Embodiment
Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.
For a kind of single-place shift matrix A of QC-LDPC code
i, j, define its shift index e
i, jif, e
i, j=a, 1≤a≤b, b is parameter submatrix exponent number, then represent A
i, jthe a of the 1st row is classified as 1, and all the other are classified as 0, and all the other each row are all ring shift rights one of lastrow; If e
i, j=0, then represent A
i, jit is full null matrix.
Such as, e
i, j=a=4, b=5, then represent A
i, jthe 4th of 1st row is classified as 1, and all the other are classified as 0, and all the other each row are all ring shift rights one of lastrow, and its structure is as follows:
Based on the character of single-place shift matrix, for making full use of the characteristic of row combine code and department's row combine code, the present invention proposes a kind of building method for code modulated QC-LDPC code.
As shown in Figure 1, described building method comprises the following steps:
S101, build female code offset address matrix E of QC-LDPC code, and to set submatrix exponent number be b, wherein,
Described matrix E is the matrix of the capable 12M row of 12M, and M is positive integer, the shift index e of described matrix E
i, jmeet 0≤e
i, j≤ b;
S102, described matrix E adds water index obtain matrix E ', the shift index e ' of described matrix E '
i, jmeet 0≤e '
i, j≤ b,
Described matrix E ' adds water index and obtains matrix E ", described matrix E " shift index e "
i, jmeet 0≤e "
i, j≤ b,
Described matrix E " above add water index obtain matrix E " ', described matrix E " ' shift index e " '
i, jmeet 0≤e " '
i, j≤ b;
S103, calculating code check are the offset address matrix E of the QC-LDPC code of 1/2
(1/2), wherein, described matrix E
(1/2)shift index
computing formula be:
1≤i≤6M,1≤j≤12M;
S104, calculating code check are the offset address matrix E of the QC-LDPC code of 2/3
(2/3), wherein, described matrix E
(2/3)shift index
computing formula be:
1≤i≤4M,1≤j≤12M;
S105, calculating code check are the offset address matrix E of the QC-LDPC code of 3/4
(3/4), wherein, described matrix E
(3/4)shift index
computing formula be:
1≤i≤3M,1≤j≤12M;
S106, calculating code check are the offset address matrix E of the QC-LDPC code of 5/6
(5/6), wherein, described matrix E
(5/6)shift index
computing formula be:
1≤i≤2M,1≤j≤12M;
S107, according to described matrix E
(1/2)with described submatrix exponent number b, generate the QC-LDPC code that code check is 1/2, code length is 12M*b,
According to described matrix E
(2/3)with described submatrix exponent number b, generate the QC-LDPC code that code check is 2/3, code length is 12M*b,
According to described matrix E
(3/4)with described submatrix exponent number b, generate the QC-LDPC code that code check is 3/4, code length is 12M*b,
According to described matrix E
(5/6)with described submatrix exponent number b, generate the QC-LDPC code that code check is 5/6, code length is 12M*b.
Optionally, step is comprised further after step S107:
S108, the numerical value of described submatrix exponent number b is revised as b ', wherein, described submatrix exponent number b ' meets
b′≥e
i,j,e′
i,j,e″
i,j,e″′
i,j,
S109, according to described matrix E
(1/2)with described submatrix exponent number b ', generate the QC-LDPC code that code check is 1/2, code length is 12M*b ',
According to described matrix E
(2/3)with described submatrix exponent number b ', generate the QC-LDPC code that code check is 2/3, code length is 12M*b ',
According to described matrix E
(3/4)with described submatrix exponent number b ', generate the QC-LDPC code that code check is 3/4, code length is 12M*b ',
According to described matrix E
(5/6)with described submatrix exponent number b ', generate the QC-LDPC code that code check is 5/6, code length is 12M*b '.
Utilize above-mentioned building method, a kind of multi code Rate of Chinese character QC-LDPC code can be obtained, comprise the FEC forward error correction coding of 4 kinds of code checks:
1, code check is (12M*b, 6M*b) code of 1/2, and offset address matrix is designated as:
2, code check is (12M*b, 8M*b) code of 2/3, and offset address matrix is designated as:
3, code check is (12M*b, 9M*b) code of 3/4, and offset address matrix is designated as:
4, code check is (12M*b, 10M*b) code of 5/6, and offset address matrix is designated as:
Wherein, M is positive integer, and b is submatrix exponent number, and different code check shift index is all more than or equal to 0 and is less than or equal to b.
