WO2023229481A1

WO2023229481A1 - Relay race representation of numerical data sets

Info

Publication number: WO2023229481A1
Application number: PCT/RU2022/000177
Authority: WO
Inventors: Александр Валерьевич ИВАНОВ
Original assignee: Александр Валерьевич ИВАНОВ
Priority date: 2022-05-27
Filing date: 2022-05-27
Publication date: 2023-11-30

Abstract

The invention relates to methods for (trans)coding digital signals, the information equivalent of which is represented in the form of a regular sequence of integers, and consists in performing actions on the initial digital signal (representation argument) to obtain a processed digital signal (representation function) with minimal delay and minimal rearrangement.

Description

Relay representation of integer data

DESCRIPTION OF THE INVENTION

Field of technology. The present invention relates to methods for encoding (English, coding) and transcoding (English, transcoding) digital signals, whose information equivalent can be represented as a regular sequence of integers, that is, in the form of numeric data.

State of the art. The prototype of the proposed invention is a method of representing ten bundles of eight binary numbers plus a sign in the form of a sequence of eighty-one binary numbers (English 80B/81B encoding), known from the following source:

[1] IEEE Std 802.3bp-2016, IEEE Standard for Ethernet - Amendment 4: Physical Layer Specifications and Management Parameters for 1 Gb/s Operation over a Single Twisted-Pair Copper Cable. — ISBN 978-1-5044-2288-8 (paper), STD21091; ISBN 978-1-5044-2289-5 (PDF), STDPD21091.

In addition, the prototype is most clearly disclosed in the following working documents preceding the above standard:

[G ¹ ] Lo, William, (Marvell's) 1000BASE-T1 PHY Encoder Proposal For Gigabit MAC Compatibility // Reduced Twisted Pair Gigabit Ethernet (RTPGE) Physical Layer. - IEEE 802.3bp Task Force, Plenary Meeting, March 2014. - Online: https://www. ieee802. org/3/bp/public/mar 14/Lo_3 bp_02_0314.pdf.

[G ² ] Lo, William, Correction to 1000BASE-T1 PHY 8N/(8N+1) Encoder Equations. - IEEE 802.3bp Task Force, Interim Meeting, May 14-15, 2014. - Online: https://www.ieee802.Org/3/bp/public/mayl4/Lo_3bp_01_0514.pdf.

Let us describe the prototype in a manner convenient for further comparison.

The original digital signal, valid in time t, 0 < t < oo, is divided into regular sections, each with a duration of t = 10 cycles of duration T _o so that within the boundaries of each section, 0 < t/T ₀ mod t < t, it is possible to select t normalized time intervals:

NVI: [0;1) [1;2) [2;3) [3;4) [4;5) [5;6) [6;7) [7;8) [8;9) [9; 10) cycle: 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

# ^ 1 2 3 4 5 6 7 8 9 10

For each such interval, #, or the cycle corresponding to it - the #th cycle, which is equivalent, there is one bunch of code plus a sign, which we will represent the information equivalent of the original digital signal on the corresponding part of its corresponding section:

# -► 1 2 3 4 5 6 7 8 9 10

'p-k ² p-k ^Z p-k ⁴ p-k ⁵ p-k ⁶ p-k ⁷ p-k ⁸ p-k ⁹ p-k ¹⁰ p-k

'code ² code 3 ^code ⁴ code ⁵ code ⁶ code ⁷ code ⁸ code ⁹ code ¹⁰ code

Each link is a code plus a sign, or, taking into account the direct indication of the cycle on which it falls, the #th code plus the #th sign, or briefly, hereinafter, the superscript is ^# code plus ^# sign, during further processing they are recognized in the following order:

(if) ^# sign means ext data octet. symbol,

(then) ^# the code itself in conjunction with ^{the #} sign is matched to one of V _D = 2 ⁸ = 256 N _c = 2 ³ = 8 allowed among

possible combinations of groups of combinations made up of eight, each of the eight binary numbers themselves and such a sign, all together falling on the #th cycle.

In turn, a combination of two or more integers can be uniquely reversible - through their weighing - expressed as one number, and then denoted all of them together as this one number.

Thus, we can conclude that the information equivalent of the original digital signal can be represented as a sequence, whose regular (that is, periodically repeated) section is formed by two rows (m columns) of m (two) integers, each belonging to a set of cardinality L / s or N , respectively:

# —> 1 2 3 4 5 6 7 8 9 10 /s E/S E/S E/S E/S E/S E/S E/S E/S Z/S

N N N N N N N N N N

The set of such numbers relating to one section of the original digital signal specifies the representation argument by [1 ⁽ " ⁾ ], both unambiguously and exhaustively - here and below, the subscript indicates position of the number within the corresponding loop:

1 2 3 4 5 6 7 8 9 10

^X D/C ^X D/CX _D / _C X _D / _C X _D / _C X _D / _C X _D /CX _D / _C X _D / _C X _D / _C

1 2 3 4 5 6 7 8 9 10 ^x0-7 ^x 0-7 x 0-7 ^x 0-7 ^x 0-7 ^x 0-7 ^x 0-7 ^x 0-7 ^x 0-7 ^x 0-7

