CN115987726A - Decoding algorithm based on combination of nonlinear equalization and FEC - Google Patents
Decoding algorithm based on combination of nonlinear equalization and FEC Download PDFInfo
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Abstract
The invention discloses a decoding algorithm based on nonlinear equalization and FEC combination, which belongs to the technical field of optical fiber communication and comprises the following steps: step A: constructing Polar codes by adopting a Gaussian approximation construction method; and B: mapping the coded code word; and C: carrying out transmission processing on the mapped signals; step D: carrying out LLR estimation on the signal; step E: and (6) decoding and judging. The method aims at soft-decision FEC, realizes a high-performance low-complexity Polar code coding and decoding PAM transmission system, aims at a non-equivalent Gaussian distribution model, combines a deep neural network, considers nonlinear damage in transmission in an LLR estimation process, and improves the decoding performance of Polar codes. Compared with the traditional method based on the same Gaussian distribution estimation, the method of the invention can obtain the gain of about 0.9 dB.
Description
Technical Field
The invention belongs to the technical field of optical fiber communication, and particularly relates to a decoding algorithm based on combination of nonlinear equalization and FEC.
Background
In the PAM transmission system, due to the limitation of cost and other factors, the bandwidth of a device is often not enough to support the transmission of signals without intersymbol interference, and device-type nonlinear damage is introduced by a modulator at a transmitting end and a detector at a receiving end. During C-band transmission, chromatic dispersion in the optical fiber interacts with chirp of the modulator, phase information is lost after square rate detection, and signal damage is also caused. The equalization techniques such as FFE and VNLE can compensate for these impairments in the optical transmission system to a certain extent, reduce their influence on the quality of transmission signals, and improve the error rate performance of the system, but this cannot fully meet the increasing demands on the optical transmission rate and the optical power budget.
In practical applications, the PAM system usually needs to combine with FEC technology after channel equalization, and a small amount of redundant information is added to a signal, so that a receiving sequence has the capability of automatically checking and correcting burst errors, thereby further reducing the error rate and improving the reliability of a transmission system. At present, the FEC technology is usually based on a mathematical model established by an additive white gaussian noise channel, and searches and researches for channel coding and decoding are performed. However, it is difficult for the equalization technique to completely eliminate the optical transmission system damage, even if the number of taps of the filter is increased and the nonlinear order and the memory depth are increased, it is difficult to completely compensate the inter-symbol interference caused by the damage by using methods such as a deep neural network equalizer, and the residual inter-symbol interference affects the signal sent to the FEC decoding, so that the symbols of each amplitude in PAM no longer satisfy independent and identically distributed, the AWGN channel theoretical assumption of the FEC coding and decoding is destroyed, and the performance of the decoder is limited.
Disclosure of Invention
Aiming at the problems that the existing equalization technology is difficult to completely eliminate the damage of an optical transmission system, the intersymbol interference caused by the damage is difficult to completely compensate by adopting methods such as an equalizer and the like, and the residual intersymbol interference can influence a signal sent to FEC decoding, so that the symbols of each amplitude in PAM do not meet independent same distribution any more, the AWGN channel theory assumption of FEC coding and decoding is damaged, the performance of a decoder and other defects are limited, the invention provides a decoding algorithm based on the combination of nonlinear equalization and FEC, aiming at soft decision FEC, the method realizes a high-performance low-complexity Polar code coding and decoding PAM transmission system, aims at an equivalent non-Gaussian distribution model, combines a deep neural network, considers the nonlinear damage in transmission in the LLR estimation process, and improves the decoding performance of Polar codes.
The invention is realized by the following technical scheme:
a decoding algorithm based on the combination of nonlinear equalization and FEC specifically comprises the following steps:
step A: constructing Polar codes by adopting a Gaussian approximation construction method;
and B: mapping the coded code words;
and C: carrying out transmission processing on the mapped signals;
step D: carrying out LLR estimation on the signal;
step E: and (6) decoding and judging.
