CN102436834A - Method and device for reading disk information - Google Patents

Abstract

The invention discloses a method and a device for reading disk information, wherein the method comprises the following steps: when reading the information on the disk, carrying out frequency domain RS coding on the read information; carrying out PR channel coding on the information subjected to the RS coding in the frequency domain; pre-decoding the information coded by the PR signal by adopting a BCJR algorithm; and decoding the information after the pre-decoding by adopting an algebraic soft decision algorithm to obtain correct information. The pre-decoding module of the invention adopts BCJR algorithm with soft information output to obtain the input information required by the RS decoding module, and uses algebraic soft decision mode to carry out RS decoding, thus having better performance error correction capability than RS hard decision decoding adopted by the existing disk, reducing the error rate of data transmission, thereby improving the storage density of the disk and saving the cost for modifying the existing disk.

Description

A kind of method of reading disk information and device

Technical field

The present invention relates to the disk storage system technical field, relate in particular to a kind of method and device of reading disk information.

Background technology

Since 21 century, people sharply increase the demand of memory capacity, and the also significantly raising thereupon of requirement to disk face density has brought serious intersymbol interference thus, has caused higher bit error rate, has reduced the performance of magnetic recording system.

Disk storage system primarily is to guarantee just to go to pursue high storage capacity and quick access after the reliability of data, and aspect such as low price and use be simple and easy.At present; (the partial reaction maximal phase seemingly for normal employing PRML in the magnetic recording; Partial Response Maximum Likelihood) technology detects to eliminate intersymbol interference channel; Its essence is that the PR with shorter ISI (Inter symbol Interference, intersymbol interference) (partial reaction, the Partial Response) signal of balanced device output is sent into Viterbi (Viterbi) detecting device; And can directly be fed into hard decision RS (Reed-Solomon) code decoder to constitute cascade system from the hard decision information of Vitebi detector output, this kind mode is applied in the current disk storage industrial standard.As systematic internal code, the RS sign indicating number is the mode of the common raising system performance that adopts in the present commercial disk as outer yard with the PR channel.But this device error correcting capability is not strong, and is more and more inapplicable in following compact disk.

To sum up, in information age now, the data volume that is explosive growth makes increasing to the capacity requirement of disk storage system.Under identical disc size, bigger capacity just corresponding higher storage density, the serious intersymbol interference that brings has thus reduced system performance.The RS sign indicating number can not adapt to the requirement of following disk storage system to the higher coding gain of error correcting code gradually as the industrial standard of error correcting code in the existing disk storage system.

Summary of the invention

The technical matters that the present invention will solve is, a kind of method and device of reading disk information is provided, and adapts to the high storage density of disk and satisfies the requirement of low error rate.

The technical scheme that the present invention adopts is that the method for said reading disk information comprises:

When step 1, the information on reading disk, the information that reads is carried out the RS Frequency Domain Coding;

Step 2, to carrying out the PR chnnel coding through the information behind the RS Frequency Domain Coding;

Step 3, employing BCJR (Bahl-Cocke-Je-linek-Raviv) algorithm are to decipher through the information after the PR signal encoding in advance;

Step 4, employing algebraically soft-decision algorithm are to deciphering the correct information that obtains through the information after deciphering in advance.

Further, said step 1 specifically comprises:

On the galois field in Abstract Algebra, calculate the polynomial each item coefficient of code word based on message polynomial, said each item coefficient is through the information behind the RS Frequency Domain Coding.

Further, said step 2 also comprises: to carrying out passing through AGWN (additive white Gaussian noise, additive white Gaussian noise) Channel Processing again after the PR chnnel coding through the information behind the RS Frequency Domain Coding.

Further, said step 3 specifically comprises:

The grid chart that is abstracted into based on the PR channel, by bcjr algorithm determine input through the optimal path of the information after the PR signal encoding along PR channel grid chart;

Maximum likelihood output probability according to each channel output sequence value constantly in the said optimal path calculates the maximum likelihood output valve, and the maximum likelihood output valve is the information after the preparatory decoding.

Further, said step 4 specifically comprises:

Information after deciphering in advance is arranged in the reliability matrix;

Is the severe matrix through the severe matrix algorithms with the reliability matrix conversion;

Information via polynomial interpolation algorithm according to the severe matrix obtains first polynomial expression;

On the first polynomial basis, obtain message polynomial through factoring algorithm;

Obtain correct information after will handling through posterior probability method based on the codeword information that message polynomial calculates.