For the argument given above, X, the representation function is uniquely invertible by 11 ⁽ ' ⁾ ], Y = Y(X), determined, in turn, by a set of the following, slightly different numbers: l ^pre 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

U o-z U o-z Uo-z Uo-z Uo-z Uo-z Uo-z Uo-z Uo-z Uo-z lpre 1 2 3 4 5 6 7 8 9 10

^R U U 4 U 4 U 4 U 4 U 4 U 4 U 4 U4 U4 U4

1 2 3 4 5 6 7 8 9 10

U 5-7 U 5-7 U 5-7 U 5-7 U 5-7 U 5-7 U 5-7 U 5-7 U 5-7 U 5-7

Finding such a function begins by filling it with numbers dependent on the argument, according to the template below:

1 ^rge 1 (octet or ext.). . . 10 (octet or exercise)

b 1„ . 10, 10

Go-3 Co-3. . . Oo-z So-z

(0) ¹ d ₄ or ^ ₄ . . . ¹⁰ d _{4 or} ¹⁰ s ₄

<45-7 'g ^with 5-7 . . . ¹⁰ I Q ₅ ^ ₇ 1°е С$ - ₇

When ^# _xD / _C denotes a data octet, the corresponding column (#) of the function contains a preliminary result consisting of eight #1 1G binary numbers do- ₇ , which together constitute one of the / _vD allowed combinations, uniquely associated with the combination _{x0 -7} .

With x _D / _C meaning control character, the (#th) preliminary # the result consists of eight binary numbers Co-?, and: the first four ^# from ₀ -з constitute one of the tn (m < N _c ) allowed among U _P = N / ( s / c ^x Ac) = 2 ⁴ = 16 possible combinations, uniquely associated with the cycle to which ^# x _D/c itself falls, the next number ^# with ₄ = 1 by definition, and all three remaining with _{5 : 7} constitute one of the Nc combinations, uniquely associated with one allowed group of the combination x ₀ - 7 and x _D/c .

Considering that the argument is delivered by the original digital signal not at all instantly, but at a finite rate of one column per cycle, we can note that the minimum number of cycles that is necessary to find the representation function by [1 ⁽ ' ⁾ ] is:

(* ^min ) T'minC^y/o = t. // "minimum delay"

Finding such a function is completed by a set of horizontal and vertical permutations of binary numbers within the framework of the preliminary result, then, those and there, if, for which and where it is necessary to make such a finding of the function uniquely reversible.

Example 0A (prototype) shows the representation function by [1 ⁽ ■ ⁾ ] when all ten (1st to 10th) connectors correspond to data octets:

1 ^rge 1 2 3 4 5 6 7 8 9 10

'do-з ² do-з ³ do-3 ⁴ do-3 ⁵ do-3 ⁶ do-3 ⁷ do-3 ⁸ do-3 ⁹ do-3 '°do-3

(0) 'd ₄ ² d ₄ ³ d ₄ ⁴ d ₄ ⁵ d ₄ ⁶ d ₄ ⁷ d ₄ ⁸ d ₄ ⁹ d ₄ ¹⁰ d ₄

Example OB (prototype) shows the representation function by [1 ⁽ ' ⁾ ], when all the same ten (from the 1st to the 10th) connectives correspond to control characters - here and below, y horizontally (from one column to another) and vertically (within the same column) of rearranged binary numbers, the upper and lower indices are underlined, respectively:

1 ^rge 1 2 3 4 5 6 7 8 9 10

4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 4-3 ^1O Co-3

Example OB (prototype) shows the representation function by [1 ⁽ " when only the first (1st) connective matches the control character: 1 ^rge 1 2 3 4 5 6 7 8 9 10

4 (0) h H H H H H ¹⁰ a ₄

Example 0G (prototype) shows the representation function by [1 ⁽ ' ⁾ ], when only the last (10th) connective corresponds to the control character: 1 ^rge 1 2 3 4 5 6 7 8 9 10

10^ 1l 21 3 . 4 5 i 6 i 71 8 91 so-z ds-6 Oz-b ds-b Oz-b bz-b Oz-b bz^b Dz- ₆ Oz-b

'H (o) H 4 H H 4 4 4 4

^{2 3} A ⁴ A 51 6 7 8 l 91 1()

<10-2 <10-2 <10-2 <10-2 <<0-2 Q-2 <1(H2 <*0-2 <10-2 C5-7

The OD example (prototype) shows the representation function by [1 ^{( }} ], when three selective (3rd, 9th, 10th) connectives correspond to control symbols: 1 ^rge 1 2 3 4 5 6 7 8 9 10 з

7

Assuming that in one cycle it is possible to rearrange any numbers in any pair of two adjacent columns, you can notice that the maximum number of cycles that is necessary to completely find the representation function by [1 ⁽ ' ⁾ ] exceeds the minimum by 2m - 1 (since this is exactly how many permutations are needed in the limit) and is:

