CN103269225B - Share quasi-cyclic LDPC serial encoder in the deep space communication of memory mechanism - Google Patents

Share quasi-cyclic LDPC serial encoder in the deep space communication of memory mechanism Download PDF

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CN103269225B
CN103269225B CN201310136858.6A CN201310136858A CN103269225B CN 103269225 B CN103269225 B CN 103269225B CN 201310136858 A CN201310136858 A CN 201310136858A CN 103269225 B CN103269225 B CN 103269225B
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CN103269225A (en
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张鹏
刘志文
张燕
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RONGCHENG DINGTONG ELECTRONIC INFORMATION TECHNOLOGY Co Ltd
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Abstract

The invention provides a kind of based on quasi-cyclic LDPC serial encoder in the deep space communication of shared memory mechanism, this encoder comprises the generator polynomial look-up table that 1 prestores circular matrix generator polynomial in all code class generator matrixes, 12 delayers of 1 slip store information bits, 2048 digit buffers of 12 buffer memory generator polynomials, 12 are carried out 2048 binary multipliers of scalar multiplication to information bit and generator polynomial, 12 are carried out to sum of products shift register content 2048 binary adders that mould 2 adds, 12 storages be recycled move to left 1 and 2048 bit shift register.Finally, checking data is contained in 12 shift registers.The quasi-cyclic LDPC code of all code classes in serial encoder provided by the invention compatible CCSDS deep space communication system, has that power consumption is little, structure is simple, memory consumption is few, low cost and other advantages.

Description

Share quasi-cyclic LDPC serial encoder in the deep space communication of memory mechanism
Technical field
The present invention relates to field of channel coding, particularly the serial encoder of quasi-cyclic LDPC code in a kind of CCSDS deep space communication system.
Background technology
Low-density checksum (Low-DensityParity-Check, LDPC) code is one of efficient channel coding technology, and quasi-cyclic LDPC (Quasic-LDPC, QC-LDPC) code is a kind of special LDPC code.The generator matrix G of QC-LDPC code and check matrix H are all the arrays be made up of circular matrix, have the feature of stages cycle, therefore are called as quasi-cyclic LDPC code.The first trip of circular matrix is the result of footline ring shift right 1, and all the other each provisional capitals are results of its lastrow ring shift right 1, and therefore, circular matrix is characterized by its first trip completely.Usually, the first trip of circular matrix is called as its generator polynomial.
CCSDS deep space communication standard have employed the QC-LDPC code of system form, and the left-half of its generator matrix G is a unit matrix, and right half part is by a × c b × b rank circular matrix G i,jthe array that (0≤i<a, a≤j<t, t=a+c) is formed, as follows:
Wherein, I is b × b rank unit matrixs, and 0 is the full null matrix in b × b rank.The continuous b of G capable and b row are called as the capable and block row of block respectively.From formula (1), G has a block capable and t block row.Make g i,jcircular matrix G i,jgenerator polynomial.CCSDS deep space communication standard have employed 9 kinds of QC-LDPC codes, all has c=12.Fig. 1 gives parameter a, b and t under different code class π.
For CCSDS deep space communication standard, the corresponding code word v=(s, p) of generator matrix G, that the front a block row of G are corresponding is information vector s=(e 0, e 1..., e a × b-1), that rear c block row are corresponding is the vectorial p=(d of verification 0, d 1..., d c × b-1).Be one section with b bit, information vector s is divided into a section, i.e. s=(s 0, s 1..., s a-1); Verify vectorial p and be divided into c section, be i.e. p=(p 0, p 1..., p 11).From v=sG, jth-a section verification vector meets
p j-a=s 0G 0,j+s 1G 1,j+…+s iG i,j+…+s a-1G a-1,j(2)
Wherein, 0≤i<a, a≤j<t, t=a+c.Order with generator polynomial g respectively i,jthe result of ring shift right n position and ring shift left n position, wherein, 0≤n≤b.So, i-th on the right of formula (2) equal sign deployable is
s i G i , j = e i &times; b g i , j r ( 0 ) + e i &times; b + l g i , j r ( l ) + &CenterDot; &CenterDot; &CenterDot; + e i &times; b + b - l g i , j r ( b - l ) - - - ( 3 )