The offset address matrix construction step of above-mentioned different code check QC-LDPC code is as follows:
S101, the capable 12M column matrix of note 12M:
E=[e
i,j]
12M×12M;
S102, the capable 12M column matrix of note 12M:
E′=[e′
i,j]
12M×12M,
E″=[e″
i,j]
12M×12M,
E″′=[e"
i,j]
12M×12M,
Wherein, E ' obtains by E basis being added water index, E " obtain by E ' basis being added water index, on E " ' by E " basis, interpolation water index obtains,
And e
i, j, e '
i, j, e "
i, j, e " '
i, jall be more than or equal to 0, be less than or equal to b;
S103, code check are (12M*b, 6M*b) code of 1/2, and its 6M capable 12M line skew address matrix is designated as:
E
(1/2)calculated by E=[ei, j] 12M × 12M, wherein,
1≤i≤6M,1≤j≤12M;
S 104, code check are (12M*b, 8M*b) code of 2/3, and its 4M capable 12M line skew address matrix is designated as:
E
(2/3)by E '=[e '
i, j]
12M × 12Mcalculate, wherein,
1≤i≤4M,1≤j≤12M,
That is, (12M*b, 6M*b) code with the pass of (12M*b, 8M*b) code is, the new water index added of removing, the i-th, i+2M, i+4M of E (1/2) passes through after space split degree, obtains E
(2/3)the i-th, i+2M capable, 1≤i≤2M;
S105, code check are (12M*b, 9M*b) code of 3/4, and its 3M capable 12M line skew address matrix is designated as:
E
(3/4) by E "=[e "
i, j]
12M × 12Mcalculate, wherein,
1≤i≤3M,1≤j≤12M,
That is, the pass of (12M*b, 6M*b) code of 1/2 code check and (12M*b, 9M*b) code of 3/4 code check is, the new water index added of removing, E
(1/2)the i-th, i+3M pass through space merge after, obtain E
(3/4)the i-th row, 1≤i≤3M;
S106, code check are (12M*b, 10M*b) code of 5/6, and its 2M capable 12M line skew address matrix is designated as:
E
(5/6)by E " '=[e " '
i, j]
12M × 12Mcalculate, wherein,
1≤i≤2M,1≤j≤12M,
That is, the pass of (12M*b, 8M*b) code of 2/3 code check and (12M*b, 10M*b) code of 5/6 code check is, the new water index added of removing, E
(2/3)the i-th, i+2M pass through space merge after, obtain E
(5/6)the i-th row, 1≤i≤2M;
S107, offset address matrix E by 4 kinds of code checks
(1/2), E
(2/3), E
(3/4), E
(5/6)with submatrix exponent number b, obtain the QC-LDPC code that these 4 kinds of code check code lengths are 12M*b.
In order to expand the range of application of above-mentioned QC-LDPC code, making full use of the quasi-cyclic of check matrix, under identical offset address conditioned matrix, by changing submatrix exponent number b to realize many code lengths scheme, other multiple business can be applicable to.For this reason, the building method of the present invention's proposition is further comprising the steps:
S108, submatrix exponent number is revised as b ', wherein, b ' must be more than or equal to different code check shift index;
S 109, offset address matrix E by above-mentioned 4 kinds of code checks
(1/2), E
(2/3), E
(3/4), E
(5/6)with new submatrix exponent number b ', obtain the QC-LDPC code that these new 4 kinds of code check code lengths are 12M*b '.
Repeat step S108 and S109, can obtain the QC-LDPC code character of 4 kinds of multiple code lengths of code-rate-compatible, wherein, the offset address matrix of above-mentioned multiple code length QC-LDPC code is E
(1/2), E
(2/3), E
(3/4), E
(5/6), the offset address matrix of above-mentioned 4 kinds of code checks can compatible multiple code length.
