CN113965293B - 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 PDFInfo
- Publication number
- CN113965293B CN113965293B CN202111231814.2A CN202111231814A CN113965293B CN 113965293 B CN113965293 B CN 113965293B CN 202111231814 A CN202111231814 A CN 202111231814A CN 113965293 B CN113965293 B CN 113965293B
- Authority
- CN
- China
- Prior art keywords
- pam4 signal
- pam4
- signal
- bit
- symbols
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0057—Block codes
Landscapes
- Engineering & Computer Science (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Detection And Prevention Of Errors In Transmission (AREA)
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 RS code is carried out on the signal matrix through the code matrix containing the optimal redundant digit of the RS code, and then the forward error correction is carried out on the received packet with errors in the generated matrix obtained by the RS code, so that the transmission efficiency of the PAM4 signal in the PAM4 signal forward error correction is improved.
Description
Technical Field
The invention belongs to the technical field of communication, and relates to a PAM4 signal forward error correction method, 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 using 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 of PAM4 encoding consists of two bits, which correspond to one voltage level, i.e. amplitude. The types of errors 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) which causes burst errors in the PAM4 signal. Errors of the PAM4 signal can cause the problems of burst packet loss and random packet loss of network data packets, and transmission of the PAM4 signal 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, error correction of the PAM4 signal is required.
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 in which a signal is encoded in advance according to a certain algorithm before being transmitted into a transmission channel, a redundant code with the characteristics of the signal itself is added, and the received signal is decoded at a receiving end according to a corresponding algorithm, so that an error code generated in the transmission process is found out and corrected. 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 publication number CN111935485A and name "an RS code forward error correction method and apparatus" discloses an RS code forward error correction method, which is implemented by the following 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 digital communication system transmitting end into J RS symbols A ＝{RS 1 ,RS 2 ,...,RS j ,...,RS J Each RS symbol RS j Comprising M PAM4 symbols
PAM 4 A Containing l bits, each PAM4 symbol
Comprises 2 bits, wherein K is more than or equal to 2, J = K/l, l is more than or equal to 2, RS j Denotes the jth RS symbol, M = l/2,
represents RS j The mth PAM4 symbol of (1);
(1b) Initializing the number of RS symbols which can correct errors in the PAM4 signal to be t, adding the number of the RS symbols after the PAM4 signal to be G, wherein the error propagation probability of the PAM4 signal is a, the number of times of retransmission required by a receiving end to receive the PAM4 signal sent by a sending end without error codes is R, wherein t is more than or equal to 0, G =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:
computing each PAM4 symbol
Random error rate of
And pass through
Calculating each RS symbol RS j Random error rate of
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 symbols A Redundant bit adding ofIs added to RS A Then, a transmission packet S including J + G RS symbols is formed 1 And through each RS symbol RS j Random error rate of
And the burst error rate p (h) of the PAM4 signal, calculating S 1 The probability CER of errors of the middle t +1 RS symbols is used as the probability of the retransmission of the PAM4 signal;
(4) Acquiring the optimal redundant bit number of RS codes for transmitting the PAM4 signal:
(4a) Calculating the transmission time length required by the receiver for receiving the error-free code after r times of retransmission of the K bit PAM4 signal sent by the sending end to obtain a transmission time length set T = { T = 0 ,T 1 ,...,T r ,...,T R And according to the time length T of the r-th retransmission r Calculating the transmission efficiency of the K bit PAM4 signal of the retransmission time to obtain a transmission efficiency set eta = { eta η) corresponding to T 0 ,η 1 ,...,η r ,...,η R }：
Wherein, BR represents the bit rate of PAM4 signal transmitted by the transmitting end, RTT represents S 1 Including path delay, inherent delay, decoding delay of forward error correction technique and round trip delay of protocol processing delay;
(4b) By S 1 Calculating 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 symbols r Obtaining a retransmission probability set P = { P = } 0 ,P 1 ,...,P r ,...,P R And calculating the mean value beta of the transmission efficiency of the K-bit PAM4 signal through P and eta e ：
P r ＝CER r *(1-CER)
