SU1295527A1 - System for decoding binary sequences - Google Patents

Abstract

This invention relates to automation. Its use in information transmission systems, in particular in synchronization systems, allows to expand the scope of application by providing the possibility of decoding Gold sequences. The binary sequence decoding system comprises a majority decoding device 4 of binary sequences. The introduction of one more such device 5, register 1 and adders 2, 3 modulo two provides the decomposition of the Gold sequence into the generators of the M-sequence with separate decoding of each of them. 3 il. SL U1 AND RY FIG. one

Description

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J5

The invention relates to automation and can be used in information transmission systems, in particular in synchronization systems.

The purpose of the invention is to expand the scope of use by allowing the Gold sequences to be decoded.

FIG. 1 is a block diagram of a binary sequence decoding system; in fig. 2 and 3 are functional diagrams of the first and second major decoding binary sequences, respectively.

Binary sequence decoding system contains a register

I, the first and second adders 2 and 3 modulo two, the first and second devices 4 and 5 of the majority decoding of binary sequences, input 6, the first and second outputs 7 and 8.

The devices 4 and 5 of the majority decoding of binary sequences include (Fig. 2 and 3) the input register 9, the block 1Q checkers, the majority element

I1, an additional register 12 and a determinant of 13 coordinates, Blocks 10 and 13 are executed on adders 14 modulo two connected in accordance with the polynomials of those M-sequences for decoding which are 25

thirty

Golds, consisting of code sequences. The structure of the proposed system and the principle of its operation are universal, i.e. are valid for any pairs of polynomials fj (x) and) of the nth degree generating Gold sequences. In general, the polynomials (k) and their accompanying matrices H have the form

 f (x)., + ... + С, x + С „;

00 ... OCO 10 ... OS, H 01 ... 0C2

00 ... 1С „

where C - weights, taking the value O or 1.

The binary sequence decoding system allows to determine the characters of the generating M-sequences, described by the polynomials f (x) and, as well as all other coordinates of the non-zero elements of the GF (2) fields, by inputting the Gold sequence characters input to register 1.

A rentable system can, without restructuring its structure and parameters, decode 511 Gold code sequences (generally 2 –1).

devices 4 and 5 are assigned. In Figures 2 and 3, examples of the implementation of the input device 35 are given. For the decoding system, no. 4 and 5 for polynomials, respectively, measure the taps of register 1 and its spacing, f, (x) x - x + x + x + 1 and f2 (x), are as follows and 5 4 "( the method of finding is the same for

 5G t X T 5fT Vr 4 V4 4 l

. l l l l .. 9 t g of any pairs of generators of the M-sequence - A pair of polynomials f, (x) x + x «+ x + x telephones).

.and

p f2 (x) x + x + x + x + x + x4x% x +1

describes the M-sequences that give rise to a family of followers. The primitive polynomials f (x) and f j, (x) in this case have accompanying matrices

,

000000001 1 00000000 010000001 001000000 000100000 00001 0000 000001000 000000101 00000001 1

Golds, consisting of code sequences. The structure of the proposed system and the principle of its operation are universal, i.e. are valid for any pairs of polynomials fj (x) and) of the nth degree generating Gold sequences. In general, the polynomials (k) and their accompanying matrices H have the form

 f (x)., + ... + С, x + С „;

00 ... OCO 10 ... OS, H 01 ... 0C2

00 ... 1С „

where C - weights, taking the value O or 1.

The binary sequence decoding system allows to determine the input symbols of register 1, the characters of the generating M-sequences described by the polynomials f (x) and, as well as all other coordinates of the non-zero elements of the GF (2) fields.

A rentable system can, without restructuring its structure and parameters, decode 511 Gold code sequences (generally 2 –1).

entrance. For the decoding system, the number of the taps of register 1 and its spacing are as follows (the method of finding the same for

Primitive polynomials f (x) and f j, (x) in this case have the accompanying matrices

g

000000001 100000001 010000001 001000001 000100001 000010001 00000 100 1 about 0000 1 00 000000011

and the column vectors of the coordinates i-ro and j-ro of the characters of the first and second components, the polynomials f ((x) and f2 (x), in the general case are of the form X; (x °, xj,

n-t

), Xj (x °, x

n-1

H

where a, b; and b: - respectively K-: the symbol of the Gold sequence, the i-th and j-th symbols of the M-sequences.