The present invention also provides a kind of device of reading disk information, comprising:

The RS coding module when being used for the information on reading disk, carries out the RS Frequency Domain Coding to the information that reads;

The PR coding module is used for carrying out the PR chnnel coding through the information behind the RS Frequency Domain Coding;

Decoding module is used to adopt bcjr algorithm to deciphering in advance through the information after the PR signal encoding in advance;

The RS decoding module is used to adopt algebraically soft-decision algorithm to deciphering the correct information that obtains through the information after deciphering in advance.

Further, said RS coding module specifically is used for:

On the galois field in Abstract Algebra, calculate the polynomial each item coefficient of code word based on message polynomial, said each item coefficient is through the information behind the RS Frequency Domain Coding.

Further, said PR coding module also is used for: to carrying out passing through the AGWN Channel Processing again after the PR chnnel coding through the information behind the RS Frequency Domain Coding.

Further, said preparatory decoding module specifically comprises:

The path determination module is used for the grid chart that is abstracted into based on the PR channel, by bcjr algorithm determine input through the optimal path of the information after the PR signal encoding along PR channel grid chart;

The decoding output module is used for calculating the maximum likelihood output valve according to the maximum likelihood output probability of each channel output sequence value constantly of said optimal path, and the maximum likelihood output valve is the information after the preparatory decoding.

Further, said RS decoding module specifically comprises:

Reliability matrix acquisition module is used for the information after deciphering in advance is arranged in the reliability matrix;

The matrix conversion module, being used for through the severe matrix algorithms is the severe matrix with the reliability matrix conversion;

The interpolation calculation module is used for obtaining first polynomial expression according to the information via polynomial interpolation algorithm of severe matrix;

The factorization module is used on the first polynomial basis, obtaining message polynomial through factoring algorithm;

Output module is selected in RS decoding, is used for obtaining correct information after the codeword information process posterior probability method processing that calculates based on message polynomial.

Adopt technique scheme, the present invention has advantage at least:

The method of reading disk information according to the invention and device; Decoding module adopts the bcjr algorithm with soft information output to obtain the needed input information of RS decoding module in advance; Use algebraically soft-decision mode to carry out RS decoding, the RS Hard decision decoding that adopts than existing disk has more excellent performance error correcting capability, has reduced the bit error rate of data transmission; Thereby improve the storage density of disk, saved the expense of transforming existing disk.

Description of drawings

Fig. 1 is the method flow diagram of reading disk information in the first embodiment of the invention;

Fig. 2 is the synoptic diagram that calculates the process of forward state metric in the first embodiment of the invention;

Fig. 3 calculates the synoptic diagram of back to the process of state measurement in the first embodiment of the invention;

Fig. 4 is the apparatus structure synoptic diagram of reading disk information in the second embodiment of the invention.

Embodiment

Reach technological means and the effect that predetermined purpose is taked for further setting forth the present invention, below in conjunction with accompanying drawing and preferred embodiment, to the present invention be elaborated as after.

First embodiment of the invention, a kind of method of reading disk information, as shown in Figure 1, comprise following concrete steps:

Step S101 during information on reading disk, carries out the RS Frequency Domain Coding to the information that reads;

Concrete, on the galois field in Abstract Algebra, calculating the polynomial each item coefficient of code word based on message polynomial, said each item coefficient is through the information behind the RS Frequency Domain Coding.

On galois field GF (q), q is the numerical range of galois field, if m ₀, m ₁..., m _K-1Be information word, then message polynomial is:

f(x)＝m ₀+m ₁x+L+m _k-1x ^k-1 (1)

The code word polynomial expression is:

c(x)＝f(1)+f(α)x+L+f(α ^q-3)x ^q-3+f(α ^q-2)x ^q-2

＝c ₀+c ₁x+L+c _q-3x ^q-3+c _q-2x ^q-2 (2)

Below with the code length on the galois field GF (8) be 7, dimension is 3 RS (7,3) sign indicating number is explained the use Frequency Domain Coding for example step.If the disc information that reads is for { m2}={101} can know that according to formula (1) concrete message polynomial is f (x)=1+x for m0, m1 ², can know that according to formula (2) the code word multinomial coefficient is then: f (1)=0, f (α)=α ⁶, f (α ²)=α ⁵, f (α ³)=α ², f (α ⁴)=α ³, f (α ⁵)=α, f (α ⁶)=α ⁴Obtaining concrete code word polynomial expression to these coefficient substitution formula (2) again is:

c(x)＝0+α ⁶x+α ⁵x ²+α ²x ³+α ³x ⁴+αx ⁵+α ⁴x ⁶

The code word of this Frequency Domain Coding be 0, α ⁶, α ⁵, α ², α ³, α, α ⁴.