More about the decoding algorithm of LDPC at present, Application comparison is the belief propagation algorithm (Belief Propagation Algorithm, BP) based on log-likelihood ratio (Logarithm Likelihood Ratio, LLR) Soft Inform ation widely.BP algorithm forms primarily of two decoding calculation step alternating iteration, i.e. operation of horizontal (Horizontal Process, HP) and vertical computing (Vertical Process, VP).Operation of horizontal by HPU(Horizontal Process Unit, horizontal arithmetic unit) perform, vertical computing by VPU(Vertical Process Unit, vertical arithmetic element) perform.For the multi code Rate of Chinese character QC-LDPC code that the present invention constructs, the HPU of different code check decoder can be multiplexing after simple combination, forms multi code Rate of Chinese character unification HPU; The VPU of different code check decoder can be completely multiplexing, forms multi code Rate of Chinese character unification VPU.Unify HPU/VPU by multi code Rate of Chinese character and can form the decoder obtaining multi code Rate of Chinese character and unify.So, based on the multi code Rate of Chinese character QC-LDPC code structural scheme that the present invention proposes, relatively low hardware implementing complexity can be ensured under the prerequisite obtaining premium properties simultaneously.
Below by specific embodiment, detailed explanation is carried out to the building method of the QC-LDPC code that the present invention proposes.
Embodiment 1:
Multi code Rate of Chinese character many code lengths QC-LDPC code that the present embodiment constructs, comprises the FEC forward error correction coding of 4 kinds of code checks, 2 kinds of code lengths:
1, code check is 1/2-b128 code (15360,7680) and the 1/2-b512 code (61440,30720) of 1/2, and these two codes have identical offset address matrix, are designated as:
Difference is the former parameter b=128, the latter parameter b=512;
2, code check is 2/3-b128 code (15360,10240) and the 2/3-b512 code (61440,40960) of 2/3, and these two codes have identical offset address matrix, are designated as:
Difference is the former parameter b=128, the latter parameter b=512;
3, code check is 3/4-b128 code (15360,11520) and the 3/4-b512 code (61440,46080) of 3/4, and these two codes have identical offset address matrix, are designated as:
Difference is the former parameter b=128, the latter parameter b=512;
4, code check is 5/6-b128 code (15360,12800) and the 5/6-b512 code (61440,51200) of 5/6, and these two codes have identical offset address matrix, are designated as:
Difference is the former parameter b=128, the latter parameter b=512.
The parameter of above-mentioned multi code Rate of Chinese character many code lengths QC-LDPC code is as shown in table 1:
The multiple code length QC-LDPC code parameters of table 1 various code rate
The construction step of the offset address matrix of 4 kinds of code checks, 2 kinds of code length QC-LDPC codes in the present embodiment is described below:
S101, note matrix E=[e
i, j]
120 × 120be 120 row 120 column matrix, the shift index of matrix E is provided by annex;
S102, note matrix E '=[e '
i, j]
120 × 120be 120 row 120 column matrix, wherein:
Note matrix E "=[e "
i, j]
120 × 120be 120 row 120 column matrix, wherein:
Note matrix E " '=[e " '
i, j]
120 × 120be 120 row 120 column matrix, wherein:
S103, code check are 1/2-b128 code (15360,7680) and the 1/2-b512 code (61440,30720) of 1/2, and their offset address matrix is designated as:
E (
1/2)be 60 row 120 column matrix, wherein,
1≤i≤60,1≤j≤120;
S104, code check are 2/3-b128 code (15360,10240) and the 2/3-b512 code (61440,40960) of 2/3, and their offset address matrix is designated as:
E
(2/3)be 40 row 120 column matrix, wherein,
1≤i≤40,1≤j≤120;
S105, code check are 3/4-b128 code (15360,11520) and the 3/4-b512 code (61440,46080) of 3/4, and their offset address matrix is designated as:
E
(3/4)be 30 row 120 column matrix, wherein,
1≤i≤30,1≤j≤120;
S106, code check are 5/6-b128 code (15360,12800) and the 5/6-b512 code (61440,51200) of 5/6, and their offset address matrix is designated as:
E
(5/6)be 20 row 120 column matrix, wherein,
1≤i≤20,1≤j≤120。
Embodiment 2:
The present embodiment slightly makes improvements the shift index of b=128 short code in embodiment 1:
S1, in embodiment 1, obtain 4 kinds of code checks offset address matrix be:
Code check is 1/2
Code check is the E of 2/3
Code check is 3/4
Code check is 5/6
S2, note improve after code check be 1/2 1/2-b128 code (15360,7680) offset address matrix be:
Wherein,
S3, note improve after code check be 2/3 2/3-b128 code (15360,10240) offset address matrix be:
Wherein,
S4, note improve after code check be 3/4 3/4-b128 code (15360,11520) offset address matrix be:
Wherein,
S5, note improve after code check be 5/6 5/6-b128 code (15360,12800) offset address matrix be:
Wherein,
The feature of a kind of many code lengths QC-LDPC code that the present embodiment constructs is, on the basis of long code QC-LDPC code offset address matrix, is obtained the QC-LDPC code offset address matrix of short code by amendment parton matrix.Wherein the amendment of parton matrix is specially: one or more cyclic determinant submatrix is revised as complete zero submatrix, or one or more complete zero submatrix is revised as cyclic determinant submatrix.