(* ^max ) T _flow (t)/To = Zt - 1. // "maximum delay"

Thus, the signal processing latency is not constant:

(*) tn < T(t)!Ta < 3m - 1 . // valid for all m > 2

Let us represent the information equivalent of an already processed digital signal as a sequence, whose regular section is formed by two ordinary lines (t regular, full columns) of t (three) integers and one long line (additional, reduced column) of t + 1 (single) integer numbers belonging to different sets of cardinalities _M _R Х N _C Х N _D/C = N, respectively: l ^pre 1 2 3 4 5 6 7 8 9 10 R m. MR _R M Mi M Mi MM

Me/s L /s M)/s Me/s Me/s ME/S M /S M>/C M)/C M)/C M>/c

Nc N _c Nc N _c N _c N _c Nc N _c Nc Me

This means that the function is delivered by the corresponding section of the processed digital signal with a duration of log ₂ (Me/s ^x M”) = 81 clock cycles with a duration of To <'/v^o, where this is l/log ₂ M

For each clock cycle of such a section there is only one single out of eighty-one (81) binary numbers, all together making up the function delivered by this section of the processed digital signal, the (numbers) in it (functions) are sequentially sorted in strict order from the first to the last - from top to bottom, inside from left to right:

1 ^rge 1 2 3 4 5 6 7 8 9 10 ...4 ^! 9... ^! 17... ^! 25... ^! 33... Ml... 49... ¹ 57... ^l 65... ^! 73...76 ll ^pre l ₅ l ₁₃ l ₂ l ^! 29 ^! 37 ^! 45 ^x 53 Ml ^! 69 ^! 77

M...8 ^! 14... ^! 22... ^! 30... ^l 38... Bw... ^! 54... ^! 62... ^! 70... ^! 78...8O

Note - For the 1000BASE-T1 protocol according to [1], T _o = 8 ns, it follows that ¹ /$T ₀ = 1 ns, while t ₀ ~ 0.9 ns < ¹ /^To.

Thus, the prototype is characterized by the following features, which are also its limitations (disadvantages) - here and further, when describing the prototype or when comparing with it, it is the general (generalized) case that is considered: the time it takes to find the representation function from the selected argument (signal processing delay) depends both on the duration of the argument (t), known initially, and on the contents of the argument, changing arbitrarily over time - see (*); In addition, finding the representation function requires rearranging the binary numbers that make up the argument, both between the columns corresponding to the cycles in which such numbers were delivered, and within these same columns, that is, both horizontal and vertical.

Therefore, (re)encoding the processed digital signal from the original digital signal will result in lag (delay) the first from the second, it is obvious that no less (!) than proportional to the maximum number of cycles required to completely find the representation function by [1 ⁽ ' ⁾ ], see (* ^max ), which is probably the most critical of the insurmountable prototypes restrictions due to the above-mentioned features.

The present invention is aimed at overcoming the limitations inherent in the prototype.

Disclosure of the invention. The proposed invention, first of all, has common features with the prototype, namely that:

| | use as presentation argument

| | | information equivalent of the original digital signal,

| | | | divided into sections, for each of which

| | | | | you can clearly indicate the moment of its end,

| | | | each lasting the selected number of repetitions

| | | | | | you can clearly indicate the moment of its end,

| | | | | walking in the appropriate area in strict order,

| | | | | | from first to last, and the moment of the end of the last

| | | | | | so that for any of the cycles, including the current one,

| | | | | | | you can unambiguously indicate its neighboring cycles,

| | | | | | | | previous to him (before him) and next to him (behind him),

| | | | | each of which has a combination of code plus sign,

| | | | | | | can be unambiguously indicated by the same (same) code or sign,

| | | | | | where the sign means that the code should be interpreted

| | | | | | | either as "data" or as "control", | | | | | | at the same time, for any sign taken by the current one,

| | | | | | | can be clearly indicated, except for himself,

| | | | | | | | whether he is the last one on the site or not, and also

| | | | | | | | (all) his previous ones on the site, when there are any, and

| | | | | | | | (one) next to him on the site, when there is one,

| | | | | | similarly, for any code taken by the current one,

| | | | | | | you can clearly indicate (one) the next one to him,

| | | | | | such (a connective) that it cannot be equated

| | as a representation function from what they find

| | | information equivalent of a processed digital signal, | | | | representable as a regular sequence -

| | | | | a collection of time-correlated series of integers.

