CN113300721B - LDPC code decoding method and storage medium - Google Patents
LDPC code decoding method and storage medium Download PDFInfo
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- CN113300721B CN113300721B CN202110583955.4A CN202110583955A CN113300721B CN 113300721 B CN113300721 B CN 113300721B CN 202110583955 A CN202110583955 A CN 202110583955A CN 113300721 B CN113300721 B CN 113300721B
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- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1148—Structural properties of the code parity-check or generator matrix
- H03M13/1151—Algebraically constructed LDPC codes, e.g. LDPC codes derived from Euclidean geometries [EG-LDPC codes]
Abstract
The invention discloses a decoding method of LDPC code and a storage medium, belonging to the technical field of channel decoding, comprising the following steps: s1, initializing an impulse noise channel, and converting information of a received LDPC code signal into log-likelihood ratio information of the channel; s2, transmitting the log-likelihood ratio information of the channel to a decoder, and outputting a soft information result of the iterative decoding; s3, processing the decoding soft information result by adopting an EM algorithm based on gradient descent to obtain a current iteration channel parameter estimation value; s4, updating log-likelihood ratio information of the channel by using the channel parameter estimation value; and repeating the steps S2-S4 until the maximum iteration times is met, and outputting a final decoding hard decision result. By adopting the method, the precision of the impulse noise channel estimation can be improved through the transmission of the soft information between the channel estimation and the sum-product decoding algorithm, so that the LDPC decoding error rate under the time-varying and burst impulse noise channel is reduced.
Description
Technical Field
The present invention relates to the field of channel decoding technologies, and in particular, to a method and a storage medium for decoding an LDPC code.
Background
Along with the establishment of the Beidou third system and the broadcasting of Beidou signals B1C and B2A of new systems, the requirements of users on GNSS service quality are gradually improved. For a receiver of a new system signal, the accuracy and reliability of GNSS positioning are directly influenced by the error-free transmission of a navigation signal and the quality of the signal, and a good navigation signal guarantees high-quality and high-stability service for subsequent positioning. In the new system Beidou signals B1C and B2A, in order to prevent the signals from generating errors in the transmission process and improve the capability of the signals for resisting various interferences in the transmission process, an error correction coding technology, namely LDPC code is applied.
The navigation messages of the Beidou signals B1C and B2A of the new system adopt LDPC coding, and the traditional LDPC decoding algorithm is divided into hard decision decoding and soft decision decoding. The hard decision decoding mainly converts a received signal into a signal only containing 0 and 1 through a hard decision device for decoding; soft decision decoding preserves channel information in the signal. Due to the improvement of the calculation power at present, the soft-decision decoding algorithm is widely applied. The GNSS receiver applies a soft-decision decoding algorithm to decode in real time, and performs real-time calculation based on a decoding output result, so that a lower decoding error rate can be realized in an ideal Gaussian white noise channel.
However, the gaussian white noise channel is a theoretical channel model, and in practical communication and navigation systems, channel noise is often non-ideal non-gaussian impulse noise, and the distribution of the channel noise is often described by a symmetric alpha distribution. Under the non-ideal non-Gaussian impulse noise channel, the performance of the traditional soft-decision decoding algorithm is greatly reduced, and the decoding error rate is high.
Disclosure of Invention
The invention aims to overcome the defects in the background technology and reduce the decoding error rate of the LDPC code under the impulse noise channel.
In order to achieve the above object, in one aspect, an LDPC code decoding method is adopted, including the steps of:
s1, initializing an impulse noise channel, and converting information of a received LDPC code signal into log-likelihood ratio information of the channel;
s2, transmitting the log-likelihood ratio information of the channel to a decoder, and outputting a soft information result of the iterative decoding;
s3, processing the decoding soft information result by adopting an EM algorithm based on gradient descent to obtain a current iteration channel parameter estimation value;
s4, updating log-likelihood ratio information of the channel by using the channel parameter estimation value;
s5, judging whether the current iteration number meets the maximum iteration number of decoding, if not, re-executing the steps S2-S4, and if so, executing the step S6;
and S6, outputting a decoding hard decision result.
