CN106685527A - Free space optical communication method and system based on LDPC code - Google Patents

Abstract

The invention provides a free space optical communication method and system based on an LDPC code. The method and system aim at a problem that the error rate, communication distance and communication bandwidth of a system are affected by the flicker and light beam drift and extension caused by atmosphere turbulence and the reduction of signal to noise ratio of a receiving end in laser communication. The method comprises the steps: firstly proposing a logarithmic normal distribution channel model under weak turbulence and a K-distribution channel model under strong turbulence according to the characteristics of atmosphere turbulence channels; secondly constructing an irregular QC-LDPC code on the basis of the proposed channel models; finally deducing an LLR probability density function, and carrying out the decoding through an LLR-BP algorithm. A confidence decoding BP result indicates the error rate of the system remarkably decreases along with the increase of signal to noise ratio. An experiment indicates that the method and system can effectively reduce the performance of an FSO system.

Description

A kind of FSO method and communication system based on LDPC code

Technical field

The present invention relates to a kind of FSO method and communication system, belong to technical field of photo communication.

Background technology

FSO (Free-Space-Optical communication, abbreviation FSO) is logical also known as wireless optical Letter (Wireless-Optical-communication, abbreviation WOC), is the transport vehicle using laser as information, and air is made For transmission medium, a kind of bi-directionally transmitted communication technology is carried out to information such as data, image, voices.On the one hand, FSO systems are adopted With during fiber optic communication the characteristics of the high transfer rate of light and photoelectric conversion technique, with high bandwidth, high modulation rate and The characteristics of frequency spectrum resource occupancy is few；On the other hand, FSO systems combine the advantage of airwave communication technology, substantially reduce The cost of communication, line construction cycle is short, system set up also more convenient.

And in near-earth laser communication system signal transmission, for the analysis that air is disturbed laser communication signal, research The absorption and scattering of air are concentrated mainly on, until the flicker, beam drift, the extension that just start to cause atmospheric turbulance in recent years And studied the problems such as atmospheric dispersion, and these factors can all affect the signal to noise ratio of receiving end signal, so as to affect system The bit error rate and communication distance, communication bandwidth.Therefore, which kind of channel model is selected, will be straight using which kind of error control coding Connect the performance for having influence on optical communication system.

LDPC code is that a class can use very sparse check matrix H (Parity-Check Matrix H) or bipartite graph (Bipartite Graph), come the Linear codes error correcting code that describes, the smallest hamming distance of LDPC code can be with the increase of code length And it is linearly increasing, carry out the feature with the bit error rate reduction with code word size increase during posterior probability iterative decoding；And And, the LDPC code for being iterated decoding algorithm has the performance for approaching shannon limit.And LDPC coding techniques now is mainly concentrated In Gaussian channel and Rayleigh channel, there is the lower bit error rate under both channels；But awgn channel and Rayleigh channel belong to The fading effect of little yardstick, can not meet the system communication performance demand under strong turbulence effect.

The content of the invention

It is an object of the invention to overcome the deficiencies in the prior art, and propose that a kind of free space optical based on LDPC code leads to Letter method and communication system, for the mushing error under the influence of atmospheric turbulance, select suitable channel model and application more optimize Channel coding so as to reduce receive signal the bit error rate.

Technical scheme that the object of the invention adopted is realized for a kind of, FSO method based on LDPC code, Comprise the steps：

(1) data model for receiving signal is set up, the channel model of different atmospheric turbulence intensities is proposed for：

(1-1) data model r (t) for receiving signal is set up,

R (t)=y (t) n₁(t)+n₀(t)

Wherein t be the time, y (t) be transmission signal, n₁T () is the multiplicative noise that atmospheric turbulance causes, n₀T () is to include heat Noise, amplification noise are in interior additive Gaussian noise, n₀T it is σ that () average is 0, variance²；

