CN103092816A - Generating device and generating method of constant coefficient matrixes in parallel reed solomon (RS) codes - Google Patents

Abstract

The invention provides a generating method of constant coefficient matrixes in parallel reed solomon (RS) codes. The generating method of the constant coefficient matrixes in the parallel RS codes is characterized in that the generating device of the constant coefficient matrixes is composed of a controller, a field element binary representation lookup table, a basis conversion matrix memory, an inverse basis conversion matrix memory, a multiplication arithmetic unit and a storage unit. As to every coefficient, (m-1)*m multiplication and (m-1)*(m-1) addition are saved, multiplier matrixes can be structured by taking out corresponding binary systems of m field elements from the field element binary representation lookup table, and the constant coefficient matrixes are generated. The generating method of the constant coefficient matrixes in the parallel RS codes is low in calculated quantity and easy to achieve, and improves generating speed of the constant coefficient matrixes obviously.

Description

Generating apparatus and the method for constant coefficient matrix in a kind of parallel RS coding

Technical field

The present invention relates to the communications field, particularly a kind of generation method of constant coefficient matrix in parallel RS coding.

Background technology

Reed---Suo Luomen (Reed-Solomon, RS) code is the multi-system BCH code that a class has very strong error correcting capability, it can be corrected random error and also can correct interchannel noise and disturb the error burst that produces, and is widely used in Modern Communication System.

The structure of parallel RS scrambler as shown in Figure 1, it mainly is comprised of shift register, Galois field totalizer and Galois field multiplier, its implementation complexity depends on Galois field multiplier to a great extent.Prior art adopts matrix to connect and takes advantage of UV (g _i) W realizes finite field multiplier, wherein matrix U and matrix W depend on and adopt which kind of reciprocal basis, constant multiplier matrix V (g _i) be the key of design.For finite field gf (2 ^m), multiplier matrix V (g _i) dimension be m * m, for each coefficient g _i, prior art need to be carried out 1 computing of tabling look-up and be obtained matrix V (g _i) the first row element, then carry out m-1 complex calculation and obtain respectively matrix V (g _i) all the other m-1 row elements, the average calculating operation amount that each complex calculation comprises is m multiplication and m-1 sub-addition.Namely for each coefficient, existing method will be carried out 1 computing of tabling look-up, m multiplying of (m-1) * and (m-1) * (m-1) sub-addition computing.When m is large, there is the very large problem of calculated amount in the multiplier number when more, this will seriously restrict the raising of constant coefficient matrix formation speed.

Summary of the invention

For the large technical disadvantages of structure multiplier matrix computations amount that parallel RS coding exists, the invention provides a kind of method of quick generation constant coefficient matrix, effectively reduce the calculated amount that matrix generates, improve the formation speed of constant coefficient matrix.

As shown in Figure 3, the generating apparatus of constant coefficient matrix mainly is comprised of controller, field element binary representation look-up table, basic transition matrix storer, contrary basic transition matrix storer, multiplying unit, storage unit six parts.The generative process of whole constant coefficient matrix divided for five steps completed: the first step, generate 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＜2 ^m-1; Second step, controller is with l(generator polynomial coefficient g _iThe power representation be α ^l) read continuous m field element α for index from field element binary representation look-up table ^l, α ^l+1..., α ^L+m-1Binary representation consist of multiplier matrix V (g _i), adopt the circulation reading manner when reading, if l〉2 ^m-m-1, namely capable when capable to the not enough m of table footline from l, then read from heading capable (the 0th row), until read the binary representation of m field element; In the 3rd step, controller reads contrary basic transition matrix U, U and V (g _i) complete 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 intermediate value T (g in storage unit _i) complete multiplication T (g in the multiplying unit _i) W, the gained product is multiplier matrix Z (g _i); The 5th step, repeat second and third, four steps, obtain the constant coefficient matrix of all coefficients.

as fully visible, compare with existing solution, for each coefficient, the present invention has removed and has constructed m-1 the complex calculation that its multiplier matrix relates to, the average calculating operation amount that each complex calculation comprises is m multiplication and m-1 sub-addition, namely for each coefficient, the present invention saves m multiplication of (m-1) * and (m-1) * (m-1) sub-addition, only need to take out the corresponding binary representation of m field element continuously and can construct its multiplier matrix from field element binary representation look-up table, and then generate its constant coefficient matrix, calculated amount is low, be easy to realize, can obviously improve the formation speed of constant coefficient matrix.