At present, what QC-LDPC serial code extensively adopted is the scheme adding accumulator (Type-IShift-Register-Adder-Accumulator, SRAA-I) circuit based on c I type shift register.Fig. 2 is the functional block diagram of single SRAA-I circuit, and information vector s by turn serial sends into this circuit.When with SRAA-I circuit to verification section p j-awhen (a≤j<t) encodes, generator polynomial look-up table prestores all generator polynomials of the jth block row of generator matrix G, and accumulator is cleared initialization.When the 0th clock cycle arrives, shift register loads the 0th piece of row of G, the generator polynomial of jth block row from generator polynomial look-up table information bit e 0move into circuit, and with the content of shift register carry out scalar multiplication, product add with content 0 mould 2 of accumulator, and deposit back accumulator.When the 1st clock cycle arrives, shift register ring shift right 1, content becomes information bit e 1move into circuit, and with the content of shift register carry out scalar multiplication, product with the content of accumulator mould 2 adds, and deposit back accumulator.Above-mentioned-the Jia that moves to right-take advantage of-storing process proceeds down.At the end of b-1 clock cycle, information bit e b-1move into circuit, that now accumulator stores is part and s 0g 0, j, this is message segment s 0to p j-acontribution.When b clock cycle arrives, shift register loads the 1st piece of row of G, the generator polynomial of jth block row from generator polynomial look-up table repeat the above-mentioned-Jia that moves to right-take advantage of-storing process.As message segment s 1when moving into circuit completely, that accumulator stores is part and s 0g 0, j+ s 1g 1, j.Repeat said process, until the whole serial of whole information vector s moves into circuit.Now, that accumulator stores is verification section p j-a.Use the serial encoder shown in c SRAA-I circuit energy pie graph 3, it obtains c verification section within a × b clock cycle simultaneously.The program needs 2 × c × b register, c × b two inputs to input XOR gate with door and c × b individual two, also needs c a × b bit ROM to store the generator polynomial of circular matrix.
For compatible 9 kinds of code classes, in CCSDS deep space communication standard, the existing solution of QC-LDPC serial code is based on 12 SRAA-I circuit, need 49152 registers, 24576 two inputs inputs XOR gate with door and 24576 two, the circular matrix generator polynomial that a ~ t-1 block also needing the ROM of 12 21504 bits to store 9 kinds of generator matrix G respectively arranges.The program has two shortcomings: one be shift register in each clock cycle or load new generator polynomial, or ring shift right 1, causes the storage content of single register constantly to change, and then causes the power consumption of circuit large; Two is that the generator polynomial of circular matrix is dispersed in multiple ROM, as everyone knows, when realizing ROM with the memory in FPGA sheet, inevitably cause the waste of memory, the more wastes of ROM number are more serious, certainly will cause that the memory of circuit is large, cost is high.
Summary of the invention
In CCSDS deep space communication system there is the shortcoming that power consumption is high, memory is large, cost is high in the existing implementation of many yards of class QC-LDPC serial codes, for these technical problems, the invention provides a kind of serial encoder based on shared memory mechanism.
As shown in Figure 5, in CCSDS deep space communication system, the serial encoder of many yards of class QC-LDPC codes forms primarily of 6 parts: generator polynomial look-up table, buffer, b position binary multiplier, b position binary adder, shift register and delayer.Cataloged procedure divides 5 steps to complete: the 1st step, resets delayer D and shift register R 0, R 1..., R 11, according to different code class π, buffer B j-aload the generator polynomial g of generator matrix G i-th piece of row, jth block row from generator polynomial look-up table when i-th × b+j-a clock cycle arrives i,j, and remain unchanged in other moment; 2nd step, when a kth clock cycle arrives, delayer D input information bits e k(0≤k<a × b), buffer B 0, B 1..., B 11in generator polynomial respectively by b position binary multiplier M 0, M 1..., M 11with the data bit D in delayer D 0, D 1..., D 11carry out scalar multiplication, b position binary multiplier M 0, M 1..., M 11product respectively by b position binary adder A 0, A 1..., A 11with shift register R 0, R 1..., R 11content be added, b position binary adder A 0, A 1..., A 11and be recycled the result after 1 that moves to left respectively stored in shift register R 0, R 1..., R 11; 3rd step, with 1 for step-length increases progressively the value changing k, repetition the 2nd step a × b time, until whole information vector s inputs complete; 4th step, when the clock cycle arrives, delayer D inputs filling bit 0, buffer B 0, B 1..., B 11in generator polynomial respectively by b position binary multiplier M 0, M 1..., M 11with the data bit D in delayer D 0, D 1..., D 11carry out scalar multiplication, b position binary multiplier M 0, M 1..., M 11product respectively by b position binary adder A 0, A 1..., A 11with shift register R 0, R 1..., R 11content be added, b position binary adder A 0, A 1..., A 11and be recycled the result after 1 that moves to left respectively stored in shift register R 0, R 1..., R 11; 5th step, repeats the 4th step 12 times, until 12 filling bits 0 input complete, now, and shift register R 0, R 1..., R 11that store is verification section p respectively 0, p 1..., p 11, they constitute the vectorial p=(p of verification 0, p 1..., p 11).