Step S102 is to carrying out the PR chnnel coding through the information behind the RS Frequency Domain Coding.This step has been simulated the intersymbol interference that information is run into, the i.e. stack of intersymbol interference in transmission course.Because the process of PR chnnel coding is a technology well known in the art, so locate not detail.Preferably, to carrying out passing through the AGWN Channel Processing again after the PR chnnel coding through the information behind the RS Frequency Domain Coding, purpose be more the white Gaussian noise in the real simulated Channel Transmission environment to the influence of signal.

Step S103 adopts BCJR (Bahl-Cocke-Je-linek-Raviv) algorithm to deciphering in advance through the information after the PR signal encoding.

Concrete, step S103 comprises:

A1, the grid chart that is abstracted into based on the PR channel, by bcjr algorithm determine input through the optimal path of the information after the PR signal encoding along PR channel grid chart.This is the core of bcjr algorithm.

Bcjr algorithm is applicable to the decoding of any linear block codes or convolutional code, and is bigger than its computation complexity of viterbi algorithm, therefore under general situation such as information bit, is more prone to adopt viterbi algorithm.Otherwise, when information bit when not being etc. general, adopts bcjr algorithm to decipher and can realize more performance, and that the information that reads from disk in the reality all is that information bit does not wait basically is general.

Move towards to calculate maximum likelihood probability p (a based on bcjr algorithm along the grid chart of PR channel _n=± 1|Y), wherein Y=(y ₁, y ₂..., Y _N) be the channel output sequence value that receives after the intersymbol interference, promptly pass through the information after the PR signal encoding, n representes variable constantly.Maximum likelihood probability p (a _n=± 1|Y) representes that also certain sequential value y gets at n+1 perhaps-1 probability constantly.In the grid chart each the time be carved with a plurality of states, distinguish with leftover bits and pieces target difference, be s such as wherein two states in a moment _iAnd s _jIf current state representes that with s then Last status is represented with s ', if current state is s ', then NextState is s, that is to say, s ' always is a s preceding state in time.

State from s ' to s, the input value a that receives _nHave only ± 1, employing formula (2):

$p(a_n=\±1|y)=\underset{s^{\′}s:a_n=\±1}{\mathrm{\Σ}}\exp \{{\stackrel{\‾}{A}}_{n-1}\left(s^{\′}\right)+c_n(s^{\′},s)+{\stackrel{\‾}{B}}_n\left(s\right)\}---\left(2\right)$

Wherein With

Be respectively forward direction with the back to state measurement, c _n(s ', s) be branch metric, forward state metric and formula (3) and the formula (4) of back below the state measurement initialization condition is respectively:

${\stackrel{\‾}{A}}_0\left(0\right)=0;{\stackrel{\‾}{A}}_0\left(s\right)=-\∞,s\≠0---\left(3\right)$

${\stackrel{\‾}{B}}_N\left(0\right)=0;{\stackrel{\‾}{B}}_N\left(s\right)=-\∞,s\≠0---\left(4\right)$

Wherein, following footnote N representes higher limit constantly, and following footnote 0 expression is initial value constantly.

The forward state metric calculation formula is:

${\stackrel{\‾}{A}}_n\left(s\right)=\underset{s^{\′}}{\ln \mathrm{\Σ}}\exp \{{\stackrel{\‾}{A}}_{n-1}\left(s^{\′}\right)+c_n(s^{\′},s)\}---\left(5\right)$

The expression of process on grid chart of calculating forward state metric is as shown in Figure 2; The rest may be inferred to obtain current forward state metric by two branch metrics of the forward state metric

of two laststates and

and input, shifts the forward state metric of n-hour onto from 0 constantly forward state metric always.