Can be further understood by ensuing detailed description and accompanying drawings about the advantages and spirit of the present invention.

Description of drawings

Fig. 1 is the structured flowchart of parallel RS scrambler;

Fig. 2 has provided the simplified flow chart that generates the constant coefficient matrix;

Fig. 3 has provided the generating apparatus functional block diagram of constant coefficient matrix.

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 scrambler is all completed 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..., γ _m-1Represent GF (2 ^m) on Standardizing Base.If other one group of base { τ ₀, τ ₁..., τ _m-1Satisfy:

$\mathrm{Tr}({\mathrm{\γ}}_i,{\mathrm{\τ}}_j)=\mathrm{\δ}(i,j)=\left\{\begin{array}{cc}1& i=j\\ 0& i\≠j\end{array}\right.---\left(1\right)$

Wherein:

Be called the Trace function.Claim base { τ ₀, τ ₁..., τ _m-1Be base { γ ₀, γ ₁..., γ _m-1Reciprocal basis.GF (2 so ^m) in arbitrary element Q can be expressed as:

$Q=\underset{i=0}{\overset{m-1}{\mathrm{\Σ}}}{q}_i{\mathrm{\γ}}_i=\underset{i=0}{\overset{m-1}{\mathrm{\Σ}}}{q}_i^{\mathrm{\τ}}{\mathrm{\τ}}_i---\left(2\right)$

Q wherein _iWith

Be respectively the coordinate of Standardizing Base and reciprocal basis.Reciprocal 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 reciprocal basis coordinate:

$\left[\begin{array}{c}{q}_0^{\mathrm{\&tau;}}\\ {\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^{\mathrm{\&tau;}}\\ .\\ .\\ .\\ q_{m-1}^{\mathrm{\&tau;}}\end{array}\right]=\left[\begin{array}{cccc}{w}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{0,1}}& ...& w_{0,m-1}\\ {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="w"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">w</figure-callout>\; </figure-callout>}}_{\mathrm{1,1}}& <figure-callout\; id="1"\; label="...\; w"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">.</figure-callout>..& w_{}{}_{1,m-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ w_{m-\mathrm{1,0}}& w_{m-\mathrm{1,1}}& ...& w_{m-1,m-1}\end{array}\right]\left[\begin{array}{c}{q}_0\\ q_1\\ .\\ .\\ .\\ q_{m-1}\end{array}\right]=W\left[\begin{array}{c}{q}_0\\ q_1\\ .\\ .\\ .\\ q_{m-1}\end{array}\right]---\left(3\right)$

Wherein W is basic transition matrix, is expressed as follows:

$W=\left[\begin{array}{cccc}{w}_{\mathrm{0,0}}& w_{\mathrm{0,1}}& ...& w_{0,m-1}\\ w_{\mathrm{1,0}}& w_{\mathrm{1,1}}& ...& w_{1,m-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ w_{m-\mathrm{1,0}}& w_{m-\mathrm{1,1}}& ...& w_{m-1,m-1}\end{array}\right]$

The reciprocal basis coordinate turns the Standardizing Base coordinate:

$\left[\begin{array}{c}{q}_0\\ {\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">q</figure-callout>}}_1\\ .\\ .\\ .\\ q_{m-1}\end{array}\right]=\left[\begin{array}{cccc}{u}_{\mathrm{0,0}}& u_{\mathrm{0,1}}& ...& u_{0,m-1}\\ u_{\mathrm{1,0}}& u_{\mathrm{1,1}}& ...& u_{1,m-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ u_{m-\mathrm{1,0}}& u_{m-\mathrm{1,1}}& ...& u_{m-1,m-1}\end{array}\right]\left[\begin{array}{c}{q}_0^{\mathrm{\&tau;}}\\ {\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^{\mathrm{\&tau;}}\\ .\\ .\\ .\\ q_{m-1}^{\mathrm{\&tau;}}\end{array}\right]=U\left[\begin{array}{c}{q}_0^{\mathrm{\&tau;}}\\ {\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^{\mathrm{\&tau;}}\\ .\\ .\\ .\\ q_{m-1}^{\mathrm{\&tau;}}\end{array}\right]---\left(4\right)$