Serial encoder structure provided by the invention is simple, the QC-LDPC code of all code classes in compatible CCSDS deep space communication system, under substantially keeping coding rate and logical resource to expend constant condition, can reduce power consumption, reduce storage requirement, cost-saving.
Be further understood by detailed description and accompanying drawings below about advantage of the present invention and method.
Accompanying drawing explanation
Fig. 1 summarizes parameter a, b and t of 9 kinds of code class QC-LDPC code generator matrixes in CCSDS deep space communication system;
Fig. 2 is the functional block diagram that I type shift register adds accumulator SRAA-I circuit;
Fig. 3 is the QC-LDPC serial encoder be made up of c SRAA-I circuit;
Fig. 4 is the functional block diagram that buffer adds shift register BASR circuit;
Fig. 5 is a kind of QC-LDPC serial encoder based on shared memory mechanism be made up of 12 BASR circuit.
Embodiment
Below in conjunction with accompanying drawing, preferred embodiment of the present invention is elaborated, can be easier to make advantages and features of the invention be readily appreciated by one skilled in the art, thus more explicit defining is made to protection scope of the present invention.
Since by the generator polynomial g of circular matrix i,jring shift right n position is equivalent to its ring shift left b-n position, namely so formula (3) can be rewritten as
s i G i , j = e i &times; b g i , j l ( b ) + e i &times; b + 1 g i , j l ( b - 1 ) + &CenterDot; &CenterDot; &CenterDot; + e i &times; b + b - 1 g i , j l ( 1 )
= ( e i &times; b g i , j ) l ( b ) + ( e i &times; b + l g i , j ) l ( b - 1 ) + &CenterDot; &CenterDot; &CenterDot; + ( e i &times; b + b - l g i , j ) l ( 1 )
= ( 0 + e i &times; b g i , j ) l ( b ) + ( e i &times; b + l g i , j ) l ( b - 1 ) + &CenterDot; &CenterDot; &CenterDot; + ( e i &times; b + b - l g i , j ) l ( 1 ) - - - ( 4 )
= ( ( 0 + e i &times; b g i , j ) l ( 1 ) + e i &times; b + l g i , j ) l ( b - 1 ) + &CenterDot; &CenterDot; &CenterDot; + ( e i &times; b + b - l g i , j ) l ( 1 )
= ( &CenterDot; &CenterDot; &CenterDot; ( ( 0 + e i &times; b g i , j ) l ( 1 ) + e i &times; b + l g i , j ) l ( 1 ) + &CenterDot; &CenterDot; &CenterDot; + e i &times; b + b - l g i , j ) l ( 1 )
Formula (4) is a process taking advantage of-Jia-move to left-store, and its realization buffer adds shift register (Buffer-Adder-Shift-Register, BASR) circuit.Fig. 4 is the functional block diagram of BASR circuit, and information vector s is sent into this circuit by serial by turn.When with BASR circuit to verification section p j-awhen (0≤j<c) encodes, generator polynomial look-up table prestores all generator polynomials of the jth block row of generator matrix G, and shift register is cleared initialization.When the 0th clock cycle arrives, buffer loads the 0th piece of row of G, the generator polynomial g of jth block row from generator polynomial look-up table 0, j, information bit e 0move into circuit, and with the content g of buffer 0, jcarry out scalar multiplication, product e 0g 0, jadd with content 0 mould 2 of shift register, and e 0g 0, jresult (the 0+e of ring shift left 1 0g 0, j) l (1)deposit travelling backwards bit register.When the 1st clock cycle arrives, the content of buffer remains unchanged, information bit e 1move into circuit, and with the content g of buffer 0, jcarry out scalar multiplication, product e 1g 0, jwith the content (0+e of shift register 0g 0, j) l (1)mould 2 adds, and (0+e 0g 0, j) l (1)+ e 1g 0, jthe result ((0+e of ring shift left 1 0g 0, j) l (1)+ e 1g 0, j) l (1)deposit travelling backwards bit register.Above-mentioned-the Jia of taking advantage of-move to left-storing process proceeds down.At the end of b-1 clock cycle, information bit e b-1move into circuit, that now shift register stores is part and s 0g 0, j, this is message segment s 0to p j-acontribution.When b clock cycle arrives, buffer loads the 1st piece of row of G, the generator polynomial g of jth block row from generator polynomial look-up table 1, j, repeat that the above-mentioned-Jia of taking advantage of-move to left-storing process.As message segment s 1when moving into circuit completely, that shift register stores is part and s 0g 0, j+ s 1g 1, j.Repeat said process, until the whole serial of whole information vector s moves into circuit.Now, that shift register stores is verification section p j-a.