§ 1. However, in order to overcome the previously identified limitations inherent in the prototype, which constitutes the technical problem solved by the proposed invention in the manner disclosed below, in the proposed invention:

11 find:

I I relay series of numbers - such that

III there is exactly one number from this series in the current cycle,

1111 uniquely reversibly comparable

III or the current code,

TIN if the current attribute means “data”,

HHI or that code in conjunction with the same attribute meaning “control” NNN, closest to the current attribute

HHHI among his previous ones on the site,

NNN if the current attribute means “control”, when among its previous ones in the section NNN there is at least one meaning “control”, for an empty condition, if the current attribute means “control”, when among its previous ones on the site

there is no one meaning “control”, III in addition,

III, for the section itself there is exactly one more number from this series, 1111 placed after the numbers falling on the cycles of this section, 1111 uniquely reversible compared because that code is in conjunction with the same sign meaning “control”, the closest to the last current sign among itself and to him previous ones on the site, if among all the signs on the site there is at least one meaning “management”, because the empty condition, if among all the signs on the site

there is no one meaning “control”;

I I running series of numbers - such that

III for the current cycle there is exactly one number from this series, 1111 is uniquely reversibly comparable to the current code, if the current sign means “data”, when among its previous ones in the section there is not a single one meaning “control”, about it to the next code, if the current sign not the last one on the site if the next sign for him means “data”, when among himself or his previous ones on the site there is at least one meaning “management”,

because of the cycle of that sign meaning “control”, the closest current attribute among itself and its previous ones on the site, if the current attribute is the last on the site or if its next attribute means “control”, when among itself or its previous ones on the site

there is at least one meaning “control”;

I I visual series of numbers - such that

III for the current cycle there is exactly one number from this series, 1111 which is uniquely reversibly comparable either to the current code, if the current attribute means “data”, or to the current code in conjunction with the current attribute,

if the current attribute means "control".

The main technical result of this solution is that it completely eliminates the rearrangement of numbers within columns, that is, between rows, and significantly reduces the time it takes for the representation function to move from the selected argument to a fixed value in two cycles, regardless of the duration and content of such an argument.

In other words, the representation function disclosed above allows you to receive a processed digital signal with a minimum delay and with a minimum, only horizontal rearrangement of numbers.

§ 2. If it is rational, then in the proposed invention:

I I cycle of that sign meaning “control”

III is used in conjunction with the same code and the same sign.

The main technical result (see § 1 earlier) with this solution is saved. An additional technical result with this solution is the ability to express the corresponding information equivalent in a more rational (optimal, compact) way.

§ 3. If the corresponding information equivalent can be written exclusively in binary numbers, then in the proposed invention:

I I numbers are chosen from sets,

III all prime power factors of which are equal to two.

The main technical result (see § 1 earlier) remains the same with this solution. An additional technical result with this solution is the ability to express the corresponding information equivalent in the most natural way for such an equivalent.

§ 4. If the corresponding information equivalent cannot be written exclusively in binary numbers, then in the proposed invention:

I I numbers are chosen from sets, at least one is prime

III power multiplier of at least one of which is not equal to two.

§ 5. If it is necessary to transform the corresponding information equivalent, expressed by one set of numbers per section, into an equivalent with a smaller number of such numbers, then in the proposed invention:

I I two or more numbers are replaced by one chosen from the set

III with power no less than the product of the powers of the sets, Illi from which the numbers to be replaced are selected.

The main technical result (see § 1 earlier) remains the same with this solution. An additional technical result with this solution is the ability to re-represent the information equivalent, expressed in a way convenient when finding the representation function, with its equivalent equivalent, expressed in a different way, convenient precisely when generating the corresponding digital signal.

§ 6. If requested, then in the proposed invention:

I I give such a processed digital signal,

III that in at least one section of the relay row 1111 all numbers are compared, including forcibly, to the IIIIII code in conjunction with the sign meaning “control”.

The main technical result (see § 1 earlier) remains the same with this solution. An additional technical result with this solution is the ability to process special signals.

§ 7. If requested, then in the proposed invention:

I I take such an original digital signal,

III that in the current cycle, in addition to the current ones, 1111 the next code and the next sign are also known to a degree of completeness IIIIII sufficient to find the current number of the running row.

The main technical result (see § 1 earlier) is improved with this solution. An additional technical result with this solution is to strengthen the main one in that part that corresponds to the time of finding the representation function, and by the fact that here such time decreases to the minimum possible value in one cycle, while, as before, remaining both fixed and independent of either the duration or the contents of the argument of such a function.

Implementation of the invention. The proposed invention can be implemented in various ways, limited only by its formula, which, however, has common fundamental features outlined below.

Each code plus sign combination delivered by the original digital signal on the corresponding (#th) cycle of its corresponding section, consisting of n > 0 such cycles, is associated with the following three numbers, one for each of the three rows - relay, running, visual, when attribute means “data”:

^# p - selected from a set of cardinality N _P >1;

^# t — selected from a set of cardinality NT > 1 + 1 ;

^# f — selected from a set of cardinality N _P d > 1 .

Each code plus sign combination delivered by the original digital signal on the corresponding (#th) cycle of its corresponding section, consisting of n > 0 such cycles, is associated with the following three numbers, one for each of the three rows - relay, running, visual, when sign means “control”:

^# b - selected from a set of power TVB > 1 + 1;

^# 1 - selected from a set with power

>n;

^# f — selected from a set of cardinality N _Pc > 1 .