Wherein U is contrary basic transition matrix, is expressed as follows:

$U=\left[\begin{array}{cccc}{u}_{\mathrm{0,0}}& u_{\mathrm{0,1}}& ...& u_{0,m-1}\\ u_{\mathrm{1,0}}& u_{\mathrm{1,1}}& ...& u_{1,m-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ u_{m-\mathrm{1,0}}& u_{m-\mathrm{1,1}}& ...& u_{m-1,m-1}\end{array}\right]$

For 0≤j≤m-1, we can obtain an important inference:

$\mathrm{Tr}\left({\mathrm{\&alpha;}}^{j}Q\right)=\mathrm{Tr}\left({\mathrm{\&alpha;}}^j\underset{i=0}{\overset{m-a}{\mathrm{\&Sigma;}}}{q}_i^{\mathrm{\&tau;}}{\mathrm{\&tau;}}_i\right)=\underset{i=0}{\overset{m-1}{\mathrm{\&Sigma;}}}{q}_i^{\mathrm{\&tau;}}\mathrm{Tr}\left({\mathrm{\&alpha;}}^j{\mathrm{\&tau;}}_i\right)=q_j^{\mathrm{\&tau;}}---\left(5\right)$

Suppose A, B, C ∈ GF (2 ^m), C=AB, wherein A is expressed as with Standardizing Base

B, C are expressed as with reciprocal basis $B=\underset{i=0}{\overset{m-1}{\mathrm{\&Sigma;}}}{b}_i^{\mathrm{\&tau;}}{\mathrm{\&tau;}}_i,$ $C=\underset{i=0}{\overset{m-1}{\mathrm{\&Sigma;}}}{c}_i^{\mathrm{\&tau;}}{\mathrm{\&tau;}}_i.$ Can be got by formula (5):

$b_i^{\mathrm{\&tau;}}=\mathrm{Tr}\left({\mathrm{\&alpha;}}^{i}B\right)---\left(6\right)$

$c_i^{\mathrm{\&tau;}}=\mathrm{Tr}\left({\mathrm{\&alpha;}}^{i}C\right)=\mathrm{Tr}\left({\mathrm{\&alpha;}}^i\mathrm{AB}\right)=\mathrm{Tr}\left(\left({\mathrm{\&alpha;}}^{i}A\right)B\right)---\left(7\right)$

Due to 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:

$c_i^{\mathrm{\&tau;}}=\mathrm{Tr}\left(\left({\mathrm{\&alpha;}}^{i}A\right)B\right)=\mathrm{Tr}\left(\underset{j=0}{\overset{m-1}{\mathrm{\&Sigma;}}}{v}_{i,j}{\mathrm{\&alpha;}}^{j}B\right)$

$=\underset{j=0}{\overset{m-1}{\mathrm{\&Sigma;}}}\mathrm{Tr}\left(v_{i,j}{\mathrm{\&alpha;}}^{j}B\right)=\underset{j=0}{\overset{m-1}{\mathrm{\&Sigma;}}}{v}_{i,j}\mathrm{Tr}\left({\mathrm{\&alpha;}}^{j}B\right)$

$=\underset{j=0}{\overset{m-1}{\mathrm{\&Sigma;}}}{v}_{i,j}{b}_j^{\mathrm{\&tau;}}---\left(8\right)$

$=\left[\begin{array}{cccc}{v}_{i,0}& v_{i,1}& ...& v_{i,m-1}\end{array}\right]\left[\begin{array}{c}{b}_0^{\mathrm{\&tau;}}\\ {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">b</figure-callout>}}_1^{\mathrm{\&tau;}}\\ .\\ .\\ .\\ b_{m-1}^{\mathrm{\&tau;}}\end{array}\right]$

We can get by formula (8):