Fig. 5 gives a kind of QC-LDPC serial encoder based on shared memory mechanism be made up of 12 BASR circuit, is made up of generator polynomial look-up table, buffer, b position binary multiplier, b position binary adder, shift register and delayer six kinds of functional modules.Generator polynomial look-up table is for storing the generator polynomial of all circular matrixes, and 12 BASR circuit share this look-up table, and timesharing therefrom reads generator polynomial.Buffer B 0, B 1..., B 11buffer memory a, a+1 respectively ..., the generator polynomial of circular matrix in t-1 block row.Buffer B 0, B 1..., B 11in generator polynomial respectively with the data bit D in delayer D 0, D 1..., D 11carry out scalar multiplication, these 12 scalar multiplications are respectively by b position binary multiplier M 0, M 1..., M 11complete.B position binary multiplier M 0, M 1..., M 11product respectively with shift register R 0, R 1..., R 11content be added, these 12 nodulo-2 additions are respectively by b position binary adder A 0, A 1..., A 11complete.B position binary adder A 0, A 1..., A 11and be recycled the result after 1 that moves to left respectively stored in shift register R 0, R 1..., R 11.Data bit D in delayer D 0~ D 11slip storage 12 bit information.
Generator polynomial look-up table stores the circular matrix generator polynomial in all code class QC-LDPC code generator matrixes, for arbitrary yard of class, first stores a in the 0th piece of row successively, a+1 ..., the generator polynomial that t-1 block row are corresponding, store a, a+1 in the 1st piece of row successively again ... the generator polynomial that t-1 block row are corresponding, the rest may be inferred, finally store successively a-1 block capable in a, a+1,, the generator polynomial that t-1 block row are corresponding.
The invention provides a kind of QC-LDPC serial encoding method based on shared memory mechanism, 9 kinds of code class QC-LDPC codes in its compatible CCSDS deep space communication standard, its coding step is described below:
1st step, resets delayer D and shift register R 0, R 1..., R 11, according to different code class π, buffer B j-aload the generator polynomial g of generator matrix G i-th piece of row, jth block row from generator polynomial look-up table when i-th × b+j-a clock cycle arrives i,j, and remain unchanged in other moment;
2nd step, when a kth clock cycle arrives, delayer D input information bits e k(0≤k<a × b), buffer B 0, B 1..., B 11in generator polynomial respectively by b position binary multiplier M 0, M 1..., M 11with the data bit D in delayer D 0,d 1 ...,d 11carry out scalar multiplication, b position binary multiplier M 0,m 1 ...,m 11product respectively by b position binary adder A 0, A 1..., A 11with shift register R 0, R 1..., R 11content be added, b position binary adder A 0, A 1..., A 11and be recycled the result after 1 that moves to left respectively stored in shift register R 0, R 1..., R 11;
3rd step, with 1 for step-length increases progressively the value changing k, repetition the 2nd step a × b time, until whole information vector s inputs complete;
4th step, when the clock cycle arrives, delayer D inputs filling bit 0, buffer B 0, B 1..., B 11in generator polynomial respectively by b position binary multiplier M 0, M 1..., M 11with the data bit D in delayer D 0, D 1..., D 11carry out scalar multiplication, b position binary multiplier M 0, M 1..., M 11product respectively by b position binary adder A 0, A 1..., A 11with shift register R 0, R 1..., R 11content be added, b position binary adder A 0, A 1..., A 11and be recycled the result after 1 that moves to left respectively stored in shift register R 0, R 1..., R 11;
5th step, repeats the 4th step 12 times, until 12 filling bits 0 input complete, now, and shift register R 0, R 1..., R 11that store is verification section p respectively 0, p 1..., p 11, they constitute the vectorial p=(p of verification 0, p 1..., p 11).