NOTE: Each of these numbers conveys a portion of the information proportional to the logarithm of the power of its set.

Note - In the optimal case, A' _in = A _P , A _t = A _L , A _Fd = A _Fc .

Example 1 shows the step-by-step determination of the representation function according to § 1, when out of n = 10 connectives, four selective (3rd, 6th, 9th, 10th) connectives correspond to control symbols:

[0;1) [1;2) [2;3) [3;4) [4;5) [5;6) [6;7) [7;8) [8;9) [9;10) ^ NVI

1 2 3 4 5 6 7 8 9 10

Start:

(0) <— “relay race” // “baton” indicating “runner”

<— relay row // records the moments of “passing the baton”

<— running row // the “runner” leaves the “track” behind him

<— visual sequence // “spectator” does not leave the occupied place step'. 1 {first} = current <— cycle

- (0) <— “relay race”

<— relay row

♦—running row

<— visual step: 1 2 = current <— cycle

- (0) <— “relay race”

*Р ² Р <— relay row h ² t <— running row

² f <—visual step'. 1 2 3 = current <— cycle

And “b <— “relay race”) = “START!” <— relay row

— the first “runner” started the “relay race” <— running row

² з f <— visual range ...continuation of example 1...

[0;1) [1;2) [2;3) [3;4) [4;5) [5;6) [6;7) [7;8) [8;9) [9;10) ^NVI

1 2 3 4 5 6 7 8 9 10 ^#

3 4 = current <— cycle

It — > 4e <— “relay race”

(0) ⁴ р <— relay row

4 4 4 4 - the “runner” has passed the nearest mark <— ... if 2 _f 3 * 4 g* ff - visual step '. 1 2 3 4 5 = current <— cycle

And * "b <— "relay race"

(0) ⁴ p ⁵ p <— relay row

4 4 4 4 4 - the “runner” has passed the next mark ... if 2 _f ³ f ⁴ f ⁵ f <— visual row

th row

4 4 4 4 4 ⁶ 1 - the new “runner” took over the “baton” if 2 _f 3 _f 4 _f 5 _f 6 g* f <— visual step '. 1 2 3 4 5 6 7 = current <— ...

It - — > ~b <— “relay race”

(0) ⁴ P ⁵ P ³ b ⁷ p <— relay row

4 4 4 4 4 4 “1 - the “runner” has passed ... the mark if 2 _f ³ f ⁴ f ⁵ f ⁶ f ⁷ f <— visual row

.. if 2 _f ³ 6f 7f 8f _ f ⁴ f ⁵ f ... end of example 1...

[0;1) [1;2) [2;3) [3;4) [4;5) [5;6) [6;7) [7;8) [8;9) [9;10) <-NVI

1 2 3 4 5 6 7 8 9 10 ^-#

step 1 2 3 4 5 6 7 8 9 10 {last}

result:

1 2 3 4 5 6 7 8 9 10 10 ^post

if 2 _f 3/? 4p 5g"6x" ? 8 9 _f

¹⁰ f NIS!”

Numbers p and f are not subject to permutation, numbers b and 1 can only move to the right (“to the future”), numbers t can only move to the left (“to the past”) and only once, which reduces the signal processing delay to a constant:

(**) T(n)/T ₀ = 2 < T(w)/T ₀ . // valid for all n = m > 2

The set of numbers N, N _D , N _c (see earlier) and 2Vp, N _T , N _Pd , N _B , N _L , N _Fc , expressing each power of the corresponding set, statically characterizes the representation function described (defined) by them, Moreover, such numbers can be interconnected - balanced among themselves - in a unique way in each practical case, including when N _c > A _Fc And, accordingly, N > n ^x (N _c / AA _C ).

Example 2 shows the characteristics of the representation function according to § 2 under the condition N _c Nc,max for N _n = N = 256 = 2 ⁸ and the following n n ^ 2-' 3 5 6 7 9 10 11 12 13

A^s.max 42 25 21 18 14 12 I 10 9

7Vp = 7V _B 2 ¹ ² 1 ² 1 ² 1 ² 1 ² ¹ 2 1 ^{2 1} 2 ¹

AA 2 ⁶ 2 ⁷ 2 ⁶ ² 6 ^{2 6} 2 ⁴ 2 ⁷ 2 ⁴ 2 ⁷

AAd = AA _c 2 ¹ 2° 2 ¹ ² 1 ^{2 1} 2 ³ 2° 2 ³ 2°

N _L 63 125 63 63 63 15 121 15 117

AA - ATL 1 3 1 1 1 1 7 1 11

Note - When # _t > N _L , (AG _T - N _L ) x A^F combinations are formed, free to compare information for any additional, special purpose, if necessary.

