CN101510803B - Error correcting system and method of wireless laser communication GF(q) domain - Google Patents

Abstract

The invention discloses an error correcting system on a wireless laser communication GF (q) domain, and an error correcting method thereof. The error correcting system comprises a data interface, an emitting part and a receiving part, wherein, the emitting part comprises an encoder module, a modulation module, a laser drive circuit, a laser and an optical emitting antenna which are connected successively, wherein the receiving part comprises a decoder module, a demodulation module, an electric signal processing circuit, an optical detector and an optical receiving antenna which are connected successively, and the encoder module, decoder module and the data interface are connected. The method comprises the following steps: encoding is firstly carried out, PPM modulation and laser drive circuit conversion are carried out to the encoded information code to generate an optical signal which is emitted into an air channel, the receiving part obtains a baseband signal by the processing of the electric signal processing circuit and the demodulation module after receiving the optical signal, and a correct decoding value is output after the decoding. The error correcting system and the error correcting method solve the problem that PPM modulation in current GF (2) domain is complex and can accurately judge the specific position of pulses with error.

Description

Error correction system and error correction method thereof on wireless laser communication GF (q) territory

Technical field

The invention belongs to communication technical field, relate to a kind of error correction system, be specifically related to the error correction system on a kind of wireless laser communication GF (q) territory, the invention still further relates to and utilize this system to carry out the method for error correction.

Background technology

During as transmission medium, natural phenomenas such as the mist in the atmosphere, rain, snow and atmospheric turbulance all can exert an influence to laser signal laser, make the pulse signal broadening with atmosphere; Signal to noise ratio reduces, and the error rate increases, even under serious situation; May cause communication disruption; And, require the data of transmission to have error correcting capability, so in wireless laser communication, must take error correction coding along with the appearance of mass-storage system in the optical communication system with to the raising of communication data reliability requirement.And chnnel coding is based on the error correction coding on GF (2) territory in the existing laser communication system, and modulation system adopts the PPM modulation.If because the existence generation error code of interchannel noise, mistake has appearred in which subframe that indicates that the error correcting code on GF (2) territory just can not be clear and definite.

Summary of the invention

The purpose of this invention is to provide the error correction system on a kind of wireless laser communication GF (q) territory, the accurate particular location of misjudgment pulse when error code takes place, and modulation system is simple.

Another object of the present invention provides the method for utilizing said system to carry out error correction.

The technical scheme that the present invention adopted is; Error correction system on a kind of wireless laser communication GF (q) territory; Comprise data-interface, radiating portion, receiving unit; Wherein, Radiating portion comprises coder module, modulation module, drive circuit for laser, laser, the optical transmitting antenna that connects successively, and receiving unit comprises decoder module, demodulation module, electric signal processing circuit, fluorescence detector, the optical receiver antenna that connects successively, and coder module, decoder module and data-interface are connected.

Another technical scheme that the present invention adopted is, a kind of method of utilizing this system to carry out error correction is carried out according to the following steps:

Step 1: external data source is sent to information sequence through data-interface carries out encoding process in the coder module, obtain message code;

Step 2: the message code that step 1 is finished sends to and carries out the PPM modulation in the modulation module; The modulated signal that modulation is produced makes the luminous generation light signal of laser through drive circuit for laser, is transmitted in the atmospheric channel after through optical transmitting antenna light signal collimation, expansion being restrainted and goes;

Step 3: adopt optical receiver antenna to receive the light signal in the atmospheric channel; The light signal that receives is converged on the fluorescence detector; Fluorescence detector passes to electric signal processing circuit with light signal; Electric signal processing circuit sends to demodulation module after converting light signal to the signal of telecommunication, and demodulation module carries out the PPM demodulation with the signal of telecommunication and restores baseband signal;

Step 4: the baseband signal that step 3 is obtained is sent into decoder module and is carried out error-correcting decoding, obtains correct decoding value;

Step 5: the correct decoding value that obtains step 4 outputs in the receiving equipment through data-interface.