Further, step a is specifically as follows:
step A1: determining the positions of the information bits and the frozen bits, and rearranging according to the bit channel capacity to obtain a bit sequence X N ；
Step A2: putting information bits into bit channel with larger capacity, putting frozen bits into bit channel with smaller capacity, and polarizing bit channel by modulo two addition method to obtain coded code word C N The process is represented as:
wherein G is N To generate the matrix, B N For bit-inverting the operation matrix, and
the n-times kronecker product of the matrix is represented.
Further, step B is specifically as follows:
step B1: sending the obtained code words into a mapper, and mapping every three bits into a group of gray into PAM8 signals;
the log-likelihood ratio LLR estimate in Polar decoder is expressed as:
wherein, b i Represents the ith bit mapped to a PAM8 symbol at the transmitting end, the value range of i is 1,2 and 3, and r represents the received PAM8 signal;
and step B2: since bits "0" and "1" in the user data are transmitted with equal probability, b i =0 and b i The probability of =1 is equal, i.e.:
according to the nature of the posterior probability, the posterior probability P (b) i =0 r) is defined as:
similarly, a posterior probability P (b) is obtained i ＝1r)
Further, step C is specifically as follows:
step C1: after pulse forming, a modulation signal is sent into an optical fiber link, and at a receiving end, the signal is subjected to timing sampling through clock recovery;
and C2: and sending the synchronized signal into an equalizer to compensate channel damage.
Further, step D is specifically as follows:
step D1: sending the equalized signal into a deep neural network, and firstly carrying out LLR estimation on the signal;
if the signal pass mean is 0 and the variance is sigma 2 Additive White Gaussian Noise (AWGN) signal ofOn the other hand, the transition probability P (r | b) of the channel i = k) is expressed as:
wherein k =0,1, and
a standard symbol representing that the mapped ith bit is k; according to equations (5) and (6), the calculation formula for obtaining the LLR is as follows:
the noise variance in the formula is estimated by adding a training sequence, i.e. at the beginning of the transmitted data, a length L is transmitted t Training sequence T of t Then the noise variance is estimated as:
wherein r is t Represents the t-th PAM signal received;
step D2: estimating parameters of a non-equivalent Gaussian distribution model by adopting a deep neural network method;
according to the rule of PAM8 symbol mapping, the LLR estimate for the first bit of the three bit positions is expressed as:
wherein, mu j Eight different amplitudes of the PAM8 signal are represented,
representing the variance of the noise at different amplitudes of the PAM8 signal, y representing the equalized signal, the second bit corresponding toThe LLR estimates and the LLR estimate corresponding to the third bit are respectively expressed as:
further, step E is specifically as follows:
step E1: and (3) placing the estimated LLR as an initial input to the rightmost side of the butterfly decoding structure by using a Serial Cancellation (SC) decoding algorithm to perform recursive computation, wherein the computation of each node is to solve the upper and lower branch nodes on the left side of different butterfly substructures, and the computation of the upper node of the butterfly structure is represented as:
and the operation of the following node is represented as:
where y represents the equalized signal, u represents the transmitted signal, o represents the odd positions, e represents the even positions, and the functions f (l, m) and g (l, m, n) are defined as follows:
g(l,m,n)＝(-1) n l+m(15)
wherein l, m and n are independent variables;
and E2: after multilayer butterfly operation, obtaining LLR value corresponding to each bit with code length N, judging LLR value according to bit sequence sequencing position when Polar code is constructed in coder to obtain original sending bit, the judging rule is:
after SC decoding, extracting the corresponding information bit according to the bit position information, namely the data received by the user.
Compared with the prior art, the invention has the following advantages:
according to the decoding algorithm based on the combination of the nonlinear equalization and the FEC, the SC algorithm considers the nonlinear damage of a channel into an initial LLR value, so that the performance of a decoder can be improved, and the error rate of the system is further reduced; compared with the traditional method based on the same Gaussian distribution estimation, the method of the invention can obtain the gain of about 0.9 dB; the method has better error rate performance, provides an effective and practical method for PAM transmission with low cost, and greatly improves the soft decision decoding performance of a transmission system.
