CN113965293A - PAM4 signal forward error correction method based on RS coding optimal redundancy bit - Google Patents

PAM4 signal forward error correction method based on RS coding optimal redundancy bit Download PDF

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CN113965293A
CN113965293A CN202111231814.2A CN202111231814A CN113965293A CN 113965293 A CN113965293 A CN 113965293A CN 202111231814 A CN202111231814 A CN 202111231814A CN 113965293 A CN113965293 A CN 113965293A
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pam4 signal
pam4
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CN113965293B (en
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初秀琴
吴枫
范傲菲
王君
罗玉焕
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Xidian University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention provides a PAM4 signal forward error correction method based on RS coding optimal redundancy bits, which comprises the following steps: initializing parameters; calculating the random error rate of each RS symbol and the burst error rate of the PAM4 signal; calculating the probability of the retransmission of the PAM4 signal; acquiring the RS coding optimal redundant digit of the PAM4 signal; the sending end carries out RS coding on the PAM4 signal and sends the PAM4 signal; and the receiving end acquires a PAM4 signal forward error correction result. According to the invention, the optimal redundant digit of the RS code for transmitting the K-bit PAM4 signal is obtained by selecting the redundant digit number corresponding to the maximum value in the mean value set of the transmission efficiency of the K-bit PAM4 signal, the signal matrix is subjected to RS coding by the coding matrix containing the optimal redundant digit of the RS code, and then the received packet with errors in the generated matrix obtained by the RS coding is subjected to forward error correction, so that the transmission efficiency of the PAM4 signal in the PAM4 signal forward error correction is improved.

Description

PAM4 signal forward error correction method based on RS coding optimal redundancy bit
Technical Field
The invention belongs to the technical field of communication, and relates to a forward error correction method for a PAM4 signal, in particular to a PAM4 signal forward error correction method based on RS coding optimal redundancy bits.
Background
A communication system is a generic term for a technical system for performing an information transmission process. Communication systems can be divided into analog communication systems, which refers to a communication scheme in which an analog signal is transmitted from a source to a sink over a channel, and digital communication systems. Digital communication systems refer to a communication scheme in which a digital signal is transmitted from a source to a sink over a channel. Compared with an analog communication system, the method has the advantages that: the anti-interference capability is strong, and no noise is accumulated; can carry on the long-distance transmission and can guarantee the quality; can meet various communication service requirements and is convenient for realizing comprehensive processing; the transmitted binary digital signal can be directly received and processed by a computer; the method is convenient to realize by adopting a large-scale integrated circuit, and the communication equipment is beneficial to integration; the encryption processing is easy to carry out, and the security is easier to be ensured.
The PAM4 signal is a line code that uses a pulse amplitude modulation technique. The PAM4 signal has four voltage levels, each amplitude level corresponding to a logic bit 00, 01, 10, and 11, respectively. Each symbol encoded by PAM4 consists of two bits, which correspond to a voltage level, i.e. amplitude. The error types of the PAM4 signal are classified into random errors and burst errors. The PAM4 signal is interfered by additive white Gaussian noise existing in a channel of a digital communication system, so that random errors occur in the PAM4 signal; the receiver of the digital communication system includes a Decision Feedback Equalizer (DFE) that causes burst errors in the PAM4 signal. The PAM4 signal error can cause the burst packet loss and random packet loss of network data packets, and the transmission of PAM4 signals is affected. In order to reduce the probability of errors in the PAM4 signal and improve the efficiency of the communication system in transmitting the PAM4 signal, the PAM4 signal needs to be error corrected.