The invention has the beneficial effects as follows:

1. the PPM modulation can make bandwidth availability ratio reduce on many first territories, can all have under the situation of requirement at average transmit power and bandwidth availability ratio, selects suitable multi-system PPM modulation system.

2. radio telecommunicaltion system stable performance, reliable operation, volume is little, cost performance is high, transmission rate 20Mbit/s, and communication distance 3～5km can transmitting multi-path video signal and voice signal.

Description of drawings

Fig. 1 is the structural representation of the error correction system on wireless laser communication GF of the present invention (q) territory;

Fig. 2 is the error correction system BCH decoding FB(flow block) on wireless laser communication GF of the present invention (q) territory.

Among the figure, 1. data-interface, 2. coder module, 3. modulation module, 4. drive circuit for laser, 5. laser, 6. optical transmitting antenna, 7. optical receiver antenna, 8. fluorescence detector, 9. electric signal processing circuit, 10. demodulation module, 11. decoder module.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is elaborated.

The structure of the error correction system on wireless laser communication GF of the present invention (q) territory; As shown in Figure 1; Comprise data-interface 1, radiating portion and receiving unit; Wherein, radiating portion comprises coder module 2, modulation module 3, drive circuit for laser 4, laser 5, the optical transmitting antenna 6 that connects successively; Receiving unit comprises decoder module 11, demodulation module 10, electric signal processing circuit 9, fluorescence detector 8, the optical receiver antenna 7 that connects successively.Coder module 2, decoder module 11 and data-interface 1 are connected.

The error correction method of the error correction system on wireless laser communication GF of the present invention (q) territory, specifically implement according to the following steps:

Step 1: external data source is sent to information sequence in the coder module 2 through data-interface 1, carries out encoding process, specifically implements according to following steps:

(1) in GF (q) territory, confirms channel coding method

If α is a finite field On a nonzero element, have integer l>=1, then code length is that n, minimum range are that the generator polynomial of BCH code on GF (q) territory of 2t+1 must be with α ^l, α ^L+1..., α ^{L+ δ-2}Be root, establish GF (q ^m) on nonzero element α ⁱBe the minimal polynomial m on GF (q) territory _i(x) root, then the generator polynomial of BCH code is expressed as

g(x)＝lcm{(m _l(x)，m _l+1(x)，…m _l+2t-1(x)} (1)

(2) coded system that obtained according to the last step is encoded

If message polynomial is m (x)=m ₀+ m ₁X+ ... + m _K-1x ^K-1, m ₀, m ₁..., m _K-1∈ GF (q), then the code word multinomial does

C(x)＝m(x)g(x)＝c ₀+c ₁x+…+c _n-1x ^n-1，c ₀，c ₁，…，c _n-1∈GF(q) (2)

BCH code is the product by k symbolic information position and generator polynomial; Compiling the code word of coming out like this is nonsystematic code; Encoder is generated by the polynomial multiplication device; Realize the polynomial multiplication process; The 2t level shift register that needs 2t memory cell to form; Also need 2t mould

adder and 2t+1 mould

often to take advantage of device

When cataloged procedure began, all registers were all clear 0, after carrying out being shifted first time, and the highest order Coefficient m of message polynomial _K-1With g _2tMultiply each other, in the polynomial high order Coefficient m of output output product _K-1g _2t, m _K-1Deposit the first order (from left to right) in, then the x of m (x) ^N-2Item coefficient m _K-2Send into shifting memory, simultaneously g _2tWith m _K-2Back and g multiply each other _2t-1With m _K-1Modulo addition is delivered to output, obtains inferior high the coefficient of C (x), repeat k displacement successively after, the coefficient of m (x) is all sent into shifting memory, after carrying out deg (m (x))+deg (g (x))+1 displacement, exports the polynomial constant term m of product at output ₀g ₀, the value full recovery in the shift register is to complete 0 state then, and one time cataloged procedure is accomplished, and prepares second group of data and encodes next time.

Step 2: the message code that step 1 is finished sends to and carries out the PPM modulation in the modulation module 3; To modulate the modulated signal that produces then and make laser 5 luminous generation light signals, and be transmitted in the atmospheric channel after through optical transmitting antenna 6 light signal collimation, expansion being restrainted and go through drive circuit for laser 4.

