases the total number of "0" in a period differs from the total number of "1" only by one unit.

It can be seen that the problem of guaranteed

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accuracy and long-term stability of probability value is a basic question when using a generator whose function is based on a physical Principle and which * is referred to as "true random". This type of generator has the disadvantages of the generator a binomial pseudo-random sequence of impulses, For example, the need to keep track of the periodicity of the main proceedings, the complicated checking the properties of the generated sequence in the case of more complex transformations, in circles with non-linearities and so forth. The random procedure, i.e. the "true random" procedure, corresponds better to the mathematical one Model description as the pseudo-random method, i.e. the "pseudo-random" method.

Method for improving the randomness accuracy value in the case of generators based on the physical principle are known, for example from the Czechoslovak patent No. 106.564- "Method and device for clarification the parameter of outputs of the generator of a random process "or loud from the Czechoslovak Patent No. 112.1.51 "Circuitry for Pulse Shapes and Pulse Keys".

The invention is based on the object of a circuit for a generator of a binomial random sequence of To create pulses that correspond to two different sizes, for example an "O" and a "1" on the one hand the result sequence of the generated pulses the accuracy of the probability value for the

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Occurrence of the pulses corresponding to the "O" or the "1" which is achieved by a generator for a binomial pseudo-random sequence of pulses, and in which on the other hand, the statistical properties of the generator based on a physical principle are retained, i.e., the randomness and independence of the binomial sequence of pulses.

This object is achieved according to the invention in that ψ at least one generator for a binomial random sequence of pulses, the puncture of which is based on a physical principle, at least one generator for a binomial Pfieuäo random sequence of pulses and at least one addition stage modulo 2 is provided that the output '"'". ■ of the generator is connected to the first input of the addition stage, the second input of which is connected to the output of the generator, that the output of the addition stage is connected to the output and that each of the generators of the circuit and the addition stage each have an input is provided for the supply of synchronization pulses. The synchronization pulses serve ^ impulse the control of the repetition frequency of the output Ψ and the coordination of function or * the mutual coupling of the generator for the binomial random sequence with the generator for the binomial pseudo-random sequence and the addition stage.

In an advantageous embodiment of the invention Circuit, the addition stages are of the "Exclusive-Or" type or fulfill the logical relationships "0 + 0 = 1 + 1

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■ - O "and" O + 1 = 1 + O »1".

Further advantages and details of the invention are to be explained with reference to the exemplary embodiments shown in FIGS. 1 and 2. Show it?

Pig. 1 shows a block diagram according to the invention with only one generator for a binomial random sequence and only one addition stage and

2 shows a block diagram according to the invention with two generators for a binomial random sequence and two addition levels.

The block diagram shown in FIG. 1 consists of the generator 101 for a binomial random sequence of, for example, an "O" and a "1" corresponding pulses, the function of which is based on a physical principle, the generator 201 for a binomial pseudo random sequence of, for example, one "0" and a "1" corresponding pulses and the addition stage 701 modulo 2, the output 301 of the generator 10} is for the bi- | nomic random sequence connected to the first input 501 of the addition stage 701 modulo 2, the second input 601 of which is connected to the output 401 of the generator 201 for the binomial pseudo random sequence and whose output 801 is connected to the output 901 of the generator 1 for a binomial random sequence of, for example, a " 0 ^M and a "1" corresponding pulses, whereby the probability for the occurrence of the pulses is a different

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shows better convergence to the value 0.5. The input of the generator 101 for the binomial random sequence, the Input 02 of the generator 201 for the binomial pseudo-random sequence and finally the third input 03 of the Addition stage 701 modulo 2 are used to supply synchronization pulses that determine the repetition frequency of the output pulses and the function or the mutual coupling of the two generators 101 and 201 and the addition stage 701 modulo 2 coordinate.

In FIG. 2 a modified block diagram of a generator 2 for two binomial random sequences of is shown, for example, a ¹¹ O "and a" 1 "corresponding pulses, the probability of the occurrence of the pulses at the two outputs 901 and 902 an improved convergence In this circuit, a total of two generators 101 and 102 are provided for a binomial random sequence, one generator 201 for a binomial pseudo random sequence and two addition stages 701 and 702 modulo 2. The output 301 of the first generator 101 for the binomial Random sequence is connected to the first input 501 of the first addition stage 701 modulo 2; the output 302 of the second generator 102 of the binomial random pulse sequence is connected to the first input 502 of the second addition stage 702 modulo 2. The output 401 of the generator 201 for the binomial pseudo-random sequence is connected to the other interconnected inputs 601 and 602 of the first addition stage 701 and the second addition stage 702 modulo 2 connected, their outputs 801 and 802, a

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'■' ■ " ^! ' ⁵ ■' ■ " ^: " ^: ""! ~: ■""■■ !! ■ !! ' sipis ■ i ""r> ■

each individually, with the corresponding outputs 901, 902 of generator 2 for a binomial random sequence of for example pulses corresponding to "O" and "1" are connected, the probability of the occurrence of the impulses being an improved convergence has a value of 0.5. The input 01 of the first generator 101 for the "binomial random sequence, the input 04 of the second generator 102 for the binomial random sequence, the input 02 of the generator 201 for the binomial pseudo-random sequence and the third inputs 03 and 05 of the ■ ' first addition stage 701 and the second addition stage 702 modulo 2 are again used to supply synchronous sation pulses, as it was described for FIG.

Me circuit according to the invention realizes a generator for a binomial random sequence in a way that differs significantly from known versions, namely by using the combination of a generator for a random sequence whose puncture on a physical principle is based, with a generator for a pseudo-random sequence on the basis of a linear recursion Procedure for generating numbers when using the Addition stage modulo 2. Such a generator for *

a pseudo-random number sequence fulfills the condition that the number of ¹¹ O "in the output sequence is one zero smaller than the number of" 1 "within the scope of a period.