(1-2) atmospheric channel is divided into strong turbulence channel and weak turbulence channel, is proposed for different atmospheric turbulence intensities Channel model；

A) model emulation, probability of light intensity V under weak turbulent-flow conditions are carried out using logarithm normal distribution under weak turbulence channel Density isWherein, σ_x ²For logarithmic amplitude variance, V₀For average intensity；

B) model emulation is carried out using K distributions under strong turbulence channel, distribution function of light intensity V under strong turbulence effect isWherein V be light intensity, Γ (α) be Gamma functions, α be k distribution orders, K_p(x) For the Bessel function of the second kind of amendment；

(1-3) for the channel model obtained in step (1-2), different log-likelihoods are obtained under strong and weak turbulent-flow conditions Than；

C) under weak turbulent-flow conditions, if during sending signal y=0 being state D₀, it is state D during sending signal y=1₁；

C-a) it is in state D₀When, the conditional probability density function for receiving signal is：

C-b) it is in state D₁When, the conditional probability density function for receiving signal is：

D) under the conditions of strong turbulence, if during sending signal y=0 being state D₀, it is state D during sending signal y=1₁；

D-a) it is in state D₀When, r (t)=n (t), the additive Gaussian noise beyond turbulent flow is 0, and it receives the bar of signal Part probability density function is：

D-b) it is in state D₁When, the conditional probability density function for receiving signal is：

(1-4) according to the conditional probability density function under the different channels obtained in step (1-3), transition probability is calculated close Degree f_i ^y, computing formula is：

(2) encode, using irregular quasi-cyclic LDPC code constructing method, particular content is as follows；

(2-1) N, M and q initialization：Code length is set as N, information bit is M, code check R=(N-M)/N, unit matrix dimension is Q=N/6；

(2-2) build check matrix H, check matrix H is made up of submatrix A and submatrix B, H=[A B], submatrix B by Secondary submatrix B₁With secondary submatrix B₂Constitute, B=[B₁B₂],

Wherein, the element of submatrix A is that unit circulates submatrix I_x, define I_xFollowed to the right by the often row of q rank unit matrix I Ring movement x positions obtain, a^k-1b^k-1>=x >=1, a and b are the prime number less than q, k >=2；Secondary submatrix B₁Element P in have and Only 3 nonzero elements and P_k-1For one of nonzero element, remaining element is zero, and it is unit circulation to define nonzero element Submatrix I_d, unit circle submatrix I_dBy the often row of q rank unit matrix I, to the right loopy moving d positions obtain, and d is random natural Number；

(2-3) syndrome matrix A, if submatrix A is singular matrix, return to step (3-1) resets N；If A is non- Singular matrix, then generator matrix G and length for N code c_n,

G=[B^-1·A I_N-M]；c_n=u_n·G

In formula, u_n=[u_{N, 0} u_{N, 1} … u_{N, M-1}], u_nIt is an information bit vector for randomly selecting；

(3) decode, comprise the following steps that：

(3-1) initialize：According to transitional provavility density f_i ^yProbability Ln of the channel transfer to variable node is set, and Corresponding likelihood ratio message data λ (L_n), then set each variable node n and be transmitted to the check-node m being adjacent, obtain Variable node passes to the initial information of check-node：

λ⁽⁰⁾(q_n,m)=λ (L_n)；

(3-2) lateral processes, update also known as check-node：I.e. to the l time iterative process of n ∈ M (m) and m ∈ N (n) Middle variable node is delivered to the information of check-node and is updated, and more new formula is as follows：

(3-3) longitudinal direction is processed, and is updated also known as variable node：I.e. to the l time iterative process of n ∈ M (m) and m ∈ N (n) Middle check-node is delivered to the information of variable node and is updated, and more new formula is as follows：

(3-4) bit decision：

(3-4-1) pseudo- posterior probability is calculated, computing formula is as follows：

If variableWork as λ^(l)(q_n) ＞ 0 when, thenOtherwise,

(3-4-2) output condition judgement is decoded, ifOr iterations exceedes the maximum iteration time of regulation, then tie Beam,As effective output valve of decoding；Otherwise return to step (3-1) and continue iteration.