Step 3: the light signal that optical receiver antenna 7 receives in the atmospheric channel; The light signal that receives is converged on the fluorescence detector 8; Fluorescence detector 8 passes to electric signal processing circuit 9 with light signal; Electric signal processing circuit 9 sends to demodulation module 10 after converting light signal to the signal of telecommunication, and demodulation module 10 carries out the PPM demodulation with the signal of telecommunication and restores baseband signal.

Step 4: the baseband signal that step 3 is obtained is sent into decoder module 11 and carried out error-correcting decoding, and is as shown in Figure 2, specifically implements according to following steps:

(1) received information sequence

If signaling vector C=is (c ₀, c ₁..., c _N-1), error vector E=(e ₀, e ₁..., e _N-1), the wrong multinomial of signaling multinomial and transmission channel is respectively

c(x)＝c ₀+c ₁x ¹+…+c _n-1x ^n-1 c ₀，c ₁，…，c _n-1∈GF(q) (3)

e(x)＝e ₀+e ₁x ¹+…+e _n-1x ^n-1 e ₀，e ₁，…，e _n-1∈GF(q) (4)

The reception vector that receives at receiving terminal is R=[r _N-1..., r ₁, r ₀], then pairing multinomial does

r(x)＝c(x)+e(x)＝r ₀+r ₁x ¹+…+r _n-1x ^n-1，r ₀，r ₁，…，r _n-1∈GF(q) (5)

(2) calculate associated polynomial

By defining of BCH code c (α ^kSet up)=0, so

s _k＝r(α ^k)＝0+e(α ^k)＝e ₀+e ₁(α ^k) ¹+…+e _n-1(α ^k) ^n-1＝e ₀+e ₁(α ¹) ^k+…+e _n-1(α ^n-1) ^k (6)

When wrong generation, e ₀, e ₁..., e _N-1Be not to be the zero heavy vector of n entirely on GF (q) territory,, then have if remove the item that does not make a mistake

s _k=e _J1γ _J1 ^k+ e _J2γ _J2 ^k+ e _Jtγ _Jt ^k=λ ₁β ₁ ^k+ λ ₂β ₂ ^k+ ... + λ _tβ _t ^k(7) λ in the formula _h=e _Jh1≤h≤t, ${\mathrm{\β}}_h={\mathrm{\γ}}^{j^h}1\≤h\≤t,$ Wherein t is the number of errors that takes place at most, and k gets values all among 1≤k≤2t successively, obtains following equation group

$\left\{\begin{array}{c}{s}_1={\mathrm{\λ}}_1{\mathrm{\β}}_1+{\mathrm{\λ}}_2{\mathrm{\β}}_2+...+{\mathrm{\λ}}_t{\mathrm{\β}}_t\\ s_2={\mathrm{\λ}}_1{{\mathrm{\β}}_1}^2+{\mathrm{\λ}}_2{{\mathrm{\β}}_2}^2+...+{\mathrm{\λ}}_t{{\mathrm{\β}}_t}^2\\ s_3={\mathrm{\λ}}_1{{\mathrm{\β}}_1}^3+{\mathrm{\λ}}_2{{\mathrm{\β}}_2}^3+...+{\mathrm{\λ}}_t{{\mathrm{\β}}_t}^3\\ .\\ .\\ .\\ s_{2t}={\mathrm{\λ}}_1{{\mathrm{\β}}_1}^{2t}+{\mathrm{\λ}}_2{{\mathrm{\β}}_2}^{2t}+...+{\mathrm{\λ}}_t{{\mathrm{\β}}_t}^{2t}\end{array}\right.---\left(8\right)$

(3) mistake in computation position multinomial coefficient

If β ₁, β ₂..., β _tThe error location polynomial that is constituted does

σ(x)＝(1-β ₁x)(1-β ₂x)…(1-β _tx)＝1+σ ₁x+σ ₂x ²+…+σ _tx ^t (9)

λ is multiply by at two ends _hβ _h ^K+1, substitution $x={\mathrm{\β}}_h^{-1}$ And h can obtain from 1 to t summation