Error correction methods for PAM4 signals are divided into feedback error correction and forward error correction. Feedback error correction may be used for bi-directional data communication and forward error correction for transmission of unidirectional digital signals. Forward error correction is an error control method, which refers to a technique that a signal is encoded according to a certain algorithm before being sent into a transmission channel, redundant codes with the characteristics of the signal are added, and a receiving end decodes the received signal according to a corresponding algorithm, so as to find out and correct error codes generated in the transmission process. The error correction capability and the transmission efficiency of the PAM4 signal are important indexes of forward error correction, wherein the transmission efficiency of the PAM4 signal is related to the random error rate of the PAM4 signal, the burst error rate of the PAM4 signal, the number of RS coding redundancy bits, the bit rate BR of a transmitting end and the round trip delay RTT of the PAM4 signal.
Forward error correction can solve the problems of burst packet loss and random packet loss of network data packets caused by network transmission, for example, a patent application with application publication number CN111935485A entitled "an RS code forward error correction method and apparatus" discloses an RS code forward error correction method, which includes the following implementation steps: receiving a feedback data packet sent by a network receiving end, and obtaining the packet loss rate of network data carried by the feedback data packet when the network data is transmitted in the current network state; according to the data transmission packet loss rate in the current network state, sending a preset number of original media packets and redundant packets obtained by multiplying an encoding matrix and a data matrix to a network receiving end; and the network receiving end recovers the lost data packet according to the relationship between the data matrix of the original media packet and the actually received media packet, the actually received redundant packet and the corresponding inverse coding matrix. The method can recover the original media packet to the maximum extent according to the redundant packet, can better solve the problems of burst packet loss and random packet loss of the network data packet caused by network transmission, but neglects the influence of the size of the redundant packet on the transmission efficiency of the digital communication system, so that the transmission efficiency of the digital communication system is reduced.
In summary, the following steps: in the process of transmitting data by using a forward error correction method in the existing digital communication system, the influence of the quantity of redundant bits on the transmission efficiency of the system is not considered. The excessive redundant bits are added to reduce the loss probability of network data packets to a certain extent, so that the integrity of data is ensured, but for a digital communication system, the transmission efficiency of the system is reduced because of the excessive redundant bits; increasing too few redundant bits will increase the probability of data packet error, and further trigger the packet loss retransmission mechanism to cause the problem of transmission efficiency decrease.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a PAM4 signal forward error correction method based on RS coding optimal redundancy bits, which can effectively improve the transmission efficiency of a digital communication system while ensuring the error correction capability.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) initializing parameters:
(1a) dividing K bit PAM4 signal generated by transmitting end of digital communication system into J RS symbolsA＝{RS1,RS2,...,RSj,...,RSJEach RS symbol RSjComprising M PAM4 symbols
Figure BDA0003316280590000021
PAM4AContaining l bits, each PAM4 symbol PAM4j mContains 2 bits, where K ≧ 2, J ═ K/l, l ≧ 2, RSjDenotes the jth RS symbol, M ═ l/2,
Figure BDA0003316280590000031
represents RSjThe mth PAM4 symbol;
(1b) the method comprises the following steps that the number of RS symbols which can correct errors in a PAM4 signal is t through initialization, the number of RS symbols which are added behind the PAM4 signal is G, the error propagation probability of the PAM4 signal is a, the number of times of retransmission which is needed when a transmitting end sends the PAM4 signal and a receiving end receives the PAM4 signal without error codes is R, wherein t is more than or equal to 0, G is 2t, and R is more than or equal to 0;
(2) calculating the random error rate of each RS symbol and the burst error rate of the PAM4 signal:
calculate each PAM4 symbol
Figure BDA0003316280590000032
Random error rate of
Figure BDA0003316280590000033
And pass through
Figure BDA0003316280590000034