Based on the described building method for code modulated QC-LDPC code, the present invention proposes a kind of code modulating method simultaneously, and as shown in Figure 2, described code modulating method comprises the following steps:
S201, the described building method for code modulated QC-LDPC code of employing, obtain QC-LDPC code;
S202, utilize described QC-LDPC code, information bit waiting for transmission is encoded, obtains coded-bit;
S203, bit mapping is carried out to described coded-bit, obtain constellation bit vectors;
S204, constellation mapping is carried out to described constellation bit vectors, obtain constellation symbol;
S205, described constellation symbol is sent to subsequent processing units.
Preferably, the code length of described QC-LDPC code is 61440 or 15360.
Preferably, step S203 specifically comprises:
S203-1, Bit Interleave is carried out to described coded-bit, obtain interleaving bits;
S203-2, bit permutation is carried out to described interleaving bits, obtains the bit vectors after replacing, and the bit vectors after described displacement is split, obtain described constellation bit vectors,
Wherein, described bit permutation refers to and all bits be mapped in one or more constellation symbol is carried out order adjustment.
Preferably, step S204 specifically comprises:
The APSK constellation of described constellation bit vectors being carried out to M point maps or qam constellation mapping, obtains described constellation symbol,
Wherein, the value of described M is 4,16,64 or 256.
Preferably, step S205 comprises further:
Described constellation symbol is carried out coordinate intertexture and symbol interleaving, then sends to described subsequent processing units.
In step S202, LDPC coding is carried out to information bit waiting for transmission, obtains coded-bit
wherein NLDPC represents that LDPC code is long.
Preferably, the code length of described LDPC code is 61440 or 15360, and code check is 1/2,2/3,3/4 or 5/6.
In step S203, bit mapping is carried out to described coded-bit, obtain constellation bit vectors, as the result of bit mapping.Wherein, first bit mapping carries out interleaving treatment to coded-bit, then intertexture result is combined as bit vectors.
Preferably, described bit mapping specifically comprises the steps:
S203-1, Bit Interleave is carried out to gained coded-bit, obtain interleaving bits.
Wherein, the feature of described Bit Interleave is, coded-bit c is write by row line by line the buffering area of the capable b row of L, obtains Matrix C, namely
Interior intertexture gone to Matrix C, obtains matrix
namely
Wherein c
lwith
respectively representing matrix C and
l capable, 1≤l<L.Will
read by column by row, obtain interleaving bits
Wherein, a kind of optimal way interweaved in row is,
and the corresponding relation between the row of C and row is as follows: make lm=mod (l, m) represent the remainder of l mould m,
wherein
represent and round downwards, m=log
2m, M represent the exponent number of follow-up constellation mapping; Then
Preferably, the value of parameter L is the value of L=120, parameter b is b=N
lDPC/ L, that is, work as N
lDPCwhen=61440, b=512, works as N
lDPCwhen=15360, b=128.
S203-2, the bit permutation of to carry out successively described interleaving bits in one or more constellation symbol, be called for short bit permutation, obtains the bit vectors after replacing, split, obtain constellation bit vectors, as the result of bit mapping to the bit vectors after displacement.
Wherein, described bit permutation refers to and all bits be mapped in one or more constellation symbol is carried out order adjustment.