The present invention also corresponds to the communication system for said method for providing, including transmitting terminal and receiving terminal, the transmitting End includes information source memory cell, LDPC coding units, modulator and the laser instrument being electrically connected with, and the receiving terminal includes electrically connecting Photodetector, demodulator, BP decoders and the stay of two nights memory cell for connecing.

The laser instrument realizes the biography of laser signal with photodetector by optical transmitting antenna and optical receiver antenna It is defeated.

As shown from the above technical solution, the FSO method based on LDPC code that the present invention is provided, including three Individual step：Step one, sets up the data model for receiving signal, is proposed for the channel model of different atmospheric turbulence intensities；Step Two, coding, using irregular quasi-cyclic LDPC code constructing method；Step 3, decoding, according to the channel mould provided in step one Type, derives LLR probability density functions, decodes with LLR-BP algorithms.

Compared with prior art, the present invention has following benefit：

1st, the present invention is according to the characteristics of atmospheric turbulence channels, proposes logarithm normal distribution channel model under weak turbulent flow and strong K distribution channel models under turbulent flow, according to atmospheric turbulence intensity size, set up respective channels model, weak rapids under strong, weak turbulent flow The multipath fading effect for flowing down selects logarithm normal distribution, and multiple scattering effect is more serious under strong turbulence, with same probability point Cloth model is compared, and K distributions can conform better to the requirement of multiple scattering mechanism, and on the basis of this channel model, the present invention is carried Go out a kind of LDPC codings being distributed based on K, LDPC codings of the prior art are carried out all on the basis of Gaussian channel, this The LDPC code Designs carried out based on K distributions in invention more press close to the actual conditions of atmospheric turbulance, and designed pattern has More superior performance；

2nd, because the presence at Fourth Ring can reduce the performance of coding, the bit error rate is increased, the present invention obtains accurate in coding method In the step of circular matrix B, introduce by 3 unit circle submatrix I_xThe ordered series of numbers constituted with 0 element, unit circle submatrix I_x Position in the first row of quasi-cyclic matrix B is not fixed, can be moved up and down, and this design can increase test matrix H and enclose length, it is to avoid Can there is Fourth Ring in check matrix H so that enclosing for the Tanner figures of LDPC code is long more than 4, that is, avoid the presence of Fourth Ring；

3rd, the present invention can preferably play LDPC volumes using the irregular QC-LDPC codings of the variable fast coding of code speed The superior function of code, in the full rank for guaranteeing row matrix and on the premise of avoiding Fourth Ring, it is possible to obtain low rate is efficiently and at a high speed The characteristics of rate is stable, reduces the iterations of algorithm, while the bit error rate after decoding can arbitrarily be reduced with the increase of signal to noise ratio, Decline the Error floor phenomenon slowed down without the bit error rate；

4th, transceiver can be installed in roof by the communication system that the present invention is provided with low power infrared laser beam as carrier Or transmission data outside window, the flexibility of FSO makes it can apply to many enterprises and school, such as connection of enterprise LAN to LAN And the connection of campus network, replace optical fiber to access each local side with FSO, not only can reduces cost, and with higher transmission speed Degree, it is low cost when the communication system is built, simple to operate, therefore terminal applies of other connections at a high speed can be used in, such as building with Between building, across the network rapid deployment side of such as highway and river etc complexity landform, disaster recovery and interim solution Case, and can perfect " last one kilometer " problem for solving communication service network.

Description of the drawings

The structure principle chart of the communication system that Fig. 1 is provided for the present invention.

Fig. 2 is the coding flow chart of irregular quasi-cyclic LDPC code.

Fig. 3 is that BP decodes flow chart.