(4c) Will be added to J RS symbols RS A The next G redundant bits are represented as a set of redundant bits λ = { λ ] starting from 0 and having a step size of 2 1 ,λ 2 ,...,λ g ,...,λ G And calculates each redundant bit lambda g Obtaining the mean value set beta = { beta ] of the transmission efficiency of the K-bit PAM4 signal by taking the mean value of the transmission efficiency of the K-bit PAM4 signal 1 ,β 2 ,...,β g ,...,β G Then selecting the number lambda of the redundant bits corresponding to the maximum value in the beta x The optimal redundancy digit of the RS code for transmitting the K bit PAM4 signal is obtained;
(5) The transmitting end carries out RS coding on the PAM4 signal and transmits:
(5a) The transmitting end transmits J RS symbols RS A Forming 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 matrices x ) J encoding matrix B;
(5b) The transmitting end multiplies the coding matrix B by the signal matrix K 'to realize the RS coding of K', and the obtained value is (J + lambda) x ) Generating a matrix S by 1, 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, if yes, the receiving packet S' is not wrong, the first J line in the S 'is an initial K bit PAM4 signal, and if not, if the V line of the receiving packet S' is wrong, the step (6 b) 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:
the invention obtains the RS coding optimal redundant digit of the K bit PAM4 signal by selecting the redundant digit number corresponding to the maximum value in the mean value set of the K bit PAM4 signal transmission efficiency, carries out RS coding on the signal matrix by the coding matrix containing the RS coding optimal redundant digit, and then carries out forward error correction on the receiving packet which is wrong in the generating matrix obtained by RS coding so as to obtain the PAM4 signal forward error correction result, thereby avoiding the defect that the PAM4 signal transmission efficiency is reduced due to too many or too few redundant digits in the prior art, ensuring the transmission efficiency of the PAM4 signal to reach the maximum value on the basis of ensuring a certain error correction capability, improving the utilization rate of a channel in a digital communication system, and reducing the transmission cost of the PAM4 signal.
Drawings
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 invention g A graph of the relationship (c);
FIG. 3 shows the probability P of r retransmissions of a PAM4 signal in the present invention r A graph of the relation with the retransmission times r;
FIG. 4 shows a transmission efficiency mean value β of PAM4 signal in the present invention g And the number of redundant bits λ g Graph 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 1 a) dividing K =5120 bit PAM4 signal generated by transmitting end of digital communication system into J =512 RS symbols A ＝{RS 1 ,RS 2 ,...,RS j ,...,RS 512 }, each RS symbol RS j Comprising 5 PAM4 symbols
PAM4 A Containing l =10 bits, each PAM4 symbol
Comprises 2 bits, wherein J =K/l，RS j Which represents the jth RS symbol, is,
represents RS j The mth PAM4 symbol.
Step 1 b) 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 =0.75, the number of times of retransmission required by the PAM4 signal sent by the sending end and received by the receiving end without error code is R, wherein t is determined by G, and the specific relationship is that t = G/2, t is more than or equal to 0, and R is more than or equal to 0.
Step 2) calculating the random error rate of each RS symbol and the burst error rate of the PAM4 signal:
when additive white Gaussian noise exists in a channel of a communication system, interference is generated on a PAM4 signal, random errors occur in the PAM4 signal, and each PAM4 symbol in the PAM4 signal is preset
Random error rate of
And pass through
Calculating each RS symbol RS j Random error rate of
The receiving end of the communication system comprises a Decision Feedback Equalizer (DFE) which causes random error propagation to a PAM4 signal to cause the 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 larger than or equal to 1, and the calculation formula is as follows:
where erfc represents a complementary error function, SNR represents a ratio of a PAM4 signal to additive white gaussian noise power, i represents the number of consecutive errors of a 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 PAM4 signal retransmission:
taking G RS symbols as 512 RS symbols A Is added at RS A Then, a transmission packet S containing 512+ G RS symbols is formed 1 . Preset S 1 Probability CER, S of error of middle t +1 RS symbols 1 The 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 S 1 Probability of a medium error RS symbol. The receiving end of the digital communication system obtains an incorrect PAM4 signal, and the sending end is required to resend the PAM4 signal, so that the retransmission probability of the PAM4 signal is CER. By each RS symbol RS j Random error rate of
And the burst error rate p (h) of the PAM4 signal, calculating the CER according to the following formula:
wherein n represents S 1 The number of middle RS symbols.