Taking AАв = max {A^ _in ,LA}, AA _L = max {LA, N}, N _FF = max{# _Fd ,#F _C }, the information equivalent of the processed digital signal, in the general case, is represented as a sequence, whose regular section is formed by numbers from sets of the following cardinalities:

1 2 3 • • • • p — 2 p~ p p ^post

LAv >v »v • • • • Vp _B 7Vp _B 7Vp _B D/ _rv

AAL AAL AAL • • • • 7V _TL AAL 7V _T[

TVFF AAF AAF • • • • A^FF AAF AAF

Each number, reflecting the power of the corresponding set, is a positive integer, (by definition) decomposable into prime factors, the combinations of which are weighted, therefore, the numbers selected from such a set are comparable.

Example FOR - cf. c 0 A - shows the representation function according to § 3 with N _D = A = 2 ⁸ , A _PB = 2 ¹ , A _TL = 2 ⁴ > p = 10, A _FF = N _c = 2 ³ and ^# p = ^# d ₀ , ^# t = ^# a ₄ , ^# f = ^# d _5-7 or ^# b = ^# Co, ^# 1 = ^# Ci-4, ^# f = ^# c _5-7 (which is similar to the prototype according to [1]), when all ten (1st to 10th) bundles correspond to data octets: 1 2 3 4 5 6 7 8 9 10 10 ^post

'do ² do ³ do ⁴ do ⁵ do ⁶ do ⁷ do ⁸ do ⁹ do ^lo do (0)

1d A ^{3 4} A 5D 7 , 8 i 9. 10J dl-4 <11-4 <11-4 <11-4 <11-4 dl-4 dl-4 di-4 di-4 d]- ₄

1 J 9J 10 . ds-7

05-7 a _5-7

Example of ST - cf. with OB - shows the representation function according to § 3, when all ten (1st to 10th) connectives correspond to ex. characters: 1 2 3 4 5 6 7 8 9 10 10 ^post

(0) “Co “Co “Co “Co -Co -Co “Co “Co “Co ~ C ₀

1 2 3„ 4 5 7 8^ 9

I -4 C 1-4 Ci-4 Ci-4 Ci-4 C1-4 C1-4 C1-4 C1-4 C1-4

1 4 6„ 7„ 1() с5-7 С5-7 ^с 5-7 С5-7 С5-7 С5-7 С5-7 С5-7 С5-7 С5-7

Example of SV - cf. with OB - shows the representation function according to § 3, when only the first (1st) connective corresponds to the control character: 1 2 3 4 5 6 7 8 9 10 10 ^post

(0) h H H H H H ‘H

2 d jl-43 l 4 l 51 6 71 8j 9j 101 10 di-4 di-4 di-4 di-4 di-4 d]-4 d]- ₄ dl-4 C1-4

1 21 3 i 41 5 61 7 i 8 J 9 l 101

C5-7 ds-7 ds-7 ds-7 ds-7 ds-7 ds-7 ds-7 ds-7 ds-7

Example ZG - cf. with 0Г - shows the representation function according to § 3, when only the last (10th) connective corresponds to the control character: 1 2 3 4 5 6 7 8 9 10 10 ^post

'do ² do ³ do ⁴ do ⁵ do ⁶ do ⁷ d ₀ ⁸ do ⁹ d ₀ (0) c ₀

Example of AP - cf. with OD - shows the representation function according to § 3, when three selective (3rd, 9th, 10th) connectives correspond to ex. characters:

1 2 3 4 5 6 7 8 9 10 10 ^post

8 _L w

'ds-7 ² ds-7 ³ C ₅ ^ ^{7 4} ds-7 ⁵ ds-7 ⁶ ds-7 ⁷ ds-7 ds ? ⁹ C ₅ -7 C5-7

Thus, in a quantitative comparison in all n = m > 2, similar to the prototype according to [1 ⁽ ' ⁾ ], the representation function is: n + 1 number p/b from sets with powers no more than 7Vp _B ; n numbers t/1 from sets of cardinality no more than AGm; n numbers f/f from sets of cardinality at most AT _F F •

For the general case, we represent the information equivalent of the processed digital signal as a sequence with a regular portion of numbers from the sets of the following powers:

1 2 3 • • • • p — 2 p— 1 p p ^post

Ap TVPB >v • • • • / _rv g _rv / _rv t / _in _TL / _TL 7V _TL • • • • y\/ _TL ;y _TL G _T

Selected factors into which numbers are decomposed, reflecting the powers of the corresponding sets may be different in different cases, including when several classes of service are needed, that is, when JVcoS > 1 and, accordingly, N _B = 1 + Msos > 1 + 1.

Example 4 shows the powers of sets in the representation function according to § 4 with # = ) = 256 = 2 ⁸ , p = 2 = 2 ¹ , MB = N _B = 1 + V _Co s = 1 + 2 = 3 = 3 ¹ , TVTL = 16 = 2 ⁴ > n = 10, = N _c = 8 = 2 ³ :

1 2 3 4 5 6 7 8 9 10 10 ^post

{2 ¹ } {Z ¹ } {Z ¹ } {Z ¹ } {Z ^{1 } {Z 1} ^} {Z ¹ } {Z ¹ } {Z ¹ } {Z ¹ } {Z ¹ }

{2 ⁴ } {2 ⁴ } {2 ⁴ } {2 ⁴ } {2 ⁴ } {2 ⁴ } {2 ⁴ } {2 ⁴ } {2 ⁴ } {2 ⁴ }

{2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ }

However, in practice, powers of a single prime number are convenient.