$\underset{h=1}{\overset{t}{\mathrm{\Σ}}}{\mathrm{\λ}}_h{\mathrm{\β}}_h^{k+t}+{\mathrm{\σ}}_1\underset{h=1}{\overset{t}{\mathrm{\Σ}}}{\mathrm{\λ}}_h{\mathrm{\β}}_h^{k+t-1}+...+{\mathrm{\σ}}_t\underset{h=1}{\overset{t}{\mathrm{\Σ}}}{\mathrm{\λ}}_h{\mathrm{\β}}_h^k=0---\left(10\right)$

Promptly have

s _k+t+σ ₁s _k+t-1+…+σ _ts _k＝0 (11)

By formula (11), draw all syndrome equation group of 1≤k≤t, it is expressed as matrix form

$\left[\begin{array}{cccc}{s}_1& s_2.& ...& s_t\\ s_2& s_3& ...& s_{t+1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ s_t& s_{t+1}& ...& s_{2t-1}\end{array}\right]\left[\begin{array}{c}{\mathrm{\σ}}_t\\ {\mathrm{\σ}}_{t-1}\\ .\\ .\\ .\\ {\mathrm{\σ}}_1\end{array}\right]=\left[\begin{array}{c}-s_{t+1}\\ -s_{t+2}\\ .\\ .\\ .\\ -s_{2t}\end{array}\right]---\left(12\right)$

Transform (12) draws

$\left[\begin{array}{c}{\mathrm{\σ}}_t\\ {\mathrm{\σ}}_{t-1}\\ .\\ .\\ .\\ {\mathrm{\σ}}_1\end{array}\right]={\left[\begin{array}{cccc}{s}_1& s_2& ...& s_t\\ s_2& s_3& ...& s_{t+1}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ s_t& s_{t+1}& ...& s_{2t-1}\end{array}\right]}^{-1}\left[\begin{array}{c}-s_{t+1}\\ -s_{t+2}\\ .\\ .\\ .\\ -s_{2t}\end{array}\right]---\left(13\right)$

Formula (13) is found the solution, obtained wrong polynomial coefficient.

(4) mistake in computation position and improper value

Again with σ ₁, σ ₂..., σ _tSubstitution formula (9) makes σ (x)=0, calculates $x_i={\mathrm{\β}}_i^{-1}(1\≤i\≤t),$ Carry out x once more _i ^I-1(1≤i≤t) computing confirms the position that all make a mistake.The group of solving an equation (8) obtains improper value λ _i(1≤i≤t).

(5) mistake in computation vector

The errors present and the improper value that obtained according to the last step, the improper value of obtaining on the corresponding errors present, all the other positions get zero, are error vector.

(6) calculate correct decoding value

By C=R-E, obtain correct decoding value, decoding finishes.

Step 5: the correct decoding value that obtained the last step outputs in the receiving equipment through data-interface 1.

Embodiment

With GF (3) territory error correcting code is example, specifies the embodiment of error correction method of the present invention.

Step 1: external data source is sent to information sequence in the coder module 2 through data-interface 1, carries out encoding process, specifically implements according to following steps:

If α is GF (3 ³) primitive element on the territory, α ³+ 2 α+1st, primitive polynomial is calculated the minimal polynomial that satisfies condition according to the cyclotomy coset.Table look-up and 1 obtain GF (3 ^m) expression formula of element power on the territory:

Table 1GF (3 ³) list of elements on the territory

The finite field element	Ternary is represented (a α 2，bα 1，cα 0)	The finite field element	Ternary is represented (a α 2，bα 1，cα 0)
				0	000	α 13＝2	002
1	001	α 14＝2α	020
				α	010	α 15＝2α 2	200
α 2	100	α 16＝2α+1	021
				α 3＝α+2	012	α 17＝2α 2+α	210
α 4＝α 2+2α	120	α 18＝α 2+2α+1	121
				α 5＝2α 2+α+2	212	α 19＝2α 2+2α+2	222
α 6＝α 2+α+1	111	α 20＝2α 2+α+1	211
				α 7＝α 2+2α+2	122	α 21＝α 2+1	101
α 8＝2α 2+2	202	α 22＝2α+2	022
				α 9＝α+1	011	α 23＝2α 2+2α	220
α 10＝α 2+α	110	α 24＝2α 2+2α+1	221
				α 11＝α 2+α+2	112	α 25＝2α 2+1	201
α 12＝α 2+2	102	α 26＝1	001