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In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings that are needed in the detailed description of the invention or the prior art will be briefly described below. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
FIG. 1 is a PAM system architecture diagram of Polar codes according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an SC butterfly decoding structure according to an embodiment of the invention;
fig. 3 is a diagram illustrating a comparison of simulation results provided by an embodiment of the present invention.
Detailed Description
For clearly and completely describing the technical scheme and the specific working process thereof, the specific implementation mode of the invention is as follows by combining the attached drawings of the specification:
example 1
The embodiment provides a decoding algorithm based on the combination of nonlinear equalization and FEC, which specifically includes the following steps:
step A: and constructing Polar codes by adopting a Gaussian approximation construction method. The position of the information bits and the frozen bits is determined and all the bits constitute a bit sequence X N Fig. 1 shows a PAM system architecture diagram of Polar encoding, at a transmitting end, data required by a user is first sent to a Polar encoder as information bits, and assuming that the number of information bits in a frame structure of the encoder is K and the code length is N, the number of frozen bits (i.e., check bits) required to be added during encoding is N-K; in Polar encoder, information bits and frozen bits need to be rearranged according to bit channel capacity to obtain bit sequence X N . There are many methods for calculating bit channel capacity, i.e. Polar code construction, such as babbitt parameter method, density evolution method and gaussian approximation method, we select gaussian approximation method, and estimate reliability through the obtained bit channel capacity, put information bits into bit channels with stronger reliability, and put frozen bits into bit channels with poorer reliability.
The bit channel will be polarized by a series of modulo two addition operations to obtain the codeword C N The process can be expressed as:
wherein G is N To generate a matrix, B N For bit-inverting the operation matrix, and
the n-times kronecker product of the matrix is represented.
And B, step B: and mapping the coded code words. And sending the obtained code word into a mapper, taking a PAM8 signal as an example, and gray mapping every three bits into a group to form the PAM8 signal.
Taking the PAM8 signal as an example, the LLR estimation in Polar decoder can be expressed as:
wherein b is i Represents the ith bit mapped to a PAM8 symbol at the transmit end, i ranges from 1,2,3, and r represents the received PAM8 signal. Since bits "0" and "1" in the user data are transmitted with equal probability, b i =0 and b i The probability of =1 is equal, i.e.:
therefore, according to the characteristic of the conditional probability, the posterior probability P (b) i =0 r) may be defined as:
similarly, the posterior probability P (b) can be obtained i ＝1r)
Step C: and carrying out transmission processing on the mapped signals. After pulse shaping, the modulated signal is sent to the optical fiber link, and at the receiving end, the signal is firstly subjected to timing sampling through clock recovery, and then the synchronized signal is sent to an equalizer to compensate channel damage.
Step D: the LLR estimation is performed on the signal. The equalized signal is fed into a deep neural network. In deep neural networks, the LLR estimation is first performed on the signal.
For the conventional scheme, it is assumed that the signal passes the mean 0 and the variance σ 2 AWGN channel of (1), transition probability P (rb) of the channel i = k) can be expressed as:
wherein k =0,1 and
indicating the mapped i-th bit as a standard symbol of k. For example, when b i When =0, there will be four different cases for the other two bits, and the probability P (yb) i = 0) will be the sum of the probabilities of these four cases, and from equations (5) and (6), the calculation formula for LLR can be found as follows:
the noise variance in the formula can be estimated by adding a training sequence, i.e. at the beginning of the transmitted data, we transmit a length L t Training sequence T of t Then the noise variance can be estimated as:
compared with the traditional mode, the estimation of the non-equivalent Gaussian distribution model can also be obtained by a method of adding the training sequence, but the cost is that the length of the training sequence is longer than that of the traditional mode, and extra information redundancy is brought. In order to avoid a large amount of data redundancy, a deep neural network method is adopted, parameters of a non-equivalent Gaussian distribution model can be dynamically estimated in a pure blind mode, and nonlinear damage in PAM short-distance transmission is dynamically resisted.