Calculating each RS symbol RSjRandom error rate of
Figure BDA0003316280590000035
Meanwhile, the burst error rate p (h) of the PAM4 signal is calculated according to the error propagation probability a of the PAM4 signal, wherein h is more than or equal to 1;
(3) calculating the probability of the PAM4 signal retransmission:
taking G RS symbols as J RS symbolsAIs added in the RSAThen, a transmission packet S including J + G RS symbols is formed1And through each RS symbol RSjRandom error rate of
Figure BDA0003316280590000036
And the burst error rate p (h) of the PAM4 signal, and calculating S1The CER is the probability that the middle t +1 RS symbols are wrong, and then the CER is used as the probability of the retransmission of the PAM4 signal;
(4) acquiring the optimal redundancy bit number of RS codes for transmitting the PAM4 signal:
(4a) calculating the transmission time length required by the receiver for receiving the K bit PAM4 signal after r times of retransmission by the transmitter to obtain a transmission time length set T ═ T0,T1,...,Tr,...,TRAnd according to the time length T of the r-th retransmissionrCalculating the transmission efficiency of the K-bit PAM4 signal retransmitted this time to obtain a transmission efficiency set eta corresponding to T ═ eta0,η1,...,ηr,...,ηR}：
Figure BDA0003316280590000037
Figure BDA0003316280590000038
Where BR denotes the bit rate of PAM4 signal transmitted from the transmitting end, and RTT denotes S1Including path delayInherent delay, forward error correction technique decoding delay and protocol processing delay;
(4b) by S1Calculating probability P of transmitting end for retransmitting K bit PAM4 signal for the r time by using probability CER of error of middle t +1 RS symbolsrObtaining a retransmission probability set P ═ { P ═ P0,P1,...,Pr,...,PRAnd calculating the mean value beta of the K bit PAM4 signal transmission efficiency through P and etae：
Pr＝CERr*(1-CER)
Figure BDA0003316280590000041
(4c) Will be added to J RS symbols RSAThe next G redundant bits are represented as a redundant bit number set λ { λ ═ λ in steps of 2 starting from 01,λ2,...,λg,...,λGAnd calculates each redundant bit lambdagObtaining the mean value of the transmission efficiency of the K-bit PAM4 signal, and obtaining the mean value set beta of the transmission efficiency of the K-bit PAM4 signal1,β2,...,βg,...,βGThen selecting the number lambda of the redundant bits corresponding to the maximum value in the betaxThe optimal redundant digit is the RS coded optimal redundant digit for transmitting the K bit PAM4 signal;
(5) and the transmitting end carries out RS coding on the PAM4 signal and transmits:
(5a) the transmitting end transmits J RS symbols RSAForming a signal matrix K' of size J1, while constructing a unit matrix of size J as the first J row, and the remaining rows of size (J + λ) from the Cauchy or Van der Mond matricesx) An encoding matrix B of J;
(5b) the transmitting end multiplies the coding matrix B by the signal matrix K ', the RS coding of K' is realized, and the value of (J + lambda) is obtainedx) 1, generating a matrix S, and sending the matrix S to a receiving end as a sending packet;
(6) the receiving end obtains a PAM4 signal forward error correction result:
(6a) the receiving end judges whether a receiving packet S 'transmitted to the receiving end by the sending packet S through a digital communication system channel is the same or not, if yes, the receiving packet S' is not wrong, the first J line in the S 'is an initial K bit PAM4 signal, otherwise, if the V line of the receiving packet S' is wrong, the step (6b) is executed;
(6b) and deleting the V-th row elements in the S ' and B by the receiving end to obtain an error code matrix E and a decoding matrix B ', and multiplying the inverse matrix of the E and the B ' to obtain a K-bit PAM4 signal, thereby realizing the forward error correction of the PAM4 signal.
Compared with the prior art, the invention has the following advantages:
according to the invention, the optimal redundancy bit number of RS codes for transmitting the K-bit PAM4 signal is obtained by selecting the redundancy bit number corresponding to the maximum value in the mean value set of the K-bit PAM4 signal transmission efficiency, the signal matrix is subjected to RS coding by the coding matrix containing the optimal redundancy bit number of the RS codes, and then the received packet with errors in the generated matrix obtained by the RS coding is subjected to forward error correction so as to obtain the PAM4 signal forward error correction result, so that the defect that the PAM4 signal transmission efficiency is reduced due to too many or too few redundancy bits in the prior art is avoided, on the basis of ensuring a certain error correction capability, the transmission efficiency of the PAM4 signal reaches the maximum value, the utilization rate of a channel in a digital communication system is improved, and the transmission cost of the PAM4 signal is reduced.
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FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 shows the probability CER and the number of redundant bits λ of the PAM4 signal retransmission in the present inventiongGraph of the relationship of (1);
FIG. 3 shows the probability P of r retransmissions of a PAM4 signal in the present inventionrA graph of the relation with the retransmission times r;
FIG. 4 shows the transmission efficiency mean value β of PAM4 signal in the present inventiongAnd the number of redundant bits λgGraph of the relationship of (c).
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the present invention includes the steps of:
step 1) initializing parameters:
step 1a) digital communicationA PAM4 signal with 5120 bits generated by a transmitting end of a signal system is divided into RS symbols with J512 bitsA＝{RS1,RS2,...,RSj,...,RS512Each RS symbol RSjComprising 5 PAM4 symbols
Figure BDA0003316280590000051
PAM4AContaining l 10 bits, each PAM4 symbol
Figure BDA0003316280590000052
Comprising 2 bits, wherein J ═ K/l, RSjRepresents the jth RS symbol, and,
Figure BDA0003316280590000053
represents RSjThe mth PAM4 symbol.
Step 1b) initializing the number of RS symbols which can correct errors in the PAM4 signal, wherein t represents the capability of forward error correction. The number of RS symbols added behind the PAM4 signal is G, the error propagation probability of the PAM4 signal is a is 0.75, the number of times of retransmission required for error-free reception of the PAM4 signal sent by the transmitting end by the receiving end is R, wherein t is determined by G, the specific relationship is that t is G/2, t is not less than 0, and R is not less than 0.
Step 2) calculating the random error rate of each RS symbol and the burst error rate of the PAM4 signal:
the PAM4 signal is interfered by additive white Gaussian noise existing in a channel of a communication system, random errors occur in the PAM4 signal, and each PAM4 symbol in the PAM4 signal is preset
Figure BDA0003316280590000054
Random error rate of
Figure BDA0003316280590000055
And pass through
Figure BDA0003316280590000056
Calculating each RS symbol RSjRandom error rate of
Figure BDA0003316280590000057
The receiving end of the communication system comprises a Decision Feedback Equalizer (DFE) which causes random error propagation to a PAM4 signal to cause a PAM4 signal to generate burst errors, and the burst error rate p (h) of the PAM4 signal is calculated according to the error propagation probability a, wherein h is more than or equal to 1, and the calculation formula is as follows:
Figure BDA0003316280590000061
Figure BDA0003316280590000062
where erfc represents a complementary error function, SNR represents a ratio of the PAM4 signal to additive white gaussian noise power, i represents the number of consecutive errors of the PAM4 symbol caused by random error propagation, and h represents the number of RS symbols of consecutive errors of the PAM4 signal.
Step 3) calculating the probability of the retransmission of the PAM4 signal:
taking G RS symbols as 512 RS symbolsAIs added in the RSAThen, a transmission packet S including 512+ G RS symbols is formed1. Preset S1Probability CER, S of middle t +1 RS symbol error1The number of RS symbols in which errors can be corrected is t, so CER can be expressed as that forward error correction cannot fully correct S1Probability of a medium error RS symbol. The receiving end of the digital communication system acquires an incorrect PAM4 signal, and the transmitting end is required to retransmit the PAM4 signal, so the retransmission probability of the PAM4 signal is CER. By each RS symbol RSjRandom error rate of
Figure BDA0003316280590000063
And the burst error rate p (h) of the PAM4 signal, calculating the CER according to the following formula:
Figure BDA0003316280590000064
wherein n represents S1Number of middle RS symbolNumber, SERRSDenotes S1The random error rate of each RS symbol.
It can be seen from the formula that the size of the CER is related to the number of redundant bits G, and the probability CER of the PAM4 signal retransmission is related to the number of redundant bits lambdagFig. 2 shows that the abscissa of fig. 2 represents the number of redundant bits and the ordinate represents the probability of retransmission of the PAM4 signal, and fig. 2 illustrates that as the number of redundant bits increases, the forward error correction capability becomes stronger, the probability of retransmission of the PAM4 signal becomes lower, and too few redundant bits increase the probability of retransmission of the PAM4 signal.
Step 4), obtaining the RS coding optimal redundant bit number of the transmission PAM4 signal:
step 4a) calculating the transmission time length required by the receiver for receiving the K-bit PAM4 signal sent by the sending end without error codes after r times of retransmission through the bit rate of the PAM4 signal sent by the sending end of the digital communication system, the round trip time RTT of the PAM4 signal and the retransmission times r, and obtaining a transmission time length set T ═ { T ═ T0,T1,...,Tr,...,TRAnd according to the time length T of the r-th retransmissionrCalculating the transmission efficiency of the K-bit PAM4 signal retransmitted this time to obtain a transmission efficiency set eta corresponding to T ═ eta0,η1,...,ηr,...,ηR}：
Figure BDA0003316280590000071
Figure BDA0003316280590000072
Where BR is 112Gb/S, which represents the bit rate of PAM4 signal transmitted by the transmitting end, RTT is 3ns, which represents S1Including path delay, inherent delay, forward error correction decoding delay, and round trip delay of protocol processing delay.
Step 4b) by S1Calculating the probability P of retransmitting K-bit PAM4 signal by the transmitting end every time by the CER of the error probability of the middle t +1 RS symbolsrObtaining a retransmission probability set P ═ { P ═ P0,P1,...,Pr,...,PRThe calculation formula is as follows:
Pr＝CERr*(1-CER)
Prthe relationship with r is shown in fig. 3, in which the abscissa of fig. 3 represents the number of retransmissions, and the ordinate represents the occurrence probability corresponding to the number of retransmissions. As can be seen from fig. 3, the larger the number r of retransmissions is, the lower the probability that r retransmissions occur.
Calculating mean value beta of K bit PAM4 signal transmission efficiency under condition of retransmitting 0 to infinite times through P and etae：
Figure BDA0003316280590000073
Step 4c) will be added to J RS symbols RSAThe next G redundant bits are represented by a set λ ═ λ { λ ═ λ of the number of redundant bits in steps starting from 0 and starting from 21,λ2,...,λg,...,λGAnd calculates each redundant bit lambdagObtaining the mean value of the transmission efficiency of the K-bit PAM4 signal, and obtaining the mean value set beta of the transmission efficiency of the K-bit PAM4 signal1,β2,...,βg,...,βGAs shown in fig. 4, the abscissa of fig. 4 represents the number of redundant bits, and the ordinate represents the transmission efficiency average of the PAM4 signal. Fig. 4 illustrates that as the redundant bits are increased, the transmission efficiency mean value of the PAM4 signal is increased and then decreased, and it can be concluded that increasing the redundant bits can improve the transmission efficiency of the PAM4 signal, but too many redundant bits can lead to the reduction of the transmission efficiency.
Selecting the number lambda of redundant bits corresponding to the maximum value in betaxThe number of the best redundant bits for transmitting the K bit PAM4 signal is 16.
Step 5), the sending end carries out RS coding on the PAM4 signal and sends:
step 5a) J RS symbols RS are transmitted by the transmitting endAForming a signal matrix K' of size J1, while constructing a unit matrix of size J as the first J row, and the remaining rows of size (J + λ) from the Cauchy or Van der Mond matricesx) J coding matrix B. Any sub-square matrix of the van der Mond matrix is a reversible square matrixAny sub-square matrix of the cauchy matrix is a singular matrix, and an inverse matrix exists. The use of the cauchy matrix has the following advantages over the van der mond matrix: the operation complexity of matrix inversion is reduced; and the multiplication is converted into the logical AND, so that the complexity of the multiplication operation is reduced.
Step 5B) the transmitting end multiplies the coding matrix B by the signal matrix K ', and RS codes the K', so as to obtain the code with the size of (J + lambda)x) 1, generating a matrix S, and sending the matrix S to a receiving end as a sending packet;
step 6), the receiving end obtains a PAM4 signal forward error correction result:
step 6a) the receiving end judges whether the receiving packets S 'transmitted to the receiving end by the sending packet S through the communication system channel are the same, if yes, the receiving packet S' is not wrong, the front J line in the S 'is the initial K bit PAM4 signal, otherwise, if the V line of the receiving packet S' is wrong, the step (6b) is executed;
and 6B) deleting the V-th row elements in the S ' and the B by the receiving end to obtain an error code matrix E and a decoding matrix B ', and multiplying the inverse matrix of the E and the B ' to obtain a K-bit PAM4 signal, thereby realizing the forward error correction of the PAM4 signal.
The foregoing description is only an example of the present invention and should not be construed as limiting the invention, as it will be apparent to those skilled in the art that various modifications and variations in form and detail can be made without departing from the principle and structure of the invention after understanding the present disclosure and the principles, but such modifications and variations are considered to be within the scope of the appended claims.

Claims (3)

1. A PAM4 signal forward error correction method based on RS coding optimal redundancy bits is characterized by comprising the following steps:
(1) initializing parameters:
(1a) dividing K bit PAM4 signal generated by transmitting end of digital communication system into J RS symbolsA＝{RS1,RS2,...,RSj,...,RSJEach RS symbol RSjComprising M PAM4 symbols
Figure FDA0003316280580000011
PAM4AContaining l bits, each PAM4 symbol
Figure FDA0003316280580000012
Contains 2 bits, where K ≧ 2, J ═ K/l, l ≧ 2, RSjDenotes the jth RS symbol, M ═ l/2,
Figure FDA0003316280580000013
represents RSjThe mth PAM4 symbol;
(1b) the method comprises the following steps that the number of RS symbols which can correct errors in a PAM4 signal is t through initialization, the number of RS symbols which are added behind the PAM4 signal is G, the error propagation probability of the PAM4 signal is a, the number of times of retransmission which is needed when a transmitting end sends the PAM4 signal and a receiving end receives the PAM4 signal without error codes is R, wherein t is more than or equal to 0, G is 2t, and R is more than or equal to 0;
(2) calculating the random error rate of each RS symbol and the burst error rate of the PAM4 signal:
calculate each PAM4 symbol
Figure FDA0003316280580000014
Random error rate of
Figure FDA0003316280580000015
And pass through
Figure FDA0003316280580000016
Calculating each RS symbol RSjRandom error rate of
Figure FDA0003316280580000017
Meanwhile, the burst error rate p (h) of the PAM4 signal is calculated according to the error propagation probability a of the PAM4 signal, wherein h is more than or equal to 1;
(3) calculating the probability of the PAM4 signal retransmission:
taking G RS symbols as J RS symbolsAIs added in the RSAThen, a transmission packet S including J + G RS symbols is formed1And throughEach RS symbol RSjRandom error rate of
Figure FDA0003316280580000018
And the burst error rate p (h) of the PAM4 signal, and calculating S1The CER is the probability that the middle t +1 RS symbols are wrong, and then the CER is used as the probability of the retransmission of the PAM4 signal;
(4) acquiring the optimal redundancy bit number of RS codes for transmitting the PAM4 signal:
(4a) calculating the transmission time length required by the receiver for receiving the K bit PAM4 signal after r times of retransmission by the transmitter to obtain a transmission time length set T ═ T0,T1,...,Tr,...,TRAnd according to the time length T of the r-th retransmissionrCalculating the transmission efficiency of the K-bit PAM4 signal retransmitted this time to obtain a transmission efficiency set eta corresponding to T ═ eta0,η1,...,ηr,...,ηR}：
Figure FDA0003316280580000021
Figure FDA0003316280580000022
Where BR denotes the bit rate of PAM4 signal transmitted from the transmitting end, and RTT denotes S1Including path delay, inherent delay, decoding delay of forward error correction technique and round trip delay of protocol processing delay;
(4b) by S1Calculating probability P of transmitting end for retransmitting K bit PAM4 signal for the r time by using probability CER of error of middle t +1 RS symbolsrObtaining a retransmission probability set P ═ { P ═ P0,P1,...,Pr,...,PRAnd calculating the mean value beta of the K bit PAM4 signal transmission efficiency through P and etae：
Pr＝CERr*(1-CER)
Figure FDA0003316280580000023
(4c) Will be added to J RS symbols RSAThe next G redundant bits are represented as a redundant bit number set λ { λ ═ λ in steps of 2 starting from 01,λ2,...,λg,...,λGAnd calculates each redundant bit lambdagObtaining the mean value of the transmission efficiency of the K-bit PAM4 signal, and obtaining the mean value set beta of the transmission efficiency of the K-bit PAM4 signal1,β2,...,βg,...,βGThen selecting the number lambda of the redundant bits corresponding to the maximum value in the betaxThe optimal redundant digit is the RS coded optimal redundant digit for transmitting the K bit PAM4 signal;
(5) and the transmitting end carries out RS coding on the PAM4 signal and transmits:
(5a) the transmitting end transmits J RS symbols RSAForming a signal matrix K' of size J1, while constructing a unit matrix of size J as the first J row, and the remaining rows of size (J + λ) from the Cauchy or Van der Mond matricesx) An encoding matrix B of J;
(5b) the transmitting end multiplies the coding matrix B by the signal matrix K ', the RS coding of K' is realized, and the value of (J + lambda) is obtainedx) 1, generating a matrix S, and sending the matrix S to a receiving end as a sending packet;
(6) the receiving end obtains a PAM4 signal forward error correction result:
(6a) the receiving end judges whether a receiving packet S 'transmitted to the receiving end by the sending packet S through a digital communication system channel is the same or not, if yes, the receiving packet S' is not wrong, the first J line in the S 'is an initial K bit PAM4 signal, otherwise, if the V line of the receiving packet S' is wrong, the step (6b) is executed;
(6b) and deleting the V-th row elements in the S ' and B by the receiving end to obtain an error code matrix E and a decoding matrix B ', and multiplying the inverse matrix of the E and the B ' to obtain a K-bit PAM4 signal, thereby realizing the forward error correction of the PAM4 signal.
2. The RS encoding optimal redundancy bit-based PAM4 signal forward error correction method of claim 1, wherein each PAM4 symbol in step (2)
Figure FDA0003316280580000031
Random error rate of
Figure FDA0003316280580000032
Each RS symbol RSjRandom error rate of
Figure FDA0003316280580000033
The burst error rate p (h) of the PAM4 signal is calculated by the following formula:
Figure FDA0003316280580000034
Figure FDA0003316280580000035
Figure FDA0003316280580000036
where erfc represents a complementary error function, SNR represents a ratio of the PAM4 signal to additive white gaussian noise power, i represents the number of consecutive errors of the PAM4 symbol caused by random error propagation, and h represents the number of RS symbols of consecutive errors of the PAM4 signal.
3. The RS encoding optimal redundancy bit-based PAM4 signal forward error correction method of claim 1, wherein the probability CER of K-bit PAM4 signal retransmission in step (3) is calculated as:
Figure FDA0003316280580000037
wherein n represents S1Number of middle RS symbols, SERRSDenotes S1The random error rate of each RS symbol.
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