The back to the state metric calculation formula is:

${\stackrel{\‾}{B}}_{n-1}\left(s^{\′}\right)=\ln \underset{s}{\mathrm{\Σ}}\{{\stackrel{\‾}{B}}_n\left(s\right)+c_n(s^{\′},s)\}---\left(6\right)$

Calculating the back represent as shown in Figure 3 on grid chart to the process of state measurement: current afterwards obtain Last status back to state measurement

and

and two branch metrics importing the rest may be inferred to state measurement

by two; Shift the back of 0 moment from the back of n-hour onto to state measurement to state measurement always; The forward state metric of state point, back be under the situation of the branch metric of state measurement and input in calculating grid chart, according to formula (2) determine jointly input through the optimal path of the information after the PR signal encoding along PR channel grid chart.

A2 calculates the maximum likelihood output valve according to the maximum likelihood output probability of each channel output sequence value constantly in the said optimal path, and the maximum likelihood output valve is the information after the preparatory decoding.

Concrete, after the conversion through formula (7), per two the continuous forward state metric and the back of using when confirming optimal path in the grid chart go out the maximum likelihood output valve to state measurement and the branch metric calculation between them.The maximum likelihood output valve is:

${\mathrm{LLR}}_n=\ln \frac{p(a_n=+1|y)}{p(a_n=-1|y)}$

$=\underset{s^{\′},s:a_n=+1}{\max }\{{\stackrel{\‾}{A}}_{n-1}\left(s^{\′}\right)+{\stackrel{\‾}{B}}_n\left(s\right)+c_n(s^{\′},s)\}$

$-\underset{s^{\′},s:a_n=-1}{\max }\{{\stackrel{\‾}{A}}_{n-1}\left(s^{\′}\right)+{\stackrel{\‾}{B}}_n\left(s\right)+c_n(s^{\′},s)\}---\left(7\right)$

Step S104 adopts algebraically soft-decision algorithm to deciphering through the information after deciphering in advance.

The coding of RS in the present embodiment (7,3) sign indicating number adopts the Frequency Domain Coding mode, supposes that the information of sending is a={010110110}, and it can be expressed as a={ α, α on GF (8) ³, α ³, and be c={ α through what obtain behind the Frequency Domain Coding, 0, α ⁶, 0, α ⁵, α ⁵, α ⁶, the information that will from the PR channel, receive is arranged as reliability matrix ∏:

$\mathrm{\Π}=\left[\begin{array}{ccccccc}0.000411455& 0.918316& 1.43046e-007& 0.75703& 5.3727e-011& 8.94092e-007& 2.36451e-010\\ 4.71426e-009& 0.0380923& 2.47079e-005& 0.00814704& 7.94034e-009& 1.66e-006& 5.49078e-006\\ 0.63889& 0.0347& 7.7352e-009& 0.000976168& 4.33421e-007& 0.0173425& 1.77542e-016\\ 0.000232139& 0.00689521& 0.00546071& 0.000976168& 8.32969e-007& 1.71524e-005& 4.30611e-005\\ 7.32012e-006& 0.00143938& 1.33609e-006& 0.00248651& 6.40553e-005& 0.0321987& 4.12282e-012\\ 0.360455& 0.000260547& 0.000295289& 1.05054e-005& 0.00671962& 0.332702& 3.2333e-011\\ 4.12994e-006& 1.08076e-005& 0.0510045& 3.20628e-006& 0.993092& 0.617705& 7.50826e-007\\ 2.65974e-009& 0.000286018& 0.943213& 0.00029793& 0.000123104& 3.18457e-005& 0.999951\end{array}\right]$

Adopt the severe matrix algorithms in the algebraically soft-decision algorithm, the reliability matrix is converted into the severe matrix, when severe in the severe matrix is not 0 number of elements when being complexity s=18, the severe matrix M is:

$M=\left[\begin{array}{ccccccc}0& 2& 0& 2& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0\\ 2& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 2& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 2& 2& 0\\ 0& 0& 2& 0& 0& 0& 2\end{array}\right]$

As shown in table 1 according to severe matrix M initialization interpolation point and weight, x, y are the horizontal ordinate and the ordinate of interpolation point.