Fig. 4 is simulation example design sketch one of the QC-LDPC codings to error performance under weak turbulent-flow conditions.

Fig. 5 is simulation example design sketch two of the QC-LDPC codings to error performance under weak turbulent-flow conditions.

Fig. 6 is simulation example design sketch one of the QC-LDPC codings to error performance under the conditions of strong turbulence.

Fig. 7 is simulation example design sketch two of the QC-LDPC codings to error performance under the conditions of strong turbulence.

Specific embodiment

The present invention is illustrated in detail with reference to the accompanying drawings and examples, present disclosure is not limited to following Embodiment.

Embodiment 1：Under weak turbulent flow condition, it is 0.2,0.4 to be respectively provided with turbulivity, and construction code check is 0.5,0.67 and 0.75 QC-LDPC codings, then carry out LLR-BP decodings；Concrete grammar is as follows：

(1) data model for receiving signal is set up, the channel model of different atmospheric turbulence intensities is proposed for：

(1-1) data model r (t) for receiving signal is set up,

R (t)=y (t) n₁(t)+n₀(t)

Wherein t be the time, y (t) be transmission signal, n₁T () is the multiplicative noise that atmospheric turbulance causes, n₀T () is to include heat Noise, amplification noise are in interior additive Gaussian noise, n₀T it is σ that () average is 0, variance²；

(1-2) channel model for weak turbulence intensity is built, model emulation, light intensity V is carried out using logarithm normal distribution Probability density under weak turbulent-flow conditions isWherein, σ_x ²For logarithmic amplitude Variance, V₀For average intensity；

(1-3) for the channel model obtained in step (1-2), under weak turbulent-flow conditions log-likelihood ratio is obtained；

C) under weak turbulent-flow conditions, if during sending signal y=0 being state D₀, it is state D during sending signal y=1₁；

C-a) it is in state D₀When, the conditional probability density function for receiving signal is：

C-b) it is in state D₁When, the conditional probability density function for receiving signal is：

(1-4) according to the conditional probability density function under the different channels obtained in step (1-3), transition probability is calculated close Degree f_i ^y, computing formula is：

(2) encode, using irregular quasi-cyclic LDPC code constructing method, referring to Fig. 2, comprise the following steps that；

(2-1) N, M and q initialization：Code length is set as N=762, code check R=(N-M)/N, unit matrix dimension is q=N/ 6, q=127, prime number a=2, b=3 are shifted, information bit M is derived according to the code check R and formula R=(N-M) for setting/N；

(2-2) build check matrix H, check matrix H is made up of submatrix A and submatrix B, H=[A B], submatrix B by Secondary submatrix B₁With secondary submatrix B₂Constitute, B=[B₁B₂],

Wherein, the element of submatrix A is that unit circulates submatrix I_x, define I_xFollowed to the right by the often row of q rank unit matrix I Ring movement x positions obtain, a^k-1b^k-1>=x >=1, a and b are the prime number less than q, k >=2；Secondary submatrix B₁Element P in have and Only 3 nonzero elements and P_k-1For one of nonzero element, remaining element is zero, and it is unit circulation to define nonzero element Submatrix I_d, unit circle submatrix I_dBy the often row of q rank unit matrix I, to the right loopy moving d positions obtain, and d is random natural Number；

(2-3) syndrome matrix A, if submatrix A is singular matrix, return to step (3-1) resets N；If A is non- Singular matrix, then generator matrix G and length for N code c_n,

G=[B^-1·A I_N-M]；c_n=u_n·G

In formula, u_n=[u_{N, 0} u_{N, 1}…u_{N, M-1}], u_nIt is an information bit vector for randomly selecting；

(3) decode, referring to Fig. 3, comprise the following steps that：

(3-1) initialize：According to transitional provavility density f_i ^yProbability Ln of the channel transfer to variable node is set, and Corresponding likelihood ratio message data λ (L_n), then set each variable node n and be transmitted to the check-node m being adjacent, obtain Variable node passes to the initial information of check-node：