The probability density curve estimated by the method is more consistent with the actual signal probability distribution, and according to the PAM8 symbol mapping rule, the LLR estimation corresponding to the first bit in the three bit positions can be expressed as
Wherein mu j Eight different amplitudes of the PAM8 signal are represented
The noise variance over different amplitudes of the PAM8 signal is represented, and in the same way, the LLR estimate for the second bit and the LLR estimate for the third bit can be represented as:
and E, step E: and (5) decoding and judging. The estimated initial LLR values are fed into the SC decoding algorithm to recover the original bit sequence.
After estimating the LLRs, the SC decoding algorithm puts the estimated LLRs as initial input to the right-most side of the butterfly decoding structure for recursive operation, taking the butterfly decoding with a code length N =8 as an example, the structure diagram is shown in fig. 2, where y on the rightmost side is the most i (i = 1-8) represents the LLR estimates of the input;
the SC algorithm performs recursive computation on initial input from right to left, wherein the computation of each node is just to solve the upper and lower branch nodes on the left side of different butterfly substructures, and the computation of the nodes under the butterfly substructures can be expressed as:
and the operation of the following node can be expressed as:
where y represents the equalized signal, u represents the transmitted signal, o represents the odd positions, e represents the even positions, and the functions f (l, m) and g (l, m, n) are defined as follows:
g(l,m,n)＝(-1) n l+m (15)
after multilayer butterfly operation, obtaining LLR value corresponding to each bit with code length N, according to the bit sequence ordering position when Polar code is constructed in the encoder, judging LLR value to obtain original sending bit, the judging rule is:
after SC decoding, extracting the corresponding information bit according to the bit position information, namely the data received by the user.
Because the SC algorithm considers the channel nonlinear damage into the initial LLR value, compared with the traditional method, the scheme can improve the performance of a decoder and further reduce the error rate of the system. As shown in the simulation result of fig. 3, in which the original signal is represented by 2 13 In Polar coding, in order to reduce coding complexity and reduce data delay, we set the code length to 1024 and the code rate to 0.5. After encoding, the code words are respectively mapped into PAM8 signals of 28Gbaud, and finally the received bit sequence with the length of 500k is compared with the original transmitted bit sequence to estimate the error rate performance, and it can be seen that the error rate is 10 -3 Compared with the traditional method based on the same Gaussian distribution estimation, the method of the embodiment can obtain the gain of about 0.9 dB; therefore, the method has better error rate performance, provides an effective and practical method for PAM transmission with low cost, and is a potential digital signal processing scheme for short-distance transmission in the future.
The preferred embodiments of the present invention have been described in detail with reference to the accompanying drawings, however, the present invention is not limited to the specific details of the above embodiments, and various simple modifications can be made to the technical solution of the present invention within the technical idea of the present invention, and these simple modifications are within the protective scope of the present invention.
It should be noted that the various technical features described in the above embodiments can be combined in any suitable manner without contradiction, and the invention is not described in any way for the possible combinations in order to avoid unnecessary repetition.
In addition, any combination of the various embodiments of the present invention can be made, and the same should be considered as the disclosure of the present invention as long as the idea of the present invention is not violated.
Claims (6)
1. A decoding algorithm based on the combination of nonlinear equalization and FEC is characterized by comprising the following steps:
step A: constructing Polar codes by adopting a Gaussian approximation construction method;
and B: mapping the coded code word;
and C: carrying out transmission processing on the mapped signals;
step D: carrying out LLR estimation on the signal;
step E: and (5) decoding and judging.
2. The decoding algorithm based on the combination of the nonlinear equalization and the FEC as claimed in claim 1, wherein the step a is as follows:
step A1: determining the positions of the information bits and the frozen bits, and rearranging according to the bit channel capacity to obtain a bit sequence X N ；
Step A2: putting information bits into bit channel with larger capacity, putting frozen bits into bit channel with smaller capacity, and polarizing bit channel by modulo two addition method to obtain coded code word C N The process is represented as:
wherein G is N To generate a matrix, B N For bit-inverting the operation matrix, and
the n-times kronecker product of the matrix is represented.