The substep of weight in table 1 interpolation arithmetic

x	y	Severe
			1	α	2
1	α 4	2
			α	0	2
α 2	α 6	2
			α 3	0	2
α 3	1	1
			α 4	α 5	2
α 5	α 4	1
			α 5	α 5	2
α 6	α 6	2

Adopt the polynomial interpolation algorithm in the algebraically soft-decision algorithm, severe is not that interpolation is carried out in 0 place in the severe matrix M, obtains interpolation polynomial according to the horizontal ordinate x and the ordinate y of severe, as follows:

P(x，y)＝α ⁶+α ²x+α ⁶x ²+x ³+α ⁴x ⁴+α ⁴x ⁵+x ⁶+α ²x ⁷+αy+αxy+x ²y+x ³y

+x ⁴y+x ⁵y+α ⁴y ²+xy ²+α ⁶x ²y ²+αx ³y ²+α ⁶y ³+α ⁶xy ³ (8)

Then, can obtain the correct factor through the factoring algorithm in the algebraically soft-decision algorithm is:

f(x)＝α+α ⁴x+α ⁴x ² (9)

On GF (8), with 1, a ..., a6 is respectively above the substitution in the formula (9),

f(1)＝α+α ⁴+α ⁴＝α，f(α)＝α+α ⁵+α ⁶＝0，

f(α ²)＝α ⁶，f(α ³)＝0，f(α ⁴)＝α ⁵，f(α ⁵)＝α ⁵，f(α ⁶)＝α ⁶

The code word that obtains at last is c '={ α, 0, α ⁶, 0, α ⁵, α ⁵, α ⁶.According to posterior probability method, can obtain correct information and be { α, α ³, α ³, being translated into Bit data output is exactly { 010110110}.

Second embodiment of the invention, a kind of device of reading disk information, as shown in Figure 4, comprise following ingredient:

1) the RS coding module 10, when being used for the information on reading disk, the information that reads carried out the RS Frequency Domain Coding.Concrete, on the galois field in Abstract Algebra, calculating the polynomial each item coefficient of code word based on message polynomial, said each item coefficient is through the information behind the RS Frequency Domain Coding.

2) the PR coding module 20, are used for carrying out the PR chnnel coding through the information behind the RS Frequency Domain Coding.PR coding module 20 has been simulated the intersymbol interference that information is run into, the i.e. stack of intersymbol interference in transmission course.Because the process of PR chnnel coding is a technology well known in the art, so locate not detail.Preferably, PR coding module 20 also is used for carrying out passing through the AGWN Channel Processing again after the PR chnnel coding through the information behind the RS Frequency Domain Coding, purpose be more the white Gaussian noise in the real simulated Channel Transmission environment to the influence of signal.

3) preparatory decoding module 30 is used to adopt bcjr algorithm to deciphering in advance through the information after the PR signal encoding.Preparatory decoding module 30 specifically comprises:

Path determination module 31 is used for the grid chart that is abstracted into based on the PR channel, by bcjr algorithm determine input through the optimal path of the information after the PR signal encoding along PR channel grid chart;

Decoding output module 32 is used for calculating the maximum likelihood output valve according to the maximum likelihood output probability of each channel output sequence value constantly of said optimal path, and the maximum likelihood output valve is the information after the preparatory decoding.

4) the RS decoding module 40, are used to adopt algebraically soft-decision mode to deciphering the correct information that obtains through the information after deciphering in advance.RS decoding module 40 specifically comprises:

Reliability matrix acquisition module 41 is used for the information after deciphering in advance is arranged in the reliability matrix;

Matrix conversion module 42, being used for through the severe matrix algorithms is the severe matrix with the reliability matrix conversion;

Interpolation calculation module 43 is used for obtaining first polynomial expression according to the information via polynomial interpolation algorithm of severe matrix;

Factorization module 44 is used on the first polynomial basis, obtaining message polynomial through factoring algorithm;

Output module 45 is selected in RS decoding, is used for obtaining correct information after the codeword information process posterior probability method processing that calculates based on message polynomial.

The method of reading disk information according to the invention and device; Decoding module adopts the bcjr algorithm with soft information output to obtain the needed input information of RS decoding module in advance; Use algebraically soft-decision mode to carry out RS decoding, the RS Hard decision decoding that adopts than existing disk has more excellent performance error correcting capability, has reduced the bit error rate of data transmission; Thereby improve the storage density of disk, saved the expense of transforming existing disk.