λ⁽⁰⁾(q_n,m)=λ (L_n)；

(3-2) lateral processes, update also known as check-node：I.e. to the l time iterative process of n ∈ M (m) and m ∈ N (n) Middle variable node is delivered to the information of check-node and is updated, and more new formula is as follows：

(3-3) longitudinal direction is processed, and is updated also known as variable node：I.e. to the l time iterative process of n ∈ M (m) and m ∈ N (n) Middle check-node is delivered to the information of variable node and is updated, and more new formula is as follows：

(3-4) bit decision：

(3-4-1) pseudo- posterior probability is calculated, computing formula is as follows：

If variableWork as λ^(l)(q_n) ＞ 0 when, thenOtherwise,

(3-4-2) output condition judgement is decoded, ifOr iterations exceedes the maximum iteration time of regulation, then tie Beam,As effective output valve of decoding；Otherwise return to step (3-1) and continue iteration.

As a result show, substantially reduce through the signal error rate of LDPC codings, the performance of FSO is obviously improved；In addition, for The LDPC codings of different code checks, when the bit error rate is 10^-6, when turbulivity is 0.2, the performance of code check R=0.5 is than 0.67 and 0.75 Under improve 5~7dB；When turbulivity is 0.4, the performance ratio of code check R=0.5 improves 7~10dB under 0.67 and 0.75； Simulation result is as shown in Figure 4 and Figure 5.

The present invention also corresponds to the communication system for said method for providing, referring to Fig. 1, including transmitting terminal and receiving terminal, The transmitting terminal includes information source memory cell, LDPC coding units, modulator and the laser instrument being electrically connected with, the receiving terminal bag Photodetector, demodulator, BP decoders and the stay of two nights memory cell of electric connection are included, laser instrument passes through light with photodetector Learn transmitting antenna and optical receiver antenna realizes the transmission of laser signal.

Embodiment 2：Under strong turbulence effect, when setting k distribution orders α is 1 and 4, corresponding turbulivity σ is 3 Hes 1.5, the QC-LDPC codings that code check is 0.5 and 0.75 are constructed respectively, then carry out LLR-BP decodings；Concrete grammar is as follows：

(1) data model for receiving signal is set up, the channel model of different atmospheric turbulence intensities is proposed for：

(1-1) data model r (t) for receiving signal is set up,

R (t)=y (t) n₁(t)+n₀(t)

Wherein t be the time, y (t) be transmission signal, n₁T () is the multiplicative noise that atmospheric turbulance causes, n₀T () is to include heat Noise, amplification noise are in interior additive Gaussian noise, n₀T it is σ that () average is 0, variance²；

(1-2) channel model for strong turbulence intensity is built, model emulation is carried out using K distributions, light intensity V is in strong turbulence Distribution function under effect isWherein V is light intensity, and Γ (α) is Gamma letters Number, it is positive parameter that α is a perseverance for depending on atmospheric turbulance, i.e. k distribution orders, K_pX () is the Equations of The Second Kind Bezier of amendment Function；

(1-3) for the channel model obtained in step (1-2), log-likelihood ratio is obtained under the conditions of strong turbulence；

D) under the conditions of strong turbulence, if during sending signal y=0 being state D₀, it is state D during sending signal y=1₁；

D-a) it is in state D₀When, r (t)=n (t), the additive Gaussian noise beyond turbulent flow is 0, and it receives the bar of signal Part probability density function is：

D-b) it is in state D₁When, the conditional probability density function for receiving signal is：

(1-4) according to the conditional probability density function under the different channels obtained in step (1-3), transition probability is calculated close Degree f_i ^y, computing formula is：

(2) encode, using irregular quasi-cyclic LDPC code constructing method, referring to Fig. 2, comprise the following steps that；