You can make a system of 2n equations

k .1 + bj ,,;

and

where X. and X j - K-th, coordinates of the i-th and j-ro characters of the first and second components, respectively, KGLO, n-lj; t - transpose sign

The symbols of a certain Gold sequence can be considered as the result of adding modulo two symbols of two generators of M-sequences shifted relative to each other.

 + bj,

 + bj.E

H + 2n-i where each of the symbols of the M-sequences in the npEBbix parts of the equations can be determined using the matrices H and H2 through the set of coordinates of the 1st and JTO symbols of the sequences.

So, using the value of the first rows of the matrices 1 H, - and Hj to some extent t, corresponding to the number of the equation of a system of 2n equations, 2n-ll), this equation can be written

,.her

ak .., hn n., x

where i and hj, - first line mat45

I

rits H, and Hj, respectively.

Given Toroj, what b | .g. ,

 for anyone, solving the system of equations allows us to determine the 0 value of the current characters of the generating M-sequences through the set of characters of the Gold sequence written to register 1, i.e. solve the problem of decoding this sequence. The symbols of the M-sequences, described by the polynomials f, (x) and f2 (x), are found with the help of the Binary Decoding System.

The use of devices of 4 and 5 m of deciphering decoding allows to provide the required error probability of determining all the coordinates of the elements of both components.

Thus, the system makes it possible to decode not only individual M-sequences, but also Gold sequences generated by them.

Claims (1)

Invention Formula terms 1295527 1-i ; .rv .. 4 acres ,, ®В, о a, ®D6-a, j, © D5 "  a ,, © D a., 3®Dio. , a ,. Both ratios for b characters  but, a.Mo®De ак.б®05 and ten ;  five 20 25 thirty 35 40 . can be written in common for these 45 I 0 th binary decoding system characters in a compact form 20-1 B Dg-a p, , 0 where b is the symbols of M-sequences, and from the expanded relations for b and bj it follows that for the characters of the first M-sequence described by the polynomial f (x), the weighting factors for, 3, 4, 5, 6, 10, 3, for the second - at 3, 4, 5, 6, 10, 13, and for other values of FII, weighting coefficients are zero for both components. The binary sequence decoding system works as follows. Gold sequence symbols are sequentially inputted from input 6 to register 1, from the outputs of which they are fed to the inputs of adders 2 and 3 modulo two. Current characters b; and b: from the outputs of adders 2 and 3, go to the corresponding devices 4 and 5 of the majority decoding of binary sequences. Each of devices 4 and 5 is configured to process its M-sequence5 device 4 - to process the components described by the polynomial f (x), and device 5 to the polynomial f (x). One pair of polynomials generates Gold sequences, which ensures decoding of all these sequences without rebuilding the system, The use of devices 4 and 5 of the majority decoding allows to ensure the required error probability of determining all coordinates of the elements of both components. Thus, the system makes it possible to decode not only individual M-sequences, but also Gold sequences generated by them. Invention Formula sequences containing per5-12 A new binary binary sequence decoding device whose outputs are the first outputs of the system, characterized in that, in order to expand the scope of application by providing the possibility of decoding gold sequences, the system has introduced a second binary sequence decoding device and two modulo two, the outputs of which are connected to the inputs of the respective devices of the majority decoding of binary sequences, the inputs of each sum tori modulo two are connected to the th register outputs, for which the weighting factor Dg 1 in the expression 2n-1 g: n, e 5 where b is the symbol of the corresponding component of the input binary sequence; k + in the K-th character of the input binary, the sequence at the em output register; n is the degree of the primitive polynomial of the corresponding component of the input binary sequence, the register input is the system input, the outputs of the second major decoding binary sequences are the second outputs of the system. 2 FIG. five