Further, the step S1: the method for initializing the impulse noise channel and converting the information of the received LDPC code signal into the log-likelihood ratio information of the channel comprises the following steps:
obtaining the amplitude y of the baseband signal of each chip of the LDPC code i ，i＝1,2,…,N；
Initializing the channel impulse noise parameter to be randomly in the range of 0 to 1 and 1 to 2;
calculating each code word x of the LDPC code according to the probability density function of symmetrical stable alpha distribution satisfied by the impulse noise i Is 0 or 1 corresponding to the amplitude y i Conditional probability P (y) of i |x i = 1) and P (y) i |x i ＝+1)；
Calculating log-likelihood ratio information of the channel as
Further, the step S2: transmitting the information of the log-likelihood ratio of the channel to a decoder, and outputting a soft information result of iterative decoding, wherein the soft information result comprises:
transmitting the log-likelihood ratio information of the channel to variable nodes at corresponding positions;
transmitting variable node information to check nodes connected with the variable nodes according to the Tanner graph of the LDPC code word so as to update check node information of corresponding positions;
updating variable node information connected with the check nodes according to the existing check node information;
and updating the channel posterior probability judgment information of the corresponding position, and outputting a decoding soft information result.
Further, the step S3: adopting an EM algorithm based on gradient descent to process a decoding soft information result to obtain a current iteration channel parameter estimation value, wherein the method comprises the following steps:
calculating an EM algorithm parameter estimation formula according to the decoding soft information result;
and for the parameter estimation formula of the EM algorithm, random gradient descent is carried out, and the maximum value point of the parameter estimation formula related to the characteristic factor alpha and the distribution parameter gamma is obtained and is used as the current iteration channel parameter estimation value.
Further, the calculating an EM algorithm parameter estimation formula according to the decoded soft information result includes:
according to the decoding soft information result information, calculating an expected Q function of the conditional probability distribution of the received signal y and the LDPC codeword x under the current m iterations
Further, the performing random gradient descent to obtain a maximum point of a parameter estimation formula as a current iteration channel parameter estimation value includes:
calculating the value of the expected Q function according to the characteristic factor alpha and the distribution parameter gamma of the impulse noise parameter;
given the small offsets of alpha and gamma, delta alpha and delta gamma, the current gradient is calculated
And
updating the parameter estimation values of the characteristic factor alpha and the distribution parameter gamma according to the calculated gradient direction;
and repeating the gradient calculation and parameter updating processes until the maximum gradient descent time condition is met or the parameter alpha and gamma estimated values are not updated any more, and taking the maximum value point of the expected Q function at the moment as the current iteration channel parameter estimated value.
Further, the step S4: updating log-likelihood ratio information of the channel using the channel parameter estimates, comprising:
and taking the parameter updating result meeting the maximum gradient descent frequency condition as an m +1 estimation result of the characteristic factor alpha and the distribution parameter gamma, transmitting the parameter updating result to a decoder, and recalculating the log likelihood ratio information of the pulse noise channel initialization.
On the other hand, a computer-readable storage medium is employed, on which a computer program is stored, the computer program being executed by a processor, the LDPC code decoding method as described above being implemented.
Compared with the prior art, the invention has the following technical effects: aiming at the problem of high traditional decoding error rate under an impulse noise channel, a decoder and an estimator are combined, the output result of the decoder under each iteration is used as the input of the next estimator for updating the channel state parameters, then the updated channel state parameters are used for correcting the output of the decoder, and finally the decoding result of the final decoder is output under the condition of meeting the maximum iteration times; aiming at the problem that the distribution of the impulse noise has no closed analytic expression, a gradient descent method is adopted to iteratively and progressively obtain the maximum value of the impulse channel parameter estimation expression, so that the channel estimation is completed, and the decoding error rate of a combined channel estimation and decoding algorithm is reduced.