It can be seen from the formula that the size of CER is related to the number of redundant bits G, the probability CER of PAM4 signal retransmission and the number of redundant bits lambda g As shown in fig. 2, 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 digit of the transmission PAM4 signal:
step 4 a) calculating the transmission time length required by the receiver for receiving the error-free code after r times of retransmission of the K bit PAM4 signal sent by the sending end through the bit rate of the PAM4 signal sent by the sending end of the digital communication system, the round trip delay RTT of the PAM4 signal and the retransmission times r, and obtaining a transmission time length set T = { T = } 0 ,T 1 ,...,T r ,...,T R And according to the time length T of the r-th retransmission r Calculating the transmission efficiency of the K bit PAM4 signal of the retransmission time to obtain a transmission efficiency set eta = { eta η) corresponding to T 0 ,η 1 ,...,η r ,...,η R }：
BR =112Gb/S, which represents the bit rate of PAM4 signal transmitted by the transmitting end, RTT =3ns, which represents S 1 Including path delay, inherent delay, forward error correction decoding delay, and round trip delay of protocol processing delay.
Step 4 b) by S 1 Calculating the probability P of retransmitting the K-bit PAM4 signal by the transmitting end according to the CER of the error probability of the middle t +1 RS symbols r Obtaining a retransmission probability set P = { P = { (P) } 0 ,P 1 ,...,P r ,...,P R The calculation formula is as follows:
P r ＝CER r *(1-CER)
P r the 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, the lower the probability of occurrence of r retransmissions.
Calculating mean value beta of transmission efficiency of K bit PAM4 signal under the condition of retransmitting 0 to infinite times through P and eta e ：
Step 4 c) will be added to J RS symbols RS A The next G redundant bits are represented as a set λ = { λ = λ ] of the number of redundant bits in a step size of 2 starting from 0 1 ,λ 2 ,...,λ g ,...,λ G And calculates each redundant bit lambda g Obtaining the mean value set beta = { beta ] of the transmission efficiency of the K-bit PAM4 signal by taking the mean value of the transmission efficiency of the K-bit PAM4 signal 1 ,β 2 ,...,β g ,...,β G As 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, which 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 beta x And the 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 5 a) J RS symbols RS are transmitted by the transmitting end A Forming 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 matrices x ) Coding matrix B of J. Any sub-square matrix of the van der mond matrix is a reversible square matrix, any 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 logical AND, so that the complexity of 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 ) Generating a matrix S by 1, 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 6 a) the receiving end judges whether the receiving packets S 'transmitted from the sending packet S to the receiving end through the communication system channel are the same, if yes, the receiving packets S' are not wrong, the front J line in S 'is the initial K bit PAM4 signal, otherwise, if the V line of the receiving packets S' is wrong, step (6 b) 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 symbols A ＝{RS 1 ,RS 2 ,...,RS j ,...,RS J }, each RS symbol RS j Comprising M PAM4 symbols
PAM 4 A Containing l bits, each PAM4 symbol
Comprises 2 bits, wherein K is more than or equal to 2, J = K/l, l is more than or equal to 2, RS j Denotes the jth RS symbol, M = l/2,
represents RS j The mth PAM4 symbol of (1);
(1b) Initializing the number of RS symbols which can correct errors in the PAM4 signal to be t, adding the number of the RS symbols after the PAM4 signal to be G, wherein the error propagation probability of the PAM4 signal is a, the number of times of retransmission required by a receiving end to receive the PAM4 signal sent by a sending end without error codes is R, wherein t is more than or equal to 0, G =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:
computing each PAM4 symbol
Random error rate of
And pass through
Calculating each RS symbol RS j Random error rate of
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 represents the number of continuous error RS symbols of the PAM4 signal, and h is more than or equal to 1;
(3) Calculating the probability of the PAM4 signal retransmission:
taking G RS symbols as J RS symbols A Is added at RS A Then, a transmission packet S including J + G RS symbols is formed 1 And through each RS symbol RS j Random error rate of