The concrete steps of bit permutation are, will
every q successive bits be classified as one group, obtain bit vectors
wherein the value of q is the positive integer times of m, and the bit vectors arranged after changing is
then
with
corresponding relation be
0≤i < q, wherein p=(p
0, p
1..., p
q-1) be called bit permutation pattern.
Wherein, the bit vectors after displacement is split, it is characterized in that, will
every m successive bits be classified as one group, obtain one or more constellation bit vectors b=(b
0, b
1..., b
m-1).
In step S204, the APSK constellation of described constellation bit vectors being carried out to M point maps or qam constellation mapping, obtains constellation symbol.Wherein, M's can selected value be 4,16,64 and 256.
Wherein, the feature of described M point APSK constellation figure is, all constellation point are distributed in N
ron individual donut, the radius of each annulus is ascending to be followed successively by
each ring has identical number of constellation points, is set to M
c, therefore M=N
r× M
c, the constellation point on each ring is uniformly distributed in phase place [0,2 π), initial phase is deflected to θ
0.Therefore, planisphere can represent with following formula:
Wherein, j is imaginary unit
n=0,1 ..., N
r-1, k=0,1 ..., M
c-1.
Preferably, if M=4, then θ
0=0; If M=16,64,256, then θ
0=π/M
c.
Preferably, when different M, annulus number N
r, number of constellation points M on each ring
c, each ring radius r value as shown in table 2, and each ring radius can zoom in or out in proportion.
Table 2 constellation mapping parameter list
In step S205, give subsequent processing units by the constellation symbol obtained, or, coordinate intertexture and symbol interleaving are carried out to described constellation symbol, then is sent to subsequent processing units.
The above is only the preferred embodiment of the present invention; it should be pointed out that for the person of ordinary skill of the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and replacement, these improve and replace and also should be considered as protection scope of the present invention.
Annex
e[1,3]=111 e[2,21]=95 e[3,34]=33 e[4,62]=116
e[1,11]=98 e[2,39]=72 e[3,66]=1 e[5,2]=8
e[1,39]=43 e[2,65]=1 e[4,5]=13 e[5,17]=40
e[1,56]=98 e[3,7]=35 e[4,8]=74 e[5,68]=1
e[2,1]=29 25 e[3,11]=54 30 e[4,45]=63 35 e[6,2]=115
e[6,10]=49 e[13,11]=81 55 e[20,6]=30 e[66,59]=95
e[6,56]=100 e[13,27]=48 e[20,16]=106 e[67,16]=12
e[6,69]=1 30 e[13,74]=17 e[20,83]=1 e[67,21]=70
e[7,6]=39 e[14,3]=17 e[61,4]=62 85 e[67,59]=84
e[7,12]=115 e[14,8]=31 e[61,16]=32 e[67,70]=1
e[7,43]=33 e[14,12]=126 60 e[61,47]=126 e[68,10]=29