1, the minimal polynomial of α:

m ₁(x)＝(x-α)(x-α ³)(x-α ⁹)＝x ³+2x+1

2, α ²Minimal polynomial:

m ₂(x)＝(x-α ²)(x-α ⁶)(x-α ¹⁸)＝x ³+x ²+x+2

3, α ⁴Minimal polynomial:

m ₄(x)＝(x-α ⁴)(x-α ¹⁰)(x-α ¹²)＝x ³+x ²+2

4, α ⁵Minimal polynomial:

m ₅(x)＝(x-α ⁵)(x-α ¹⁵)(x-α ¹⁹)＝x ³+2x ²+x+1

If the number of correcting a mistake is t, the error correcting capability that requires according to reality obtains the different BCH code of parameter:

When t=1, then

g ₁(x)=lcm{m ₁(x), m ₂(x) }=lcm{x ³+ 2x+1, x ³+ x ²+ x+2}=x ⁶+ x ⁵+ 2x ³+ 2x+2 is by deg (g (x))=6, n=26, and k=n-deg (g (x))=20 can construct with g ₁(x) for generating polynomial BCH [26,20].

When t=2, then

g ₂(x)＝lcm{m ₁(x)，m ₂(x)，m ₃(x)，m ₄(x)}＝lcm{x ³+2x+1，x ³+x ²+x+2，x ³+2x+1，x ³+x ²+2}

＝x ⁹+2x ⁸+x ⁷+x ⁶+x ⁵+2x ⁴+2x ³+2x ²+x+1

By deg (g (x))=9, n=26, k=n-deg (g (x))=17 can construct with g ₂(x) for generating polynomial BCH [26,17].

When t=3, then

g ₃(x)＝lcm{m ₁(x)，m ₂(x)，m ₃(x)，m ₄(x)，m ₅(x)，m ₆(x)}

＝lcm{x ³+2x+1，x ³+x ²+x+2，x ³+2x+1，x ³+x ²+2，x ³+2x ²+x+1，x ³+x ²+x+2}

＝x ¹²+x ¹¹+2x ⁶+x ³+2x ²+2x+1

By deg (g (x))=12, n=26, k=n-deg (g (x))=14 can construct with g ₃(x) for generating polynomial BCH [26,14].

Step 2: the message code that step 1 is finished sends to and carries out the PPM modulation in the modulation module 3; The modulated signal that modulation is produced makes laser 5 luminous generation light signals through drive circuit for laser 4, is transmitted in the atmospheric channel after through optical transmitting antenna 6 light signal collimation, expansion being restrainted and goes.

Step 3: the light signal that optical receiver antenna 7 receives in the atmospheric channel; The light signal that receives is converged on the fluorescence detector 8; Fluorescence detector 8 passes to electric signal processing circuit 9 with light signal; Electric signal processing circuit 9 sends to demodulation module 10 after converting light signal to the signal of telecommunication, and demodulation module 10 carries out the PPM demodulation with the signal of telecommunication and restores baseband signal.

Step 4: the baseband signal that step 3 is obtained is sent into decoder module 11 and is carried out error-correcting decoding, specifically implements according to following steps:

(1) received information sequence

The transmission code word is C=(00000000000000001211122211); If the error vector of channel is E=(02200000000000000000000000); Through after the Channel Transmission; At the reception vector R=(02200000000000001211122211) of receiving terminal after input, promptly receiverd polynomial does

r(x)＝2x ²⁴+2x ²³+x ⁹+2x ⁸+x ⁷+x ⁶+x ⁵+2x ⁴+2x ³+2x ²+x+1

(2) calculate associated polynomial

s ₁＝r(α)＝2α ²⁴+2α ²³+α ⁹+2α ⁸+α ⁷+α ⁶+α ⁵+2α ⁴+2α ³+2α ²+α+1＝α ¹⁹

In like manner α ², α ³, α ⁴Be updated in the receiverd polynomial and can obtain

s ₂＝r(α ²)＝α ²，s ₃＝r(α ³)＝α ⁵，s ₄＝r(α ⁴)＝α ¹⁹

(3) mistake in computation position multinomial coefficient

Order $M=\left[\begin{array}{cc}{s}_1& s_2\\ s_2& s_3\end{array}\right],$ $\mathrm{Det}M=s_1{s}_3+2s_2^2$

${\mathrm{\σ}}_1=\frac{s_2{s}_3+2s_1{s}_4}{s_1{s}_3+2s_2^2}={\mathrm{\α}}^{19}$ ${\mathrm{\σ}}_2=\frac{2s_3^2+s_2{s}_4}{s_1{s}_3+2s_2^2}={\mathrm{\α}}^{21}$

(4) mistake in computation position and improper value

Wrong multinomial coefficient by the last step obtains gets error location polynomial σ (x)=1+ α ¹⁹X+ α ²¹x ²Make σ (x)=0, calculate the position β that makes a mistake ₁=α ²⁴, β ₂=α ²³

If the improper value of errors present is λ ₁, λ ₂, then have

$\left[\begin{array}{cc}{\mathrm{\β}}_1& {\mathrm{\β}}_2\\ {\mathrm{\β}}_1^2& {\mathrm{\β}}_2^2\end{array}\right]\left[\begin{array}{c}{\mathrm{\λ}}_1\\ {\mathrm{\λ}}_2\end{array}\right]=\left[\begin{array}{c}{s}_1\\ s_2\end{array}\right]$

Finding the solution the improper value that obtains occurring in the error bit is λ ₁=2, λ ₂=2.

(5) mistake in computation vector

Errors present and improper value based on the last step obtains obtain error vector

E＝(02200000000000000000000000)。

(6) calculate correct decoding value

C＝R-E＝(02200000000000001211122211)-(02200000000000000000000000)

＝(00000000000000001211122211)

Step 5: the correct decoding value that obtained the last step outputs in the receiving equipment through data-interface 1.

Error correction system and error correction method thereof on wireless laser communication GF of the present invention (q) territory have solved in present GF (2) territory PPM modulation complicated problems, and the accurate particular location of misjudgment pulse.

Claims (1)

1. the error correction method on a wireless laser communication GF (q) territory is characterized in that, specifically implements according to following steps:

Step 1: external data source is sent to coder module to information sequence through data-interface (1)

(2) carry out encoding process in, obtain message code; Specifically implement according to following steps:

(1) in GF (q) territory, confirms channel coding method

If α is a finite field

On a nonzero element, have integer l>=1, code length is that n, minimum distance are that the generator polynomial of BCH code on GF (q) territory of 2t+1 is with α ^l, α ^L+1..., α ^{L+ δ-2}Be root, establish GF (q ^m) on nonzero element α ⁱBe the minimal polynomial m on GF (q) territory _i(x) root, the generator polynomial of BCH code is expressed as

g(x)＝lcm{(m _l(x)，m _l+1(x)，…m _l+2t-1(x)}；

(2) coded system that obtained based on the last step is encoded to external data source

If message polynomial is m (x)=m ₀+ m ₁X+ ... + m _K-1x ^K-1, m ₀, m ₁..., m _K-1∈ GF (q), then the code word multinomial does

C(x)＝m(x)g(x)＝c ₀+c ₁x+…+c _n-1x ^n-1，c ₀，c ₁，…，c _n-1∈GF(q)