Drawings
The following detailed description of embodiments of the invention refers to the accompanying drawings in which:
FIG. 1 is a flow chart of a method of decoding LDPC codes;
FIG. 2 is a graph of Mean of GB-EM algorithm versus the estimation of the characteristic factor α versus the number of EM iterations;
FIG. 3 is a plot of RMSE of GB-EM algorithm versus the estimation of the characteristic factor α versus the number of EM iterations;
FIG. 4 is a plot of Mean of the GB-EM algorithm on the estimation of the distribution parameter gamma versus the number of EM iterations;
FIG. 5 is a plot of RMSE of GB-EM algorithm versus distribution parameter γ estimate versus number of EM iterations;
FIG. 6 is a graph of the decoding error rate for a comparison between the GB-EM algorithm proposed by the invention for an LDPC codebook of N =8000 length and the conventional algorithm;
FIG. 7 is a flow chart of the GB-EM algorithm proposed by the present invention;
fig. 8 is a process of finding the extreme point of the desired Q function for gradient descent in one iteration estimation.
Detailed Description
To further illustrate the features of the present invention, refer to the following detailed description of the invention and the accompanying drawings. The drawings are for reference and illustration purposes only and are not intended to limit the scope of the present disclosure.
As shown in fig. 1 and fig. 7, the present embodiment discloses an LDPC code decoding method, which includes the following steps S1 to S6:
s1, initializing an impulse noise channel, and converting the information of the received LDPC code signal into the log-likelihood ratio information of the channel;
s2, transmitting the log-likelihood ratio information of the channel to a decoder, and outputting a soft information result of the iterative decoding;
s3, processing the decoding soft information result by adopting an EM algorithm based on gradient descent to obtain a current iteration channel parameter estimation value;
s4, updating log-likelihood ratio information of the channel by using the channel parameter estimation value;
s5, judging whether the current iteration number meets the maximum iteration number of decoding, if not, re-executing the steps S2-S4, and if so, executing the step S6;
and S6, outputting a decoding hard decision result.
As a further preferable technical solution, the step S1: initializing an impulse noise channel, and converting the received information of the LDPC code signal into log-likelihood ratio information of the channel, specifically:
for the N-length LDPC code, the amplitude y of each chip baseband signal is obtained i ，i＝1,2,…,N；
Initializing impulse noise parameters, randomly setting the distribution parameter gamma and the characteristic factor alpha of the impulse noise parameters within the ranges of 0 to 1 and 1 to 2 respectively;
calculated by using a numerical integration method, each code word x of the LDPC i An amplitude y of 0 or 1 i Conditional probability P (y) of i |x i = 1) and P (y) i |x i = 1), log likelihood ratio information of the channel is
It should be noted that the code word used in this embodiment is a Mackay configuration code, the code rate r =0.5, the code length N =8000, (3,6) regular LDPC code, and the decoded channel model is y i ＝x i +n i Where i =1,2, …,8000, n i In order to satisfy impulse noise of symmetrical α distribution, the distribution is determined by the characteristic factor α and the distribution parameter γ.
The probability density distribution function of the symmetric alpha distribution is
As can be seen from the inverse fourier transform, the probability density distribution function of the symmetric alpha distribution has no closed form expression. However, by numerical integration, the probability density function per point can be approximatedThe value of (c) is programmed as the stablepdf function. Thus, for each chip i, initially given randomly values in 0 to 1 and 1 to 2 for the eigenfactor α and the distribution parameter γ, the log-likelihood ratio information for the channel under the impulse channel can be calculated as follows:
for a decoder, after log-likelihood ratio information of an input channel is known, variable node information of a corresponding position is endowed with an initial value:
wherein check node C j Is and variable node V i And (4) connected check nodes.
As a more preferable embodiment, the step S2: transmitting the log-likelihood ratio information of the channel to a decoder, and outputting a soft information result of one-time iterative decoding, wherein the method comprises the following subdivision steps:
transmitting the log-likelihood ratio information of the channel to variable nodes at corresponding positions;
transmitting variable node information to check nodes connected with the variable nodes according to the Tanner graph of the LDPC code word so as to update check node information of corresponding positions;
updating variable node information connected with the check nodes according to the existing check node information;
and updating the channel posterior probability judgment information of the corresponding position, and outputting a decoding soft information result.