$\left[\begin{array}{c}{c}_0^{\mathrm{\&tau;}}\\ {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">c</figure-callout>}}_1^{\mathrm{\&tau;}}\\ .\\ .\\ .\\ c_{m-1}^{\mathrm{\&tau;}}\end{array}\right]=\left[\begin{array}{cccc}{v}_{\mathrm{0,0}}& v_{\mathrm{0,1}}& ...& v_{0,m-1}\\ v_{\mathrm{1,0}}& v_{\mathrm{1,1}}& ...& v_{1,m-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ v_{m-\mathrm{1,0}}& v_{m-\mathrm{1,1}}& ...& v_{m-1,m-1}\end{array}\right]\left[\begin{array}{c}{b}_0^{\mathrm{\&tau;}}\\ {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">b</figure-callout>}}_1^{\mathrm{\&tau;}}\\ .\\ .\\ .\\ b_{m-1}^{\mathrm{\&tau;}}\end{array}\right]=V\left(A\right)\left[\begin{array}{c}{b}_0^{\mathrm{\&tau;}}\\ {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">b</figure-callout>}}_1^{\mathrm{\&tau;}}\\ .\\ .\\ .\\ b_{m-1}^{\mathrm{\&tau;}}\end{array}\right]---\left(9\right)$

Wherein V (A) is the multiplier matrix, is expressed as follows:

$V\left(A\right)=\left[\begin{array}{cccc}{v}_{\mathrm{0,0}}& v_{\mathrm{0,1}}& ...& v_{0,m-1}\\ v_{\mathrm{1,0}}& v_{\mathrm{1,1}}& ...& v_{1,m-1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ v_{m-\mathrm{1,0}}& v_{m-\mathrm{1,1}}& ...& v_{m-1,m-1}\end{array}\right]$

I row element v in multiplier matrix V (A) _{I, 0}, v _i,1..., v _{I, m-1}α 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-1}α 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.

Derive and to get by formula (3), (4), (9)

$\left[\begin{array}{c}{c}_0\\ {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\\ .\\ .\\ .\\ c_{m-1}\end{array}\right]=\mathrm{UV}\left(A\right)W\left[\begin{array}{c}{b}_0\\ {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">b</figure-callout>}}_1\\ .\\ .\\ .\\ b_{m-1}\end{array}\right]=Z\left(A\right)\left[\begin{array}{c}{b}_0\\ {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="DEST\_PATH\_HDA00002819872300011.png"\; state="\{\{state\}\}">b</figure-callout>}}_1\\ .\\ .\\ .\\ b_{m-1}\end{array}\right]---\left(10\right)$

Z (A)=UV (A) W wherein.For the RS coding, multiplier A is generator polynomial coefficient g _i(0≤i＜n-k), 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 reciprocal basis, Z (g _i) all fix, so this method does not need to seek optimum reciprocal basis, we can adopt any one reciprocal basis, such as triangular basis, thereby obtain corresponding basic transition matrix W and contrary basic transition matrix U.

According to formula (10) 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.

Second step is with l(generator polynomial coefficient g _iThe power representation be α l) read continuous m field element α for index from field element binary representation look-up table ^l, α ^l+1..., α ^L+m-1Binary representation consist of multiplier matrix V (g _i), adopt the circulation reading manner when reading, if l〉2 ^m-m-1, namely capable when capable to the not enough m of table footline from l, then read from heading capable (the 0th row), until read the binary representation of m field element.

In the 3rd step, complete matrix and even take advantage of UV (g _i) W, can obtain coefficient g _IConstant coefficient matrix Z (g _i).

Fig. 2 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) read α for index from field element binary representation look-up table ^lThereby binary representation obtain multiplier matrix V (g _i) the first row element, then carry out m-1 complex calculation and obtain respectively multiplier matrix V (g _i) all the other m-1 row elements.As seen existing method will be carried out m-1 computing for each coefficient more, the average calculating operation amount that each complex calculation comprises is m multiplication and m-1 sub-addition, namely for each coefficient, existing method will be carried out m multiplication of (m-1) * and (m-1) * (m-1) sub-addition more.Large as m, when coefficient number is more, existing methodical operand will sharply increase, this will seriously restrict the formation speed of constant coefficient matrix.

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 3.This constant coefficient matrix generation device realizes simple, mainly is comprised of controller, field element binary representation look-up table, basic transition matrix storer, contrary basic transition matrix storer, multiplying unit, storage unit six parts.Controller is controlled the reading of the reading of look-up table, basic transition matrix, contrary reading with matrix of basic transition matrix connects 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＜2 ^m-1.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 result T (g that takes advantage of _i).