When cataloged procedure began, all shift registers were all clear 0, after carrying out being shifted first time, and the highest order Coefficient m of message polynomial _K-1With g _2tMultiply each other, in the polynomial high order Coefficient m of output output code word _K-1g _2t, m _K-1Deposit the first order from left to right in, then the x of m (x) ^N-2Item coefficient m _K-2Send into shift register, simultaneously g _2tWith m _K-2Back and g multiply each other _2t-1With m _K-1The product modulo addition deliver to output; Obtain inferior high the coefficient of C (x), after repeating successively to be shifted for k time, the coefficient of m (x) is all sent into shift register; After carrying out deg (m (x))+deg (g (x))+1 displacement, at the polynomial constant term m of output output code word ₀g ₀, the value full recovery in the shift register is to complete 0 state then, and one time cataloged procedure is accomplished, and prepares second group of data and encodes next time;

Step 2: the message code that step 1 is finished sends to and carries out the PPM modulation in the modulation module (3); The modulated signal that modulation is produced makes the luminous generation light signal of laser (5) through drive circuit for laser (4), is transmitted in the atmospheric channel after through optical transmitting antenna (6) light signal collimation, expansion being restrainted and goes;

Step 3: adopt optical receiver antenna (7) to receive the light signal in the atmospheric channel; The light signal that receives is converged on the fluorescence detector (8); Fluorescence detector (8) passes to electric signal processing circuit (9) with light signal; Electric signal processing circuit (9) sends to demodulation module (10) after converting light signal to the signal of telecommunication, and demodulation module (10) carries out the PPM demodulation with the signal of telecommunication and restores baseband signal;

Step 4: the baseband signal that step 3 is obtained is sent into decoder module (11) and is carried out error-correcting decoding, obtains correct decoding value; Specifically implement according to following steps:

(1) received information sequence

If signaling vector C=is (c ₀, c ₁..., c _N-1), error vector E=(e ₀, e ₁..., e _N-1), the wrong multinomial of signaling multinomial and transmission channel is respectively

c(x)＝c ₀+c ₁x ¹+…+c _n-1x ^n-1 c ₀，c ₁，…，c _n-1∈GF(q)

e(x)＝e ₀+c ₁x ¹+…+e _n-1x ^n-1 e ₀，e ₁，…，e _n-1∈GF(q)

The reception vector that receives at receiving terminal is R=[r _N-1..., r ₁, r ₀], pairing multinomial does

r(x)＝c(x)+e(x)＝r ₀+r ₁x ¹+…+r _n-1x ^n-1，r ₀，r ₁，…，r _n-1∈GF(q)

(2) calculate associated polynomial

s _k＝r(α ^k)＝e(α ^k)＝e ₀+e ₁(α ^k) ¹+…+e _n-1(α ^k) ^n-1＝e ₀+e ₁(α ¹) ^k+…+e _n-1(α ^n-1) ^k

When wrong generation, e ₀, e ₁..., e _N-1Be not to be the zero heavy vector of n entirely on GF (q) territory, remove the item that does not make a mistake, then have

wherein t is the number of errors that takes place at most; K gets values all among 1≤k≤2t successively, obtains following equation group

(3) mistake in computation position multinomial coefficient

If β ₁, β ₂..., β _tThe error location polynomial that is constituted does

σ (x)=(1-β ₁X) (1-β ₂X) ... (1-β _tX)=1+ σ ₁X+ σ ₂x ²+ ... + σ _tx ^tTwo ends multiply by

Substitution

And h obtains from 1 to t summation

Promptly have

s _k+t+σ ₁s _k+t-1+…+σ _ts _k＝0

Draw all syndrome equation group of 1≤k≤t, it is expressed as matrix form

Obtain after the conversion

Find the solution the coefficient that obtains error location polynomial;

(4) mistake in computation position and improper value

Again with σ ₁, σ ₂..., σ _tThe substitution error location polynomial makes σ (x)=0, calculates

Carry out once more

(1≤i≤t) computing confirms the position that all make a mistake, and separates the equation group in the step (2), obtains improper value λ _i(1≤i≤t);

(5) mistake in computation vector

According to errors present and the improper value that the last step obtains, on the errors present of correspondence, get improper value, the surplus position of improper value is got zero, promptly obtain error vector;

(6) calculate correct decoding value

By C=R-E, obtain correct decoding value, decoding finishes;

Step 5: the correct decoding value that obtains step 4 outputs in the receiving equipment through data-interface (1).

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