Example 5 shows the powers of sets in the representation function according to § 5 with N _P = 2 ¹ ,

before and after replacement type (N _BB ) ⁵ -> in*, where (in) ⁵ = З ⁵ = 243 < 256 = 2 ⁸ = Мв*: before 1 2 3 4 5 6 7 8 9 10 10 ^post

{2 ¹ } {3} {3} {3} {3} {3} {3} {3} {3} {3} {3}

{2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ^{3 } {2 3} } {2 ³ } { ^{2 3} ^} after 1 2 3 4 5 6 7 8 9 10 10 ^post

{2 ¹ } - - - - {2 ⁸ } - - - - {2 ⁸ }

{2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ } {2 ³ }

Note - The case of replacing a group of w numbers in a separate row, selected from a set of cardinality N^, with one number selected from a set of cardinality Ny* > (N ) ^w , an example of which is given above, is the most practical, but not at all unique, since in the general case the optimal group of replaceable numbers can include numbers from several series, based on the specific conditions of such optimality.

Given p, AG _R , N _B , V _TL , /p _F and a set of substitution types

if necessary, there is a total number of samples (as results of finding) of the representation function:

Under the same conditions, among the total number of samples, the number of natural samples of the following representation function is determined:

Therefore, under the same conditions, among the total number, the number of forced samples of the same function is also available:

0 < AA forced - A total native •

Example 6 shows examples for the representation function according to § 6 with

= 7V _B = B - 2 ¹ , N _TL = 2 ⁴ > 10 = n, Np = 2 ³ and no replacements, taking

^# y ₀ = 0 for empty condition, ^# y ₀ = 1 for control character: general pattern of patterns:

= N _PB -(N _?B -NN _fr y = 2 ^s "' = 2 ⁸¹

| "generalization criterion"'. ”' ^post yo, ^# У/ ⁼ 0 or 1; z = 0...7, # = 1...I forced samples template: // _for ced ⁼ (t/t)” ⁼ 2 ⁷ ” = 2 ⁷⁰ < T totai 1 2 3 4 5 6 7 8 9 10 10 ^post

(1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1)

1 2 3 4 5 6 7 8 9 10

У1-4 Уь4 УН У1-4 УН4 У1-4 УН4 У1Н У1Н У1Н

template of natural samples: // N _natve = otai brced = 2 ⁸¹ - 2 ⁷⁰ < _tot ai

Typically, the presentation function is adapted to the characteristics of existing digital signals, especially the original one; if technically possible, however, the opposite is also possible.

Example 7 A shows modified to achieve compatibility

2 with the representation function according to § 7 with k < 2 version of the MP protocol:

}var., line—» ^TX EN:ERR ^TX D0:l=U0,Ul ^TX D2:3=U2,U3

“data” = {0:0} u ₀ (7), uj(/) u ₂ ( , u ₃ (/)

"ex. + words d." {0:0} and ₀ (0, {0} u ₂ (/ + To), u ₃ (r + To)

"control" {0:0} u ₀ (/), {1} are ignored

Example 7B shows a modified version of the GMII protocol to achieve compatibility with the representation function according to § 7 for k < 2 ⁴ :

{.var., line—» EN:ERR U0-HJ2 U3 U4-U7

"ex. + words d." {0:0} Uo- ₂ (/) {0} U ₄ -7(? + To)

"control" {0:0} and ^gC {1} are ignored

Example 7B shows modified to achieve compatibility with representation function according to § 7 with k < 2 protocol version 64V/66V

{.var., l.—> UO:U1 U2-HJ5 U6 U7-U9 U10-U65

"y. + words d." t {0: 1 } u ₂ ^ ₅ (0 {0} u _7-9 (Z + To) u io-6s(

"exercise" + {0:1} u _2-5 (Z) {1 } ignore. Uio^65(

Obviously, this approach allows you to reduce the signal processing delay to the minimum possible:

(***) Tk T = 1 < T(t 1T . // valid for all k = m > 2

Note – The sequence numbers of the argument and/or representation function can be scrambled if necessary.

Industrial applicability. Based on the above, the author believes that the invention he proposes is industrially applicable in those telecommunications applications where the prototype and similar encoding and transcoding methods are applicable.

Applicability in other applications is also quite possible due to the universality of the proposed invention in its essence.

It is sets of integers that are the basic information objects on which a digital computing tool operates, and any other type of information is only reduced to them. The finiteness of such sets and such numbers is predetermined by the digital nature of the calculations, which are initially limited by the bit grid of the tool itself.