The present invention has designed the generation method of constant coefficient matrix in 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, and 0≤j＜2 ^m-1.

Second step, controller is with l(generator polynomial coefficient g _iThe power representation be α ^l) read continuous m field element α for index from field element binary representation look-up table ^l, α ^l+1..., α ^L+m-1Binary representation consist of multiplier matrix V (g _i), adopt the circulation reading manner when reading, if l〉2 ^m-m-1, namely capable when capable to the not enough m of table footline from l, then read from heading capable (the 0th row), until read the binary representation of m field element.

In the 3rd step, controller reads contrary basic transition matrix U, U and V (g _i) complete 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 intermediate value T (g in storage unit _i) complete 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 coefficients.

as fully visible, compare with existing solution, for each coefficient, the present invention has removed and has constructed m-1 the complex calculation that its multiplier matrix relates to, the average calculating operation amount that each complex calculation comprises is m multiplication and m-1 sub-addition, namely for each coefficient, the present invention saves m multiplication of (m-1) * and (m-1) * (m-1) sub-addition, only need to take out the corresponding binary representation of m field element continuously and can construct its multiplier matrix from field element binary representation look-up table, and then generate its constant coefficient matrix, calculated amount is low, be 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.

Claims (4)

1. the generating apparatus of constant coefficient matrix during a parallel RS encodes, constant coefficient matrix Z (g _i)=UV (g _i) W, wherein U is contrary basic transition matrix, W is basic transition matrix, V (g _i) be the multiplier matrix, g _iFor generating polynomial coefficient, system adopts finite field gf (2 ^m) on the RS code, it is characterized in that, described device comprises with lower component:

Controller, be used for to control the reading of the reading of look-up table, basic transition matrix, contrary basic transition matrix read and matrix connects storage that multiplication, matrix connect the intermediate result of taking advantage of and reads;

Field element binary representation look-up table is for the binary representation of storage field element;

Base transition matrix storer is used for storing basic transition matrix W;

Contrary basic transition matrix storer is used for the contrary basic transition matrix U of storage;

The multiplying unit is used for realization matrix and even takes advantage of UV (g _i) W;

Storage unit is used for storage matrix and connects the intermediate result T (g that takes advantage of _i)=UV (g _i).

2. constant coefficient matrix generation device as claimed in claim 1, is characterized in that, the index of described field element binary representation look-up table is the power j of field element, wherein, and 0≤j＜2 ^m-1, the content that each storage unit is preserved is the binary representation of field element.

3. constant coefficient matrix generation device as claimed in claim 1, is characterized in that, described multiplying unit is used for realization matrix and connects and take advantage of UV (g _i) W:

Matrix U multiply by matrix V (g _i), gained product T (g _i) be stored in storage unit;

T(g _i) multiply by matrix W, the gained product is constant coefficient matrix Z (g _i).

4. the generation method of constant coefficient matrix during a parallel RS encodes, constant coefficient matrix Z (g _i)=UV (g _i) W, wherein U is contrary basic transition matrix, W is basic transition matrix, V (g _i) be the multiplier matrix, g _iFor generating polynomial coefficient, system adopts finite field gf (2 ^m) on the RS code, it is characterized in that, said method comprising the steps of:

(1) generate field element binary representation look-up table according to primitive polynomial, the index of look-up table is the power j of field element, wherein, and 0≤j＜2 ^m-1;

(2) controller is with l(generator polynomial coefficient g _iThe power representation be α ^l) read continuous m field element α for index from field element binary representation look-up table ^l, α ^l+1..., α ^L+m-1Binary representation consist of multiplier matrix V (g _i), adopt the circulation reading manner when reading, if l〉2 ^m-m-1, namely capable when capable to the not enough m of table footline from l, then read from heading capable (the 0th row), until read the binary representation of m field element;

(3) controller reads contrary basic transition matrix U, U and V (g _i) complete multiplication UV (g in the multiplying unit _i), gained product T (g _i) write storage unit;

(4) controller reads basic transition matrix W, with the product intermediate value T (g in storage unit _i) complete multiplication T (g in the multiplying unit _i) W, the gained product is constant coefficient matrix Z (g _i);

(5) repeating step (2), (3), (4) obtain the constant coefficient matrix of all coefficients.

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