Be not difficult to find out from above step, whole cataloged procedure needs a × b+12 clock cycle altogether, more than the existing serial encoding method based on 12 SRAA-I circuit 12 clock cycle.For 9 kinds of QC-LDPC codes that CCSDS deep space communication standard adopts, a × b has 16384,4096,1,024 three kinds of possibilities.12 3 ~ 4 magnitudes less of a × b, can ignore.Visible, the speed of two kinds of coding methods is substantially identical.
In CCSDS deep space communication standard, the existing solution of QC-LDPC serial code needs 49152 registers, 24576 two inputs inputs XOR gate with door and 24576 two, and the present invention needs 49164 registers, 24576 two inputs and door and 24576 two to input XOR gate.Two kinds of coding methods expend equal number with door and XOR gate, the present invention is multiplex 12 registers.12 much smaller than 49152, can ignore.Visible, the register that two kinds of coding methods expend is also substantially identical.
To sum up, two kinds of coding methods have almost identical coding rate and logical resource to expend.But the present invention has two clear superiorities, overcome the shortcoming of the existing solution of QC-LDPC serial code in CCSDS deep space communication standard.In existing solution, shift register is in each clock cycle or load new generator polynomial, ring shift right 1, the storage content of single register constantly changes and causes the power consumption of circuit large, and the present invention uses the generator polynomial of buffer load circular matrix, without the need to loopy moving, the every b of its content clock cycle change once, significantly reduces power consumption.This is first advantage of the present invention.Second advantage adopts to share memory mechanism, single ROM and same data/address bus is used to realize generator polynomial look-up table, overcome that the waste that in existing solution, multiple ROM brings is many, memory is large, cost high shortcoming, enormously simplify the project organization of generator polynomial look-up table, farthest save memory space, reduce cost.
In brief, for the serial code of 9 kinds of QC-LDPC codes in CCSDS deep space communication standard, compared with existing solution, the present invention maintains identical coding rate substantially and logical resource expends, and has that power consumption is little, structure is simple, memory consumption is few, low cost and other advantages.
The above; be only one of the specific embodiment of the present invention; but protection scope of the present invention is not limited thereto; any those of ordinary skill in the art are in the technical scope disclosed by the present invention; the change can expected without creative work or replacement, all should be encompassed within protection scope of the present invention.Therefore, the protection range that protection scope of the present invention should limit with claims is as the criterion.

Claims (3)

1. a quasi-cyclic LDPC serial encoder in the deep space communication of shared memory mechanism, the generator matrix G of quasi-cyclic LDPC code is divided into the capable and t block row of a block, and the part generator matrix that rear c block row are corresponding is by a × c b × b rank circular matrix G i,jthe array formed, g i,jcircular matrix G i,jgenerator polynomial, wherein, t=a+c, a, b, c, i, j and t is nonnegative integer, 0≤i<a, a≤j<t, CCSDS deep space communication standard have employed the quasi-cyclic LDPC code of 9 kinds of different code class π, π is 0 respectively, 1, 2, 3, 4, 5, 6, 7, 8, for these 9 kinds different code class quasi-cyclic LDPC codes, all there is c=12, parameter a corresponding to 9 kinds of different code classes is 8 respectively, 8, 8, 16, 16, 16, 32, 32, 32, parameter b corresponding to 9 kinds of different code classes is 2048 respectively, 512, 128, 1024, 256, 64, 512, 128, 32, parametric t corresponding to 9 kinds of different code classes is 20 respectively, 20, 20, 28, 28, 28, 44, 44, 44, the corresponding code word v=(s of generator matrix G, p), that the front a block row of G are corresponding is information vector s=(e 0, e 1..., e a × b-1), that rear c block row are corresponding is the vectorial p of verification, is one section, verifies vectorial p and be divided into c section, be i.e. p=(p with b bit 0, p 1..., p 11), it is characterized in that, described encoder comprises following parts:
Generator polynomial lookup table memories, for storing the generator polynomial of circular matrix in all generator matrix G;
Delayer D, its data bit D 0, D 1..., D 11slip storage 12 bit information;
Buffer B 0, B 1..., B 11, share generator polynomial lookup table memories, timesharing therefrom reads generator polynomial, buffer B j-aload the generator polynomial g of generator matrix G i-th piece of row, jth block row from generator polynomial lookup table memories when i-th × b+j-a clock cycle arrives i,j, and remain unchanged in other moment;
B position binary multiplier M 0, M 1..., M 11, respectively to data bit D 0, D 1..., D 11with buffer B 0, B 1..., B 11in generator polynomial carry out scalar multiplication;
B position binary adder A 0, A 1..., A 11, respectively to b position binary multiplier M 0, M 1..., M 11sum of products shift register R 0, R 1..., R 11content carry out mould 2 and add;
Shift register R 0, R 1..., R 11, store b position binary adder A respectively 0, A 1..., A 11and be recycled the move to left result after 1 and final verification section p 0, p 1..., p 11.
2. quasi-cyclic LDPC serial encoder in the deep space communication of a kind of shared memory mechanism according to claim 1, it is characterized in that, described generator polynomial lookup table memories stores the circular matrix generator polynomial in all code class quasi-cyclic LDPC code generator matrixes, for arbitrary yard of class, first store a in the 0th piece of row successively, a+1, the generator polynomial that t-1 block row are corresponding, store a in the 1st piece of row successively again, a+1, the generator polynomial that t-1 block row are corresponding, the rest may be inferred, last store successively a-1 block capable in a, a+1, the generator polynomial that t-1 block row are corresponding.
3. a quasi-cyclic LDPC serial encoding method in the deep space communication of shared memory mechanism, the generator matrix G of quasi-cyclic LDPC code is divided into the capable and t block row of a block, and the part generator matrix that rear c block row are corresponding is by a × c b × b rank circular matrix G i,jthe array formed, g i,jcircular matrix G i,jgenerator polynomial, wherein, t=a+c, a, b, c, i, j and t is nonnegative integer, 0≤i<a, a≤j<t, CCSDS deep space communication standard have employed the quasi-cyclic LDPC code of 9 kinds of different code class π, π is 0 respectively, 1, 2, 3, 4, 5, 6, 7, 8, for these 9 kinds different code class quasi-cyclic LDPC codes, all there is c=12, parameter a corresponding to 9 kinds of different code classes is 8 respectively, 8, 8, 16, 16, 16, 32, 32, 32, parameter b corresponding to 9 kinds of different code classes is 2048 respectively, 512, 128, 1024, 256, 64, 512, 128, 32, parametric t corresponding to 9 kinds of different code classes is 20 respectively, 20, 20, 28, 28, 28, 44, 44, 44, the corresponding code word v=(s of generator matrix G, p), that the front a block row of G are corresponding is information vector s=(e 0, e 1..., e a × b-1), that rear c block row are corresponding is the vectorial p of verification, is one section, verifies vectorial p and be divided into c section, be i.e. p=(p with b bit 0, p 1..., p 11), it is characterized in that, described coding method comprises the following steps:
1st step, resets delayer D and shift register R 0, R 1..., R 11, buffer B 0, B 1..., B 11share generator polynomial lookup table memories, timesharing therefrom reads generator polynomial, according to different code class π, buffer B j-aload the generator polynomial g of generator matrix G i-th piece of row, jth block row from generator polynomial lookup table memories when i-th × b+j-a clock cycle arrives i,j, and remain unchanged in other moment;
2nd step, when a kth clock cycle arrives, delayer D input information bits e k, buffer B 0, B 1..., B 11in generator polynomial respectively by b position binary multiplier M 0, M 1..., M 11with the data bit D in delayer D 0, D 1..., D 11carry out scalar multiplication, b position binary multiplier M 0, M 1..., M 11product respectively by b position binary adder A 0, A 1..., A 11with shift register R 0, R 1..., R 11content be added, b position binary adder A 0, A 1..., A 11and be recycled the result after 1 that moves to left respectively stored in shift register R 0, R 1..., R 11, wherein, 0≤k<a × b;
3rd step, with 1 for step-length increases progressively the value changing k, repetition the 2nd step a × b time, until whole information vector s inputs complete;
4th step, when the clock cycle arrives, delayer D inputs filling bit 0, buffer B 0, B 1..., B 11in generator polynomial respectively by b position binary multiplier M 0, M 1..., M 11with the data bit D in delayer D 0, D 1..., D 11carry out scalar multiplication, b position binary multiplier M 0, M 1..., M 11product respectively by b position binary adder A 0, A 1..., A 11with shift register R 0, R 1..., R 11content be added, b position binary adder A 0, A 1..., A 11and be recycled the result after 1 that moves to left respectively stored in shift register R 0, R 1..., R 11;
5th step, repeats the 4th step 12 times, until 12 filling bits 0 input complete, now, and shift register R 0, R 1..., R 11that store is verification section p respectively 0, p 1..., p 11, they constitute the vectorial p=(p of verification 0, p 1..., p 11).
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