e[8,1]=41 e[14,63]=71 e[61,64]=1 e[68,27]=35
e[8,7]=6 35 e[15,9]=43 e[62,6]=59 e[68,43]=70
e[8,16]=91 e[15,12]=60 e[62,13]=101 90 e[68,48]=34
e[8,71]=1 e[15,15]=25 e[62,15]=111 e[69,14]=57
e[9,3]=83 e[15,51]=101 65 e[62,47]=39 e[69,30]=102
e[9,6]=98 e[16,10]=91 e[63,1]=9 e[69,42]=4
e[9,15]=120 40 e[16,11]=52 e[63,15]=111 e[69,72]=1
e[9,35]=85 e[16,15]=25 e[63,59]=98 95 e[70,1]=63
e[10,8]=20 e[16,77]=78 e[63,63]=91 e[70,11]=122
e[10,17]=33 e[16,79]=1 70 e[64,9]=44 e[70,45]=68
e[10,21]=112 e[17,16]=57 e[64,16]=73 e[70,73]=1
e[10,42]=37 45 e[17,78]=48 e[64,27]=41 e[71,4]=83
e[11,5]=63 e[17,80]=1 e[64,67]=1 100 e[71,16]=124
e[11,13]=44 e[18,1]=57 e[65,9]=25 e[71,34]=80
e[11,49]=101 e[18,10]=47 75 e[65,15]=24 e[71,74]=1
e[11,73]=127 e[18,11]=26 e[65,43]=41 e[72,6]=115
e[12,34]=3 50 e[18,16]=34 e[65,49]=126 e[72,9]=20
e[12,42]=88 e[19,14]=7 e[65,56]=76 105 e[72,18]=51
e[12,64]=24 e[19,17]=35 e[66,12]=44 e[73,6]=110
e[12,75]=1 e[19,81]=71 80 e[66,14]=122 e[73,18]=25
e[13,2]=127 e[20,2]=72 e[66,45]=50 e[73,35]=95
e[73,76]=1 e[81,1]=59 55 e[84,58]=43 e[87,90]=1
e[74,16]=75 e[81,5]=117 e[84,60]=35 e[88,4]=5
e[74,49]=68 30 e[81,13]=18 e[84,76]=74 e[88,5]=112
e[74,75]=92 e[81,17]=127 e[84,87]=1 85 e[88,11]=114
e[74,77]=1 e[81,29]=87 e[85,1]=69 e[88,17]=81
e[75,69]=104 e[81,30]=92 60 e[85,5]=34 e[88,25]=9
e[75,71]=67 e[81,51]=123 e[85,12]=90 e[88,46]=59
e[75,78]=1 35 e[81,84]=1 e[85,18]=17 e[88,90]=29
e[76,4]=60 e[82,3]=13 e[85,25]=5 90 e[88,91]=1
e[76,29]=13 e[82,7]=67 e[85,58]=23 e[89,1]=74
e[76,32]=2 e[82,9]=47 65 e[85,79]=2 e[89,9]=44
e[77,7]=113 e[82,18]=13 e[85,88]=1 e[89,10]=113
e[77,14]=58 40 e[82,31]=64 e[86,3]=76 e[89,16]=78
e[77,29]=6 e[82,67]=19 e[86,8]=35 95 e[89,46]=114
e[77,58]=45 e[82,84]=93 e[86,11]=66 e[89,52]=7
e[78,35]=121 e[82,85]=1 70 e[86,15]=77 e[89,89]=4
e[78,51]=8 e[83,8]=84 e[86,24]=114 e[89,92]=1
e[78,80]=102 45 e[83,13]=79 e[86,55]=85 e[90,2]=15
e[78,81]=1 e[83,18]=74 e[86,82]=10 100 e[90,6]=54
e[79,6]=46 e[83,32]=115 e[86,89]=1 e[90,13]=34
e[79,25]=51 e[83,60]=123 75 e[87,1]=17 e[90,16]=62
e[79,32]=4 e[83,83]=126 e[87,7]=112 e[90,24]=78
e[79,82]=1 50 e[83,86]=1 e[87,14]=30 e[90,61]=92
e[80,11]=77 e[84,3]=38 e[87,15]=53 105 e[90,87]=92
e[80,30]=79 e[84,6]=59 e[87,31]=44 e[90,93]=1
e[80,31]=57 e[84,10]=10 80 e[87,60]=1 e[91,7]=1
e[80,41]=19 e[84,17]=102 e[87,88]=2 e[91,12]=6
e[91,17]=116 e[94,97]=1 55 e[98,12]=47 e[101,38]=16
e[91,24]=100 e[95,1]=58 e[98,18]=60 e[101,102]=101
e[91,65]=101 30 e[95,8]=7 e[98,62]=34 e[101,104]=1
e[91,72]=59 e[95,14]=91 e[98,68]=20 85 e[102,4]=65
e[91,94]=1 e[95,18]=119 e[98,95]=113 e[102,8]=120
e[92,2]=44 e[95,46]=14 60 e[98,101]=1 e[102,10]=65
e[92,7]=23 e[95,61]=22 e[99,1]=117 e[102,17]=108
e[92,11]=116 35 e[95,94]=21 e[99,9]=15 e[102,37]=41
e[92,17]=25 e[95,98]=1 e[99,11]=21 90 e[102,66]=82
e[92,36]=90 e[96,1]=36 e[99,18]=59 e[102,103]=43
e[92,52]=38 e[96,6]=32 65 e[99,40]=11 e[102,105]=1
e[92,85]=60 e[96,13]=24 e[99,66]=26 e[103,3]=1
e[92,95]=1 40 e[96,17]=26 e[99,97]=122 e[103,9]=68
e[93,8]=46 e[96,55]=53 e[99,102]=1 95 e[103,12]=51
e[93,12]=67 e[96,70]=68 e[100,3]=110 e[103,17]=105
e[93,16]=20 e[96,98]=118 70 e[100,5]=99 e[103,57]=52
e[93,36]=57 e[96,99]=1 e[100,12]=64 e[103,61]=49
e[93,41]=73 45 e[97,2]=103 e[100,18]=83 e[103,100]=101
e[93,91]=69 e[97,5]=83 e[100,40]=123 100 e[103,106]=1
e[93,96]=1 e[97,15]=26 e[100,53]=105 e[104,4]=116
e[94,4]=73 e[97,18]=7 75 e[100,93]=103 e[104,7]=31
e[94,6]=80 e[97,22]=39 e[100,103]=1 e[104,13]=83
e[94,14]=117 50 e[97,36]=123 e[101,2]=50 e[104,18]=39
e[94,17]=79 e[97,99]=17 e[101,8]=119 105 e[104,55]=110
e[94,26]=88 e[97,100]=1 e[101,10]=17 e[104,69]=33
e[94,52]=65 e[98,4]=110 80 e[101,18]=54 e[104,106]=112
e[94,96]=79 e[98,6]=44 e[101,26]=75 e[104,107]=1
e[105,3]=128 e[108,22]=124 55 e[111,108]=106 e[115,10]=101
e[105,7]=5 e[108,23]=29 e[111,114]=1 e[115,13]=83
e[105,13]=95 30 e[108,37]=2 e[112,4]=13 e[115,19]=29
e[105,26]=20 e[108,101]=93 e[112,10]=109 85 e[115,33]=14
e[105,41]=91 e[108,111]=1 e[112,15]=110 e[115,64]=66
e[105,44]=34 e[109,4]=11 60 e[112,38]=49 e[115,116]=42
e[105,105]=63 e[109,7]=88 e[112,44]=10 e[115,118]=1
e[105,108]=1 35 e[109,12]=81 e[112,54]=43 e[116,5]=76
e[106,5]=41 e[109,22]=125 e[112,111]=13 90 e[116,7]=75
e[106,9]=34 e[109,50]=29 e[112,115]=1 e[116,12]=127
e[106,13]=113 e[109,54]=102 65 e[113,5]=50 e[116,23]=81
e[106,40]=74 e[109,86]=66 e[113,10]=40 e[116,28]=76
e[106,50]=62 40 e[109,112]=1 e[113,14]=11 e[116,38]=31
e[106,63]=82 e[110,3]=12 e[113,50]=98 95 e[116,114]=96
e[106,92]=113 e[110,5]=68 e[113,57]=1 e[116,119]=1
e[106,109]=1 e[110,14]=42 70 e[113,65]=62 e[117,3]=7
e[107,4]=40 e[110,19]=114 e[113,115]=46 e[117,10]=62
e[107,8]=23 45 e[110,54]=122 e[113,116]=1 e[117,13]=114
e[107,11]=9 e[110,68]=83 e[114,2]=113 100 e[117,20]=127
e[107,23]=17 e[110,107]=42 e[114,7]=91 e[117,28]=43
e[107,57]=52 e[110,113]=1 75 e[114,15]=12 e[117,53]=75
e[107,67]=60 e[111,2]=65 e[114,20]=87 e[117,110]=121
e[107,109]=59 50 e[111,8]=68 e[114,33]=9 e[117,120]=1
e[107,110]=1 e[111,14]=19 e[114,62]=68 105 e[118,2]=112
e[108,3]=21 e[111,20]=14 e[114,113]=14 e[118,9]=41
e[108,9]=73 e[111,37]=37 80 e[114,117]=1 e[118,14]=56
e[108,13]=79 e[111,70]=26 e[115,2]=110 e[118,33]=34
e[118,39]=77
e[118,53]=3
e[118,104]=31
e[118,119]=49
e[119,5]=84
e[119,8]=19
e[119,15]=46
e[119,19]=75
e[119,47]=7
e[119,48]=75
e[119,112]=48
e[119,120]=26
e[120,4]=59
e[120,9]=98
e[120,14]=10
e[120,28]=107
e[120,44]=2
e[120,48]=69
e[120,117]=108
e[120,118]=116 。