And the burst error rate p (h) of the PAM4 signal, calculating S 1 The CER of the error probability of the middle t +1 RS symbols is used as the probability of the retransmission of the PAM4 signal;
(4) Acquiring the optimal redundant bit number of RS codes for transmitting the PAM4 signal:
(4a) Calculating the transmission time length required by the receiving end for error-free code receiving after r times of retransmission of the K bit PAM4 signal sent by the sending end to obtainTransmission duration set T = { T = { (T) 0 ,T 1 ,...,T r ,...,T R And according to the time length T of the r-th retransmission r Calculating the transmission efficiency of the K bit PAM4 signal of the retransmission time to obtain a transmission efficiency set eta = { eta η) corresponding to T 0 ,η 1 ,...,η r ,...,η R }：
Wherein BR represents the bit rate of PAM4 signal transmitted by the transmitting end, RTT represents S 1 The round-trip delay comprises path delay, inherent delay, forward error correction technology decoding delay and protocol processing delay;
(4b) By S 1 Calculating 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 symbols r Obtaining a retransmission probability set P = { P = } 0 ,P 1 ,...,P r ,...,P R And calculating the mean value beta of the transmission efficiency of the K-bit PAM4 signal through P and eta e ：
P r ＝CER r *(1-CER)
(4c) Will be added to J RS symbols RS A The next G redundant bits are represented as a set of redundant bits λ = { λ ] starting from 0 and having a step size of 2 1 ,λ 2 ,...,λ g ,...,λ G And calculates each redundant bit lambda g Obtaining the mean value set beta = { beta ] of the transmission efficiency of the K-bit PAM4 signal by taking the mean value of the transmission efficiency of the K-bit PAM4 signal 1 ,β 2 ,...,β g ,...,β G Then selecting the number lambda of the redundant bits corresponding to the maximum value in the beta x The optimal redundancy digit of the RS code for transmitting the K bit PAM4 signal is obtained;
(5) The transmitting end carries out RS coding on the PAM4 signal and transmits:
(5a) The transmitting end transmits J RS symbols RS A Forming 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 matrices x ) An encoding matrix B of J;
(5b) The transmitting end multiplies the coding matrix B by the signal matrix K 'to realize the RS coding of K', and the obtained value is (J + lambda) x ) Generating a matrix S by 1, 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, if yes, the receiving packet S' is not wrong, the first J line in the S 'is an initial K bit PAM4 signal, and if not, if the V line of the receiving packet S' is wrong, the step (6 b) 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-encoded optimal redundancy bit-based PAM4 signal forward error correction method as claimed in claim 1, wherein each PAM4 symbol in step (2)
Random error rate of
Each RS symbol RS j Random error rate of
The burst error rate p (h) of the PAM4 signal is calculated by the following formula:
where erfc represents a complementary error function, SNR represents a ratio of a PAM4 signal to additive white gaussian noise power, and i represents the number of consecutive errors of a PAM4 symbol due to random error propagation.
3. The method for forward error correction of PAM4 signal based on RS encoded optimal redundancy bits according to claim 1, wherein the probability CER of retransmission of K-bit PAM4 signal in step (3) is calculated as:
wherein n represents S 1 The number of middle RS symbols.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111231814.2A CN113965293B (en) | 2021-10-22 | 2021-10-22 | PAM4 signal forward error correction method based on RS coding optimal redundancy bit |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111231814.2A CN113965293B (en) | 2021-10-22 | 2021-10-22 | PAM4 signal forward error correction method based on RS coding optimal redundancy bit |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113965293A CN113965293A (en) | 2022-01-21 |
| CN113965293B true CN113965293B (en) | 2022-10-04 |
Family
ID=79466094
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111231814.2A Active CN113965293B (en) | 2021-10-22 | 2021-10-22 | PAM4 signal forward error correction method based on RS coding optimal redundancy bit |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113965293B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117294392A (en) * | 2023-09-25 | 2023-12-26 | 海光信息技术股份有限公司 | Forward error correction method, forward error correction device, electronic device and storage medium |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104639919A (en) * | 2013-11-14 | 2015-05-20 | 杭州海康威视数字技术股份有限公司 | Data transmission method and data transmission system for digital video optical transceiver system |