(2-1) N, M and q initialization：Code length is set as N=762, code check R=(N-M)/N, unit matrix dimension is q=N/ 6, q=127, prime number a=2, b=3 are shifted, information bit M is derived according to the code check R and formula R=(N-M) for setting/N；

(2-2) build check matrix H, check matrix H is made up of submatrix A and submatrix B, H=[A B], submatrix B by Secondary submatrix B₁With secondary submatrix B₂Constitute, B=[B₁B₂],

Wherein, the element of submatrix A is that unit circulates submatrix I_x, define I_xFollowed to the right by the often row of q rank unit matrix I Ring movement x positions obtain, a^k-1b^k-1>=x >=1, a and b are the prime number less than q, k >=2；Secondary submatrix B₁Element P in have and Only 3 nonzero elements and P_k-1For one of nonzero element, remaining element is zero, and it is unit circulation to define nonzero element Submatrix I_d, unit circle submatrix I_dBy the often row of q rank unit matrix I, to the right loopy moving d positions obtain, and d is random natural Number；

(2-3) syndrome matrix A, if submatrix A is singular matrix, return to step (3-1) resets N；If A is non- Singular matrix, then generator matrix G and length for N code c_n,

G=[B^-1·A I_N-M]；c_n=u_n·G

In formula, u_n=[u_{N, 0} u_{N, 1}…u_{N, M-1}], u_nIt is an information bit vector for randomly selecting；

(3) decode, referring to Fig. 3, comprise the following steps that：

(3-1) initialize：According to transitional provavility density f_i ^yProbability Ln of the channel transfer to variable node is set, and Corresponding likelihood ratio message data λ (L_n), then set each variable node n and be transmitted to the check-node m being adjacent, obtain Variable node passes to the initial information of check-node：

λ⁽⁰⁾(q_n,m)=λ (L_n)；

(3-2) lateral processes, update also known as check-node：I.e. to the l time iterative process of n ∈ M (m) and m ∈ N (n) Middle variable node is delivered to the information of check-node and is updated, and more new formula is as follows：

(3-3) longitudinal direction is processed, and is updated also known as variable node：I.e. to the l time iterative process of n ∈ M (m) and m ∈ N (n) Middle check-node is delivered to the information of variable node and is updated, and more new formula is as follows：

(3-4) bit decision：

(3-4-1) pseudo- posterior probability is calculated, computing formula is as follows：

If variableWork as λ^(l)(q_n) ＞ 0 when, thenOtherwise,

(3-4-2) output condition judgement is decoded, ifOr iterations exceedes the maximum iteration time of regulation, then Terminate,As effective output valve of decoding；Otherwise return to step (3-1) and continue iteration.

As a result show, substantially reduce through the signal error rate of LDPC codings, the performance of FSO is obviously improved；And for not Encode with the LDPC of code check, when the bit error rate is 10^-6, when turbulivity is 3, code check is that 0.5 performance ratio improves under 1.5 and connects Nearly 15dB；When turbulivity is 4, code check is that 0.5 performance ratio improves close 20dB under 0.75；Simulation result such as Fig. 6 and Shown in Fig. 7.

The present invention also corresponds to the communication system for said method for providing, referring to Fig. 1, including transmitting terminal and receiving terminal, The transmitting terminal includes information source memory cell, LDPC coding units, modulator and the laser instrument being electrically connected with, the receiving terminal bag Photodetector, demodulator, BP decoders and the stay of two nights memory cell of electric connection are included, laser instrument passes through light with photodetector Learn transmitting antenna and optical receiver antenna realizes the transmission of laser signal.