3. The decoding algorithm based on the combination of the nonlinear equalization and the FEC as claimed in claim 1, wherein the step B is as follows:
step B1: sending the obtained code words into a mapper, and mapping every three bits into a group of gray into PAM8 signals;
the log-likelihood ratio LLR estimate in Polar decoder is expressed as:
wherein, b i Represents the ith bit mapped to a PAM8 symbol at the transmitting end, the value range of i is 1,2 and 3, and r represents the received PAM8 signal;
and step B2: since bits "0" and "1" in the user data are transmitted with equal probability, b i =0 and b i The probability of =1 is equal, i.e.:
according to the nature of the posterior probability, the posterior probability P (b) i =0 r) is defined as:
similarly, the posterior probability P (b) is obtained i ＝1r)
4. The decoding algorithm based on non-linear equalization and FEC combination as claimed in claim 1, wherein step C is as follows:
step C1: after pulse forming, a modulation signal is sent into an optical fiber link, and at a receiving end, the signal is subjected to timing sampling through clock recovery;
and step C2: and sending the synchronized signal to an equalizer to compensate channel damage.
5. The decoding algorithm based on the combination of nonlinear equalization and FEC as claimed in claim 1, wherein the step D is specifically as follows:
step D1: sending the equalized signal into a deep neural network, and firstly carrying out LLR estimation on the signal;
if the signal pass mean is 0 and the variance is sigma 2 Of an Additive White Gaussian Noise (AWGN) channel, the transition probability P (rb) of the channel i = k) is expressed as:
wherein k =0,1, and
a standard symbol representing that the mapped ith bit is k; from equations (5) and (6), the calculation formula for obtaining LLR is as follows:
noise in the formulaThe acoustic variance is estimated by adding a training sequence, i.e. transmitting a length L at the beginning of the transmitted data t Training sequence T of t Then the noise variance is estimated as:
wherein r is t Represents the t-th PAM signal received;
step D2: estimating parameters of a non-equivalent Gaussian distribution model by adopting a deep neural network method;
according to the rule of PAM8 symbol mapping, the LLR estimate for the first bit of the three bit positions is expressed as:
wherein, mu j Eight different amplitudes of the PAM8 signal are represented,
representing the noise variance at different amplitudes of the PAM8 signal, y represents the equalized signal, and the LLR estimate for the second bit and the LLR estimate for the third bit are respectively represented as:
6. the decoding algorithm based on the combination of the nonlinear equalization and the FEC as claimed in claim 1, wherein the step E is as follows:
step E1: and (3) placing the estimated LLR as an initial input to the rightmost side of the butterfly decoding structure by using a Serial Cancellation (SC) decoding algorithm to perform recursive computation, wherein the computation of each node is to solve the upper and lower branch nodes on the left side of different butterfly substructures, and the computation of the upper node of the butterfly structure is represented as:
and the operation of the following node is represented as:
where y represents the equalized signal, u represents the transmitted signal, o represents the odd positions, e represents the even positions, and the functions f (l, m) and g (l, m, n) are defined as follows:
wherein l, m and n are independent variables;
and E2: after multilayer butterfly operation, obtaining LLR value corresponding to each bit with code length N, according to the bit sequence ordering position when Polar code is constructed in the encoder, judging LLR value to obtain original sending bit, the judging rule is:
after SC decoding, extracting the corresponding information bit according to the bit position information, namely the data received by the user.
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| CN114257342A (en) * | 2021-12-22 | 2022-03-29 | 哈尔滨工业大学 | Coding and decoding method for two-user multiple access system based on non-binary polarization code |
| CN114938259A (en) * | 2022-04-13 | 2022-08-23 | 苏州大学 | Probability shaping PAM-8 signal short-distance transmission method and system |
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| CN114257342A (en) * | 2021-12-22 | 2022-03-29 | 哈尔滨工业大学 | Coding and decoding method for two-user multiple access system based on non-binary polarization code |
| CN114938259A (en) * | 2022-04-13 | 2022-08-23 | 苏州大学 | Probability shaping PAM-8 signal short-distance transmission method and system |
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