Through the explanation of embodiment, should be to reach technological means and the effect that predetermined purpose takes to be able to more deeply and concrete understanding to the present invention, yet appended diagram only provide the usefulness of reference and explanation, is not to be used for the present invention is limited.

Claims (10)

1. the method for a reading disk information is characterized in that, comprising:

When step 1, the information on reading disk, the information that reads is carried out the RS Frequency Domain Coding;

Step 2, to carrying out the PR chnnel coding through the information behind the RS Frequency Domain Coding;

Step 3, employing bcjr algorithm are to decipher through the information after the PR signal encoding in advance;

Step 4, employing algebraically soft-decision algorithm are to deciphering the correct information that obtains through the information after deciphering in advance.

2. the method for reading disk information according to claim 1 is characterized in that, said step 1 specifically comprises:

On the galois field in Abstract Algebra, calculate the polynomial each item coefficient of code word based on message polynomial, said each item coefficient is through the information behind the RS Frequency Domain Coding.

3. the method for reading disk information according to claim 1 is characterized in that, said step 2 also comprises: to carrying out passing through additive white Gaussian noise AGWN Channel Processing again after the PR chnnel coding through the information behind the RS Frequency Domain Coding.

4. the method for reading disk information according to claim 1 is characterized in that, said step 3 specifically comprises:

The grid chart that is abstracted into based on the PR channel, by bcjr algorithm determine input through the optimal path of the information after the PR signal encoding along PR channel grid chart;

Maximum likelihood output probability according to each channel output sequence value constantly in the said optimal path calculates the maximum likelihood output valve, and the maximum likelihood output valve is the information after the preparatory decoding.

5. according to the method for each described reading disk information among the claim 1-4, it is characterized in that said step 4 specifically comprises:

Information after deciphering in advance is arranged in the reliability matrix;

Is the severe matrix through the severe matrix algorithms with the reliability matrix conversion;

Information via polynomial interpolation algorithm according to the severe matrix obtains first polynomial expression;

On the first polynomial basis, obtain message polynomial through factoring algorithm;

Obtain correct information after will handling through posterior probability method based on the codeword information that message polynomial calculates.

6. the device of a reading disk information is characterized in that, comprising:

The RS coding module when being used for the information on reading disk, carries out the RS Frequency Domain Coding to the information that reads;

The PR coding module is used for carrying out the PR chnnel coding through the information behind the RS Frequency Domain Coding;

Decoding module is used to adopt bcjr algorithm to deciphering in advance through the information after the PR signal encoding in advance;

The RS decoding module is used to adopt algebraically soft-decision algorithm to deciphering the correct information that obtains through the information after deciphering in advance.

7. the device of reading disk information according to claim 6 is characterized in that, said RS coding module specifically is used for:

On the galois field in Abstract Algebra, calculate the polynomial each item coefficient of code word based on message polynomial, said each item coefficient is through the information behind the RS Frequency Domain Coding.

8. the device of reading disk information according to claim 6 is characterized in that, said PR coding module also is used for: to carrying out passing through the AGWN Channel Processing again after the PR chnnel coding through the information behind the RS Frequency Domain Coding.

9. the device of reading disk information according to claim 6 is characterized in that, said preparatory decoding module specifically comprises:

The path determination module is used for the grid chart that is abstracted into based on the PR channel, by bcjr algorithm determine input through the optimal path of the information after the PR signal encoding along PR channel grid chart;

The decoding output module is used for calculating the maximum likelihood output valve according to the maximum likelihood output probability of each channel output sequence value constantly of said optimal path, and the maximum likelihood output valve is the information after the preparatory decoding.

10. according to the device of each described reading disk information among the claim 6-9, it is characterized in that said RS decoding module specifically comprises:

Reliability matrix acquisition module is used for the information after deciphering in advance is arranged in the reliability matrix;

The matrix conversion module, being used for through the severe matrix algorithms is the severe matrix with the reliability matrix conversion;

The interpolation calculation module is used for obtaining first polynomial expression according to the information via polynomial interpolation algorithm of severe matrix;

The factorization module is used on the first polynomial basis, obtaining message polynomial through factoring algorithm;

Output module is selected in RS decoding, is used for obtaining correct information after the codeword information process posterior probability method processing that calculates based on message polynomial.

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