It should be noted that, after the calculation of the initialization information is completed, the calculation process of the LDPC code soft decision decoding Log-BP algorithm is performed, in a one-time iteration process, check node information of a corresponding position is calculated according to the initialized variable node information, and a Tanner graph corresponding to the LDPC code and a check node C are to be obtained j The set of connected variable nodes is denoted as N (C) j ) Then, the updating calculation method of the check node information is as follows:
in the belief propagation soft-decision decoding algorithm, after check node information at a corresponding position is obtained through calculation, decoding information needs to be reversely propagated to a variable node at the corresponding position, so that the information updating calculation method of the variable node comprises the following steps:
wherein, the variable node V in the Tanner graph corresponding to the LDPC code i The set of connected check nodes is denoted M (V) i ). Calculating the posterior soft decision information in the iterative process by combining the variable node information of the existing position
The method comprises the following steps:
LDPC codeword soft decision by posteriori information for decoding output
Determine when
If the decoding output chip i is less than 0, the decoding output chip i is 1; when in use
Greater than 0, the decoded output chip i is 0. For impulse noise channel, the posterior soft decision information calculated in the decoding process is needed
And outputting the signal to a channel estimator to finish updating the pulse noise parameter estimated value by channel estimation.
As a more preferable embodiment, the step S3: the method comprises the following steps of processing a decoding soft information result by adopting an EM algorithm based on gradient descent to obtain a current iteration channel parameter estimation value, wherein the steps from S31 to S32 are subdivided as follows:
s31, calculating an EM algorithm parameter estimation formula according to the decoding soft information result;
the method specifically comprises the following steps: according to the decoding soft information result, calculating an expected Q function of the conditional probability distribution of the received signal y and the LDPC codeword x under the current m iterations
It should be noted that, a posteriori soft decision information for obtaining an iterative decoding output is obtained
It is possible to calculate the E-step in the EM algorithm, i.e. calculate the expected Q-function of the conditional probability distribution of the received signal y and the LDPC codeword x
By means of a posteriori soft decision information, it is possible to calculate the received signal y per chip i The posterior probability of (a) is:
receiving signal y with each chip i Taking the posterior probability of (a) as a consideration, the calculation method that can obtain the expected Q function is:
and S32, carrying out random gradient descent on the EM algorithm parameter estimation formula to obtain a maximum value point of the parameter estimation formula related to the characteristic factor alpha and the distribution parameter gamma as a current iteration channel parameter estimation value.
The method comprises the following specific steps: calculating the value of the expected Q function according to the characteristic factor alpha and the distribution parameter gamma of the impulse noise parameter;
given the small offsets of alpha and gamma, delta alpha and delta gamma, the current gradient is calculated
And
updating the parameter estimation values of the characteristic factor alpha and the distribution parameter gamma according to the calculated gradient direction;
and repeating the gradient calculation and parameter updating processes until the maximum gradient descent time condition is met or the estimated values of the parameters alpha and gamma are not updated any more, and taking the maximum value point of the expected Q function at the moment as the estimated value of the current iteration channel parameter.
It should be noted that the nature of the EM estimation algorithm is maximum likelihood estimation, and therefore the estimation value of the impulse noise parameter is the point where the desired Q function takes an extreme value, which is also the M step in the EM algorithm. And solving the deviation of the expected Q function, so that the values of parameters alpha and gamma with the deviation of 0 are estimated values. However, since the probability density distribution function of the symmetric α distribution has no closed-form expression, the extreme point can be approximated by a gradient descent method. Considering Δ α and Δ γ as the small offsets of the parameters α and γ, the gradient of the Q function at the points of the parameters α and γ is:
the gradient descent algorithm calculates the gradient of each point and the parameter update rate eta corresponding to the parameters alpha and gamma α And η γ Approximating the extreme, parameter of the expectation functionThe updating calculation method of alpha and gamma comprises the following steps:
the gradient calculation and the updating of the parameters α and γ are repeated until the maximum gradient descent update times are satisfied or the parameters α and γ are not updated any more.