The basis of the proposed invention is the processing of precisely finite integers inside finite sets of such numbers as sections of a certain sequence, regular, that is, repeatable in their structure, imaginary in a table, the numbers of which fill its relay row (sentence in English, pit/baton row - "РВ row, PBR), running row (sent. English, track/leg row - TL row, TLR), visual row (sent. English, fan/fan row - * FF row, FFR).

The very order of such processing, imagined as a kind of relay race, completely fits into the model determined by the digital nature of calculations, and therefore is completely embodied by such a means.

Therefore, we can assume that the level of development of semiconductor technology and the computer technology implemented on its basis that is already available is sufficient for the relay race representation of integer data proposed by the author to find its application in new, modern means of communication.

Claims

— 27 —

Relay representation of integer data

FORMULA OF THE INVENTION of a special (re)coding of digital signals, called relay representation of integer data, in which the information equivalent of the original digital signal is used as a representation argument, | divided into sections, for each of which | | you can unambiguously indicate the moment of its end, | each lasting the selected number of repetitions | | cycle duration, for each of which | | | you can unambiguously indicate the moment of its end, | | walking in the appropriate area in strict order, | | | from first to last, with the moment of the end of the last | | | | coincides with the end of the section, | | | so that for any of the cycles, including the current one, | | | | you can unambiguously indicate its neighboring cycles, | | | | | previous to him (before him) and next to him (behind him), | | each of which has a combination of code plus sign, | | | mutual belonging of which to that (ligament) | | | | can be unambiguously indicated by the same (same) code or sign, | | | where the sign means that the code should be interpreted | | | | | | | either as "data" or as "control",

| | | | | | at the same time, for any sign taken by the current one,

| | | | | | | can be clearly indicated, except for himself,

| | | | | | | | whether he is the last one on the site or not, and also

| | | | | | | | (all) his previous ones on the site, when there are any, and

| | | | | | | | (one) next to him on the site, when there is one,

| | | | | | similarly, for any code taken by the current one,

| | | | | | | you can clearly indicate (one) the next one to him,

| | | | | such (a connective) that it cannot be equated

I I relay series of numbers - such that

III for the current cycle there is exactly one number from this series, 1111 is uniquely reversible

III or the current code, if the current attribute means “data”,

HHI or that code in conjunction with the same UNN attribute meaning “management”, the closest to the current HHHI attribute among its previous ones in the area, NHH if the current attribute means “management”, HHHI when among its previous ones in the area HIHHI there is at least one meaning “management” yes, III or an empty condition, nnn if the current attribute means “control”, IHIHI when among its previous ones on the site

there is no one meaning “control”,

III In addition,

III per section itself there is exactly one more number from this series, 1111 placed after the numbers falling on the cycles of this section, 1111 uniquely reversibly comparable

III, or that code in conjunction with the same sign meaning “management” of a research institute, the closest to the last current sign among itself and its predecessors on the site, 111111 if among all the signs on the site there is at least one signifying “management”,

IIIIII or an empty condition,

research institute if among all the signs on the site there is not a single one meaning “management”;

I I running series of numbers - such that

III for the current cycle there is exactly one number from this series, 1111 is uniquely reversibly comparable to the current code, if the current sign means “data”, when among its previous ones in the section there is not a single one meaning “control”, about it to the next code, if the current sign not the last one on the site if the next sign means “data” for him, when among himself or his previous ones on the site there is at least one signifying “control”, because the cycle of that sign meaning “control” is closest to the current sign among himself and his previous ones on area, area

if the current sign is the last one on the section NIN or if the next sign for him means “management”, when among himself or his previous ones in the section nnnn there is at least one meaning “management”;

I I visual series of numbers - such that

III there is exactly one number from this series in the current cycle,

NN uniquely reversible comparable

III or the current code, nnn if the current attribute means “data”,

IIII or the current code in conjunction with the current attribute, IHIH if the current attribute means “control”.

2. Method according to claim 1,

| characterized in that

I I cycle of that sign meaning “control”

III is used in conjunction with the same code and the same sign.

3. Method according to claim 1 or claim 2,

| characterized in that

I I numbers are chosen from sets,

III all prime power factors of which are equal to two.

4. Method according to claim 1 or claim 2,

| characterized in that

I I numbers are chosen from sets, at least one is prime

III power multiplier of at least one of which is not equal to two.

5. Method according to clause 3 or clause 4,

| characterized in that

1 1 two or more numbers are replaced by one chosen from the set — 31 —

III is no less powerful than the product of the cardinalities of the sets, 1111 of which the numbers to be replaced are chosen.

6. Method according to clause 3, clause 4, or clause 5, | characterized in that

I I give such a processed digital signal,

III that in at least one section of the relay row

1111 all numbers are compared, including forced,

III code in conjunction with the sign meaning “control”.

7. Method according to clause 3, clause 4, clause 5, or clause 6,

| characterized in that

I I take such an original digital signal,

III that in the current cycle, in addition to the current ones, the 1111 next code and the next sign are also known to the degree of completeness,

IIIIII sufficient to find the current number of the running row.