The function of the generator can best be explained with the aid of the circuit according to FIG. The pulse sequence / ""? /} ^On -A- ¹¹⁸ S ⁸¹¹ S 5 ^{01 of the} generator 101 for the random sequence, whose function is based on a physical principle

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is based, and the pulse sequence / ^ uJ at the output 401 of the generator 201 are given to the two inputs 501 and 501 of the addition stage 701 modulo 2. Bs it is assumed that both pulse trains / £ 7 I and j'tjj. are generated synchronously, ie in corresponding moments and in the corresponding form, for example a "0" and a "1" accordingly.

The pulse sequence at the output 801 of the addition stage 701, or at the output 90I of the generator 1 with improved convergence, is denoted by / ^ Z. In the case of the pseudo-random sequence fjij , the probability P (O) -s »P (1) is generally assumed, that is, P (O)« P (1) = 2 £ c , where £ | the deviation from the ideal value means 0.5. In the case of the random sequence fy / J , P (O) - P (1) «2 £ γ applies accordingly. The new result pulse train

is given by adding the corresponding terms modulo 2, i.e. the terms

; iuz + ^ r ^z i

_Ä Bs is possible to prove that the newly created

W. Sequence [tJ ^ · ^ΘΙ> deviation value £> · from the ideal value 0.5

by the formula

given is.

When using a generator for a pseudo random sequence with, for example, a sequence length of 1023 bits, this device, which contains a ten-bit register, is relatively simple, 512 are the "1" and 511 are the "0"

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contain speaking impulses. The relative number of pulses for the "1" is therefore 0.500488, from which the deviation value is derived

—4

£ t, = 4.88.10 results. The deviation value g-% in the binomial sequence, which is generated by the generator based on a physical principle, is, for example, £ y => 1 «10 ~, a value with which this random sequence can easily be realized. After substituting the values £ j and E.γ in the above equation, the value of the result sequence ij = 1.10 "" is obtained Deviation values £ γ = 1.10 and £ § as. 1 _e ^{1o J can} be seen, i.e. the deviation value of the binomial result random sequence of pulses is 1000 times smaller than the deviation value of the binomial random sequence, which is generated by the generator based on a physical principle without using the circuit is formed according to the invention.

The circuit of the generator according to the invention has several advantages. First, the advantages and the value properties of the generator for the binomial random sequence, whose function is based on a physical principle λ , are practically retained because the use of the generator of the pseudo random sequence in the function of a "corrector" of the statistical parameters, compared to all known circuits, seems to be the best. Second, the generator designed according to the invention is overall simpler because, in the case of a generator whose function is based on a physical principle, an increase in the requirements for accuracy and repetition frequency of the initial process, according to the invention

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Generator compared to a disproportionately high effort. In the circuit according to the invention, "both Generators, i.e. the generator, which functions on the basis of a physical principle, and the generator for the binomial pseudo-random sequence, relatively simple.

Third, the one provided with a circuit according to the invention Generator can also be used at high repetition rates. The generator based on a physical Principle is based - see also "second" - would have to be for attainment the same parameters for the binomial output random sequence would be complex, i.e. it would be costly and be technically demanding.

Fourth, the test results show that the circuit according to the invention significantly improves the statistical Output sequence parameters enabled.

The modulo 2 addition stage used is a common design, which is known from the general theory of logical networks. She is of the type - "Exclusive-or" or satisfies the logical relationships O + O «1 + 1 * O, 0 + 1 * 1 + 0-1.

The inputs for the supply of the synchronization pulses, which in the generators 101 and 102 for the binomial Random sequence, with the generator 201 for the binomial pseudo-random sequence and with the addition stages 701 and 702 modulo 2, check the repetition frequency of the output pulses and coordinate the function or the mutual coupling of the generators and the addition stages. In this way, e.g. the synchronous Input of the corresponding pulses from the generators 101 and

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201 in addition stage 701 possible. The impulses which are fed to the synchronization inputs 01, 02, OJ, allow - in the circuit according to Fig. 1 - the sequence of operations, i.e. the formation of a bit of the binomial pseudo-random sequence, one bit of the binomial random sequence and the addition modulo 2.

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Claims (2)

- 12 - Pa te η ta η s ρ r ü c h e Circuit of a generator for a binomial random sequence of pulses which "correspond to two different quantities, for example a" 0 "and a" 1% ", the probability of the occurrence of these pulses having an improved convergence to the value 0.5 as a result characterized in that at least one generator (101, 102) for a binomial random sequence of pulses whose function is based on a physical principle, at least one generator (201) for a binomial pseudo random sequence of pulses and at least one addition stage (701, 702) modulo 2 is provided is that the output (301) of the generator (101) is connected to the first input (501) of the addition stage (701), the second input (601) of which is connected to the output (401) of the generator (201), / that the output (801) of the addition stage (701) is connected to the output (901) of the circuit and that each of the generators (101, 102 or 201) and die'.Additipnsstufe (701, 702) each with a u. Input,. (Pi ».02, 0>, 04 or 05) for the supply of Synchjfeöriisatipnsimpuls is provided. ""'''. 2.) Circuit according to claim 1, characterized in that the addition stages (701, 702) of the 3 ^ pe "Exdlusiye-Or ¹¹ are or · the logical relationships 'φ + ΟβΊ + ΙβΟ' * and" 0 + 1 ■ 1 + 0-1 "meet '. _''" ■■ -; * ■ .10982.1 / 1750. ■ * ■■ - ν- *.