FIG. 8 is an example process of a gradient descent method finding an extremum of a desired Q function in an EM algorithm in one iteration of estimation. In an initialization stage, the characteristic factor alpha and the distribution parameter gamma are respectively set to be 1.392 and 0.372 at random, the characteristic factor alpha and the distribution parameter gamma in an actual pulse channel are 1.5 and 0.45, the parameters are updated through 20 times of gradient descent, the parameter estimation values of the characteristic factor alpha and the distribution parameter gamma are 1.4837 and 0.443, and the estimation result is very close to the real value. At the initial stage of parameter updating, the initial values and the real values of the characteristic factor alpha and the distribution parameter gamma are greatly different, so that the gradient is caused
And
the parameter updating step length is large in the initial stage, and each parameter updating step length is large in the initial stage; in the later stage of gradient descent, the characteristic factor alpha and the distribution parameter gamma are relatively close to the true values, and the gradient
And
and gradually decreasing, the step length of parameter updating is gradually decreased, and the estimated parameters are gradually converged towards the position of the true value of the characteristic factor alpha and the distribution parameter gamma.
As a further preferable technical solution, the step S4: updating log-likelihood ratio information of the channel using the channel parameter estimates, comprising:
and taking the parameter updating result meeting the maximum gradient descent frequency condition as the m +1 estimation results of the characteristic factor alpha and the distribution parameter gamma, transmitting the parameter updating result to a decoder, and recalculating the log likelihood ratio information of the pulse noise channel initialization.
It should be noted that, when the parameter estimation values of the characteristic factor α and the distribution parameter γ in one EM iteration estimation are obtained by the gradient descent method, the parameter estimation value of this time is applied in the next EM iteration estimation, and the log likelihood ratio information of the channel needs to be updated first. And after each EM iterative estimation, the Log-likelihood ratio information of the channel is more reliable, and the result obtained by decoding through a soft-decision decoding Log-BP algorithm is more accurate. In next EM iterative estimation, the posterior decision soft information obtained by the last calculation of the Log-BP algorithm is fed back to the EM estimator, the posterior decision soft information is more reliable, and the characteristic factor alpha and the distribution parameter gamma obtained by estimation are closer to the true value. And repeating the steps S2 to S4 until the maximum iteration times is met, and performing hard decision on the posterior soft information output by the last iteration decoding to obtain a decoding result. When the number of iterations of EM estimation is more, the information transmitted between the decoder and the estimator is more accurate and reliable, so that the final decoding output result is more accurate, and the decoding error rate is lower. Fig. 2, fig. 3, fig. 4 and fig. 5 respectively plot the accuracy of the algorithm of the present invention for the estimation of the characteristic factor α and the distribution parameter γ under the impulse noise environment with different intensities, fig. 2 and fig. 3 show the Mean value (Mean) and the Root Mean Square Error (RMSE) of the algorithm for the estimation of the characteristic factor α, fig. 4 and fig. 5 show the Mean value and RMSE of the algorithm for the estimation of the distribution parameter γ, and fig. 6 shows the Error rate of the decoding of the GB-EM algorithm. The estimated values of the characteristic factor alpha and the distribution parameter gamma are generally smaller than the real estimated values, the more the iteration times of the EM estimation are, the more the RMSE and Mean of the characteristic factor alpha and the distribution parameter gamma tend to be 0, and the lower the error rate of decoding output is.
The invention uses a combined channel estimation and decoding frame and provides an EM algorithm (GB-EM) Based on Gradient descent, thereby realizing accurate estimation of non-ideal impulse noise channel parameters, reducing the error rate of decoding LDPC codes in a non-ideal impulse noise environment, and obtaining more decoding gains compared with a traditional decoding method under white Gaussian noise. By the invention, the navigation messages obtained by decoding and outputting the Beidou signals B1C and B2A of the new system by the receiver have higher reliability, more accurate information transmission and higher positioning precision and reliability.