| CN106375068A (en) * | 2016-09-09 | 2017-02-01 | 北京邮电大学 | Method and device for regulating error correcting capability strength of RS (Reed-Solomon) code |
| CN110521152A (en) * | 2018-02-14 | 2019-11-29 | 华为技术有限公司 | Decoding method, coding and decoding device and coding/decoding apparatus |
| CN110971345A (en) * | 2019-11-22 | 2020-04-07 | 北京麦哲科技有限公司 | Improved FEC algorithm and device thereof |
| CN111935485A (en) * | 2020-08-10 | 2020-11-13 | 北京佳讯飞鸿电气股份有限公司 | RS code forward error correction method and device |
-
2021
- 2021-10-22 CN CN202111231814.2A patent/CN113965293B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104639919A (en) * | 2013-11-14 | 2015-05-20 | 杭州海康威视数字技术股份有限公司 | Data transmission method and data transmission system for digital video optical transceiver system |
| CN106375068A (en) * | 2016-09-09 | 2017-02-01 | 北京邮电大学 | Method and device for regulating error correcting capability strength of RS (Reed-Solomon) code |
| CN110521152A (en) * | 2018-02-14 | 2019-11-29 | 华为技术有限公司 | Decoding method, coding and decoding device and coding/decoding apparatus |
| CN110971345A (en) * | 2019-11-22 | 2020-04-07 | 北京麦哲科技有限公司 | Improved FEC algorithm and device thereof |
| CN111935485A (en) * | 2020-08-10 | 2020-11-13 | 北京佳讯飞鸿电气股份有限公司 | RS code forward error correction method and device |
Non-Patent Citations (2)
| Title |
|---|
| 120 GBaud PAM-4/PAM-6 Generation and Detection by Photonic Aided Digital-to-Analog Converter and Linear Equalization;Haiyun Xin，etc.;《Journal of Lightwave Technology》;20200114;全文 * |
| 一种改进的高速链路前向纠错编码;冯璇等;《计算机工程与科学》;20170515(第05期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113965293A (en) | 2022-01-21 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US7823041B2 (en) | Techniques for decoding information from signals received over multiple channels | |
| US8737519B2 (en) | Apparatus and method for channel coding in a communication system | |
| JP4990298B2 (en) | Method and apparatus for transmitting and receiving data blocks in a wireless communication system | |
| CN109889308B (en) | Hybrid automatic repeat request method for joint polarization coding and decoding in Internet of things | |
| US11271685B2 (en) | Method of hybrid automatic repeat request implementation for data transmission with multilevel coding | |
| US20190207719A1 (en) | Method of hybrid automatic repeat request implementation for data transmission with multi-level coding | |
| KR20010080224A (en) | Accumulative arq method and system | |
| CN113965293B (en) | PAM4 signal forward error correction method based on RS coding optimal redundancy bit | |
| US6088390A (en) | Integrating decision feedback equalization and forward error correction to improve performance in point-to-multipoint digital transmission | |
| Sastry | Performance of hybrid error control schemes of satellite channels | |
| CN113542167A (en) | Underwater acoustic communication method using polarization code and equalizer | |
| CN109194336B (en) | Method, system and device for coding and decoding cascade Spinal code | |
| CN113746766B (en) | Channel self-adaptive noise aggregation wireless secure transmission method | |
| CN113438055A (en) | Convolutional network coding transmission method based on unequal redundancy insertion | |
| CN113765623B (en) | Bidirectional communication method based on superposition coding and extra information transmission | |
| US20190319645A1 (en) | Method and device for correcting low-latency errors for retrieving data packets | |
| Lu et al. | Progressive joint source-channel coding in feedback channels | |
| Benelli | A new method for the integration of modulation and channel coding in an ARQ protocol | |
| Kohno et al. | Design of automatic equalizer including a decoder of error-correcting code | |
| CN115987726B (en) | Decoding method based on nonlinear equalization and FEC combination | |
| WO2008043315A1 (en) | A method and system for applying the error correction code technology to the data transmission | |
| Hamdan et al. | Analysis and performance evaluation of convolutional codes over binary symmetric channel using MATLAB | |
| RU2276837C1 (en) | Method for transferring information using adaptive interference-resistive encoding | |
| Xu et al. | efficient multicast schemes in vehicle network based on Luby transform codes | |
| Cheng et al. | Efficient partial retransmission ARQ strategy with error detection codes by feedback channel |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |