Embodiment
The invention will be further described below in conjunction with the drawings and specific embodiments, but not as a limitation of the invention.
Computing in the RS encoder is all finished in galois field, galois field GF (2
m) in arbitrary element Q can with the base 1, α ..., α
M-1}={ γ
0, γ
1..., γ
M-1Represent, we claim this base to be Standardizing Base.Usually with { γ
0, γ
1...,
M-1Represent GF (2
m) on Standardizing Base.If other one group of base { τ
0, τ
1..., τ
M-1Satisfy:
Wherein:
Be called the Trace function.Then claim base { τ
0, τ
1..., τ
M-1Be base { γ
0, γ
1..., γ
M-1Reciproccal basis.GF (2 so
m) in arbitrary element Q can be expressed as:
Q wherein
iWith
Be respectively the coordinate of Standardizing Base and reciproccal basis.Reciproccal basis coordinate and Standardizing Base coordinate can be changed mutually, and conversion can be with matrix representation as shown in the formula (3), (4).
The Standardizing Base coordinate turns the reciproccal basis coordinate:
Wherein W is basic transition matrix, is expressed as follows:
The reciproccal basis coordinate turns the Standardizing Base coordinate:
Wherein U is contrary basic transition matrix, is expressed as follows:
For 0≤j≤m-1, we can obtain an important inference:
Suppose A, B, C ∈ GF (2
m), C=AB, wherein A is expressed as with Standardizing Base
B, C are expressed as with reciproccal basis
Can be got by formula (5):
Because A ∈ GF (2
m), so α
iA ∈ GF (2
m), α
iA can be expressed as
V wherein
I, j(0≤j<m) is α
iA is at GF (2
m) on binary representation.Will
Bringing formula (7) into gets:
We can get by formula (8):
Wherein V (A) is the multiplier matrix, is expressed as follows:
I row element v in the multiplier matrix V (A)
I, 0, v
I, 1..., v
I, m-1α
iA is at GF (2
m) on binary representation, i+1 row element v
I+1,0, v
I+1,1..., v
I+1, m-1α
I+1A=(α
iA) α is at GF (2
m) on binary representation.The power representation of supposing multiplier A is α
l, the m row element of matrix V (A) is respectively α so
l, α
L+1..., α
L+m-1At GF (2
m) on binary representation.
For ATSC system, m=8.The former multinomial of RS code book is p (x)=x
8+ x
4+ x
3+ x
2+ 1.Make p (α)=0, get α
8=α
4+ α
3+ α
2+ 1.Fig. 5 has provided the binary representation of part field element, and as can be seen from the figure, each element is that a upper element multiply by α.For the coding of RS (207,187) code, the multiplier of multiplication is generator polynomial coefficient g
i(0≤i<20), for example for the constant term of generator polynomial, multiplier A=g
0=α
190=α
1+ α
2+ α
3+ α
5+ α
7, we need only and sequentially take out continuous 8 field element α
190, α
191..., α
197At GF (2
8) on binary representation can obtain multiplier matrix V (α
190) as shown in the formula (10).
Derive and to get by formula (3), (4), (9)
Z (A)=UV (A) W wherein.We just obtain determining constant coefficient g like this
iConstant coefficient matrix Z (g
i).Easily prove constant coefficient matrix Z (g
i) for the coefficient g that determines
iBe unique, that is to say, no matter adopt which kind of reciproccal basis, Z (g
i) all fix, so this method does not need to seek optimum reciproccal basis, we can adopt any one reciproccal basis, such as triangular basis, thereby obtain corresponding basic transition matrix W and contrary basic transition matrix U.
According to formula (11) and multiplier matrix V (g
i) design feature, the present invention designs a kind of generating algorithm of constant coefficient matrix, concrete steps are as follows:
The first step generates field element binary representation look-up table according to primitive polynomial, and the index of look-up table is the power of field element, and the content of the every row of look-up table is the binary representation of field element.
Second step is with l(generator polynomial coefficient g
iThe power representation be α
l) from field element binary representation look-up table, read continuous 8 field element α for index
l, α
L+1..., α
L+7Binary representation consist of multiplier matrix V (g
i), adopt the circulation reading manner when reading, if l+7〉254, namely capable during to table footline less than 8 row from l, then then read from heading capable (the 0th row), until read the binary representation of 8 field elements.
In the 3rd step, finish matrix and even take advantage of UV (g
i) W, can obtain coefficient g
iConstant coefficient matrix Z (g
i).
Fig. 3 generates constant coefficient matrix Z (g
i) simplified flow chart.
Existing method is identical with the first, the 3rd step of algorithm of the present invention, and the way of second step is first with l(generator polynomial coefficient g
iThe power representation be α
l) from field element binary representation look-up table, read α for index
lThereby binary representation obtain multiplier matrix V (g
i) the first row element, then carry out 7 complex calculation and obtain respectively multiplier matrix V (g
i) all the other 7 row elements.As seen existing method will be carried out 7 computings for each coefficient more, and the average calculating operation amount that each complex calculation comprises is 8 multiplication and 7 sub-additions.The ATSC system has 20 generator polynomial coefficients, and therefore, existing method needs carry out 20*7*8=1120 multiplication and 20*7*7=980 sub-addition more, and the operand of two kinds of constant coefficient matrix generation schemes as shown in Figure 6.
According to above-mentioned rigorous derivation, we have drawn multiplier matrix V (g
i) design feature, based on these characteristics, the invention provides a kind of device of quick generation constant coefficient matrix, as shown in Figure 4.This constant coefficient matrix generation device realizes simple, mainly is comprised of controller, field element binary representation look-up table, basic transition matrix memory, contrary basic transition matrix memory, multiplying unit, memory cell six parts.The reading of the reading of controller control look-up table, basic transition matrix, contrary reading with matrix of basic transition matrix connect multiplication.The binary representation of field element binary representation look-up table stores field element, the index of table are the power j of field element, wherein, and 0≤j<255.Base transition matrix memory stores matrix W.Contrary basic transition matrix memory stores matrix U.Multiplying unit realization matrix connects takes advantage of UV (g
i) W.The cell stores matrix connects the intermediate object program T (g that takes advantage of
i).
The present invention has designed the generation method of constant coefficient matrix in the following RS coding:
The first step generates field element binary representation look-up table according to primitive polynomial, and the index of look-up table is the power j of field element, wherein, 0≤j<255, the content of the every row of look-up table is the binary representation of field element.
Second step, controller is with l(generator polynomial coefficient g
iThe power representation be α
l) from field element binary representation look-up table, read continuous 8 field element α for index
l, α
L+1..., α
L+7Binary representation consist of multiplier matrix V (g
i), adopt the circulation reading manner when reading, if l+7〉254, namely capable during to table footline less than 8 row from l, then then read from heading capable (the 0th row), until read the binary representation of 8 field elements.
In the 3rd step, controller reads contrary basic transition matrix U, U and V (g
i) finish multiplication UV (g in the multiplying unit
i), gained product T (g
i) write storage unit.
In the 4th step, controller reads basic transition matrix W, with the product median T (g in the memory cell
i) finish multiplication T (g
i) W, the gained product is constant coefficient matrix Z (g
i).
In the 5th step, repeat second and third, four steps obtained the constant coefficient matrix of all 20 coefficients.
As fully visible, compare with existing solution, 20*7*8=1120 multiplication that the present invention has removed that structure multiplier matrix relates to and 20*7*7=980 sub-addition are for each generator polynomial coefficient g
i, the binary representation that only needs to take out corresponding continuous 8 field elements from field element binary representation look-up table can be constructed its multiplier matrix, and then generates the constant coefficient matrix, and amount of calculation is low, is easy to realize, can obviously improve the formation speed of constant coefficient matrix.
Below through the specific embodiment and the embodiment the present invention is had been described in detail, some distortion that those skilled in the art carries out in the technical solution of the present invention scope and improvement all should be included in protection scope of the present invention.