Another embodiment of the present invention also discloses a computer-readable storage medium, on which a computer program is stored, the computer program being executed by a processor, and the LDPC code decoding method as described above can be implemented.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (5)
1. An LDPC code decoding method, comprising:
s1, initializing an impulse noise channel, and converting information of a received LDPC code signal into log-likelihood ratio information of the channel;
s2, transmitting the log-likelihood ratio information of the channel to a decoder, and outputting a soft information result of the iterative decoding;
s3, processing the decoding soft information result by adopting an EM algorithm based on gradient descent to obtain a current iteration channel parameter estimation value;
s4, updating log-likelihood ratio information of the channel by using the channel parameter estimation value;
s5, judging whether the current iteration number meets the maximum decoding iteration number, if not, executing the steps S2-S4 again, and if so, executing the step S6;
s6, outputting a decoding hard decision result;
wherein, the step S3: processing the decoding soft information result by adopting an EM algorithm based on gradient descent to obtain a current iteration channel parameter estimation value, wherein the method comprises the following steps:
calculating an EM algorithm parameter estimation formula according to the decoding soft information result;
for the parameter estimation formula of the EM algorithm, carrying out random gradient descent to obtain a maximum value point of the parameter estimation formula related to the characteristic factor alpha and the distribution parameter gamma as a current iteration channel parameter estimation value;
the calculating an EM algorithm parameter estimation formula according to the decoding soft information result specifically includes:
according to the decoding soft information result, calculating an expected Q function of the conditional probability distribution of the received signal y and the LDPC codeword x under the current m iterations
The performing random gradient descent to obtain a maximum value point of a parameter estimation formula as a current iteration channel parameter estimation value specifically includes:
calculating the value of the expected Q function according to the characteristic factor alpha and the distribution parameter gamma of the impulse noise parameter;
given the small offsets of alpha and gamma, delta alpha and delta gamma, the current gradient is calculated
And
updating the parameter estimation values of the characteristic factor alpha and the distribution parameter gamma according to the calculated gradient direction;
and repeating the gradient calculation and parameter updating processes until the maximum gradient descent time condition is met or the parameter alpha and gamma estimated values are not updated any more, and taking the maximum value point of the expected Q function at the moment as the current iteration channel parameter estimated value.
2. The LDPC code decoding method as claimed in claim 1, wherein the step S1: the method for initializing the impulse noise channel and converting the information of the received LDPC code signal into the log-likelihood ratio information of the channel comprises the following steps:
obtaining the amplitude y of the baseband signal of each chip of the LDPC code i ，i＝1,2,…,N；
Initializing channel impulse noise parameters randomly in the range of 0 to 1 and 1 to 2;
calculating each code word x of the LDPC code according to the probability density function of symmetrical stable alpha distribution satisfied by the impulse noise i An amplitude y of 0 or 1 i Conditional probability P (y) of i |x i = -1) and P (y) i |x i ＝+1)；
Calculating log-likelihood ratio information of the channel as
3. The LDPC code decoding method of claim 1, wherein the step S2: transmitting the log-likelihood ratio information of the channel to a decoder, and outputting a soft information result of one-time iterative decoding, wherein the soft information result comprises the following steps:
transmitting the log-likelihood ratio information of the channel to variable nodes at corresponding positions;
transmitting variable node information to check nodes connected with the variable nodes according to the Tanner graph of the LDPC code word so as to update check node information of corresponding positions;
updating variable node information connected with the check nodes according to the existing check node information;
and updating the channel posterior probability judgment information of the corresponding position, and outputting a decoding soft information result.
4. The LDPC code decoding method as claimed in claim 3, wherein the step S4: updating log-likelihood ratio information of the channel using the channel parameter estimates, comprising:
and taking the parameter updating result meeting the maximum gradient descent frequency condition as an m +1 estimation result of the characteristic factor alpha and the distribution parameter gamma, transmitting the parameter updating result to a decoder, and recalculating the log likelihood ratio information of the pulse noise channel initialization.
5. A computer-readable storage medium having stored thereon a computer program, wherein the computer program is executed by a processor to implement the LDPC code decoding method according to any one of claims 1 to 4.
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