Claims (3)

1. a kind of FSO method based on LDPC code, it is characterised in that comprise the steps：

(1) data model for receiving signal is set up, the channel model of different atmospheric turbulence intensities is proposed for：

(1-1) data model r (t) for receiving signal is set up,

R (t)=y (t) n₁(t)+n₀(t)

Wherein t be the time, y (t) be transmission signal, n₁T () is the multiplicative noise that atmospheric turbulance causes, n₀T () is to include that heat is made an uproar Sound, amplification noise are in interior additive Gaussian noise, n₀T it is σ that () average is 0, variance²；

(1-2) atmospheric channel is divided into strong turbulence channel and weak turbulence channel, is proposed for the channel of different atmospheric turbulence intensities Model；

A) model emulation, probability density of light intensity V under weak turbulent-flow conditions are carried out using logarithm normal distribution under weak turbulence channel ForWherein, σ_x ²For logarithmic amplitude variance, V₀For average intensity；

B) model emulation is carried out using K distributions under strong turbulence channel, distribution function of light intensity V under strong turbulence effect isWherein V be light intensity, Γ (α) be Gamma functions, α be k distribution orders, K_p(x) For the Bessel function of the second kind of amendment；

(1-3) for the channel model obtained in step (1-2), different log-likelihood ratios are obtained under strong and weak turbulent-flow conditions；

C) under weak turbulent-flow conditions, if during sending signal y=0 being state D₀, it is state D during sending signal y=1₁；

C-a) it is in state D₀When, the conditional probability density function for receiving signal is：

$f\left(r\right|D_0)=\frac{1}{\sqrt{2{{\mathrm{\π\σ}}_x}^2}}\exp \{-\frac{r^2}{2{{\mathrm{\σ}}_x}^2}\};$

C-b) it is in state D₁When, the conditional probability density function for receiving signal is：

$f\left(r\right|D_1)=\frac{1}{\sqrt{2{{\mathrm{\π\σ}}_x}^2}}\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}f\left(V\right)\exp \{-\frac{{(r-V)}^2}{2{{\mathrm{\σ}}_x}^2}\}dx;$

D) under the conditions of strong turbulence, if during sending signal y=0 being state D₀, it is state D during sending signal y=1₁；

D-a) it is in state D₀When, r (t)=n (t), the additive Gaussian noise beyond turbulent flow is 0, and it receives the conditional probability of signal Density function is：

$f\left(r\right|D_0)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}\exp \{-\frac{r^2}{2{\mathrm{\σ}}^2}\};$

D-b) it is in state D₁When, the conditional probability density function for receiving signal is：

$f\left(r\right|D_1)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}\underset{0}{\overset{\mathrm{\∞}}{\∫}}{f}_I\left(V\right)\exp \{-\frac{{(r-V)}^2}{2{\mathrm{\σ}}^2}\}dV;$

(1-4) according to the conditional probability density function under the different channels obtained in step (1-3), transitional provavility density is calculated f_i ^y, computing formula is：

$\left\{\begin{array}{c}{f}_i^0=\frac{f\left(r\right|D_0)}{f\left(r\right|D_0)+f\left(r\right|D_1)}\\ f_i^1=\frac{f\left(r\right|D_1)}{f\left(r\right|D_0)+f\left(r\right|D_1)}\end{array}\right.;$

(2) encode, using irregular quasi-cyclic LDPC code constructing method, particular content is as follows；

(2-1) N, M and q initialization：Code length is set as N, information bit is M, and code check R=(N-M)/N, unit matrix dimension is q= N/6；

(2-2) check matrix H is built, check matrix H is made up of submatrix A and submatrix B, H=[AB], and submatrix B is by secondary Submatrix B₁With secondary submatrix B₂Constitute, B=[B₁ B₂],

$A=\left[\begin{array}{cccc}{I}_1& I_a& ...& I_{a^{k-1}}\\ I_b& I_{ab}& ...& I_{a^{k-1}b}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ I_{b^{k-1}}& I_{{\mathrm{ab}}^{k-1}}& ...& I_{a^{k-1}{b}^{k-1}}\end{array}\right],B_1=\left[\begin{array}{c}{P}_1\\ P_2\\ .\\ .\\ .\\ P_{k-1}\end{array}\right],$

Wherein, the element of submatrix A is that unit circulates submatrix I_x, define I_xBy the often row of q rank unit matrix I, to the right circulation is moved Dynamic x positions obtain, a^k-1b^k-1>=x >=1, a and b are the prime number less than q, k >=2；Secondary submatrix B₁Element P in have and only 3 nonzero elements and P_k-1For one of nonzero element, remaining element is zero, and it is that unit circulates sub- square to define nonzero element Battle array I_d, unit circle submatrix I_dBy the often row of q rank unit matrix I, to the right loopy moving d positions obtain, and d is random natural number；

(2-3) syndrome matrix A, if submatrix A is singular matrix, return to step (3-1) resets N；If A is nonsingular Matrix, then generator matrix G and length for N code c_n,

G=[B^-1·A I_N-M]；c_n=u_n·G

In formula, u_n=[u_{N, 0} u_{N, 1} ···· u_{N, M-1}], u_nIt is an information bit vector for randomly selecting；

(3) decode, comprise the following steps that：

(3-1) initialize：According to transitional provavility density f_i ^ySet probability Ln of the channel transfer to variable node, and correspondence Likelihood ratio message data λ (L_n), then set each variable node n and be transmitted to the check-node m being adjacent, the variable for obtaining Node passes to the initial information of check-node：

$\mathrm{\λ}\left(L_n\right)=ln\left(\frac{f_i^0}{f_i^1}\right)$

λ⁽⁰⁾(q_n,m)=λ (L_n)；

(3-2) lateral processes, update also known as check-node：I.e. to becoming in the l time iterative process of n ∈ M (m) and m ∈ N (n) Amount node is delivered to the information of check-node and is updated, and more new formula is as follows：

${\mathrm{\λ}}^{\left(l\right)}\left(r_{nm}\right)=2{\tanh }^{-1}\[\underset{m^{\′}\∈N\left(n\right)\backslash m}{\mathrm{\Π}}\tanh \left(\frac{{\mathrm{\λ}}^{(l-1)}\left(q_{m^{\′},n}\right)}{2}\right)\]$

(3-3) longitudinal direction is processed, and is updated also known as variable node：I.e. to the l time iterative process lieutenant colonel of n ∈ M (m) and m ∈ N (n) Test node and be delivered to the information of variable node and be updated, more new formula is as follows：

${\mathrm{\λ}}^{\left(l\right)}\left(q_{nm}\right)=L_n+\underset{m^{\′}\∈N\left(n\right)\backslash m}{\mathrm{\Σ}}{L}^{\left(l\right)}\left(r_{m^{\′}n}\right)$

(3-4) bit decision：

(3-4-1) pseudo- posterior probability is calculated, computing formula is as follows：

${\mathrm{\λ}}^{\left(l\right)}\left(q_n\right)=L_n+\underset{n^{\′}\∈M\left(m\right)}{\mathrm{\Σ}}{L}^{\left(l\right)}\left(r_{mn}\right)$

If variableWork as λ^(l)(q_n) ＞ 0 when, thenOtherwise,

(3-4-2) output condition judgement is decoded, ifOr iterations exceedes the maximum iteration time of regulation, then terminate,As effective output valve of decoding；Otherwise return to step (3-1) and continue iteration.

2. a kind of communication system of the FSO method for being based on LDPC code described in claim 1, including transmitting End and receiving terminal, it is characterised in that：The transmitting terminal includes information source memory cell, LDPC coding units, the modulation being electrically connected with Device and laser instrument, the receiving terminal includes photodetector, demodulator, BP decoders and the stay of two nights memory cell being electrically connected with.

3. communication system according to claim 2, it is characterised in that：The laser instrument is sent out with photodetector by optics Penetrate antenna and optical receiver antenna realizes the transmission of laser signal.