CN116846407A - Fading channel polarization code construction structure based on maximized mean value difference - Google Patents
Fading channel polarization code construction structure based on maximized mean value difference Download PDFInfo
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- 238000005562 fading Methods 0.000 title claims abstract description 60
- 230000010287 polarization Effects 0.000 title claims abstract description 58
- 238000010276 construction Methods 0.000 title claims abstract description 24
- 238000009826 distribution Methods 0.000 claims abstract description 38
- 238000000034 method Methods 0.000 claims abstract description 38
- 239000013598 vector Substances 0.000 claims abstract description 20
- 238000007619 statistical method Methods 0.000 claims abstract description 5
- 238000005259 measurement Methods 0.000 abstract description 7
- 238000000342 Monte Carlo simulation Methods 0.000 description 7
- 238000010586 diagram Methods 0.000 description 7
- 238000004422 calculation algorithm Methods 0.000 description 6
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- 230000000996 additive effect Effects 0.000 description 3
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- 238000004891 communication Methods 0.000 description 3
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- 230000001172 regenerating effect Effects 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 238000009825 accumulation Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008030 elimination Effects 0.000 description 1
- 238000003379 elimination reaction Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000013138 pruning Methods 0.000 description 1
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- 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
- H03M13/13—Linear codes
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- 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
- H04L1/0045—Arrangements at the receiver end
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- 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
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Abstract
The invention provides a fading channel polarization code construction structure based on maximized mean value difference, which consists of an initial receiving vector module, a measurement distribution difference module, a noise standard deviation calculating module and a polarization code generating module. And calculating the distribution difference of the receiving vectors of the Rayleigh fading channel and the Gaussian channel in a measurement distribution difference module, wherein when the noise variances of the two channels are equal, the fading channel is equivalent to the Gaussian channel. In the structure, firstly, the receiving vectors of an initial Rayleigh fading channel and a Gaussian channel are obtained, the noise standard deviation of an equivalent channel is found after the difference of the two distributions is measured, and the noise standard deviation is used as an initial value of a Gaussian approximation method to generate a polarization code. The statistical method used in the distribution difference measuring module is to maximize the mean difference, the scheme for constructing the polarization codes can more accurately obtain the reliable channel distribution under the fading channel, and the constructed polarization codes can be directly input into a fading channel encoder, so that the encoding complexity in the fading channel is reduced.
Description
Technical Field
The invention belongs to the technical field of decoding of communication channel coding, and relates to a fading channel polarization code construction structure based on maximized mean value difference. The statistical method for measuring the channel difference is to maximize the mean value difference, so that the reliable channel distribution under the fading channel can be obtained more accurately to construct the polarization code, and the polarization code after the construction can be directly used in the Rayleigh fading channel without regenerating the polarization code during encoding and decoding.
Background
The polarization code is first proposed by Arikan in 2007, can reach Shannon limit under binary discrete memory-free channel, and is the basis of the current 5G channel coding field. For the coding structure of the polarization code, arikan proposes a continuous cancellation (Successive Cancellation, SC) decoding algorithm, which has low decoding complexity, and when the code length approaches infinity, the decoding performance is excellent, but the performance is not ideal under the medium-short code length. To improve the performance of SC decoding, a successive cancellation list (Successive Cancellation List, SCL) decoding algorithm is proposed. The SCL decoder is currently the most widely used decoder in terms of polar code decoding, and SCL decoding performs path splitting and pruning on each information bit, while retaining L decoded candidate paths, each path having a path metric value that measures the path reliability. The smaller the path metric value, the more reliable the path, and the greater the probability of being retained as a final decoding result. SCL decoding achieves very superior performance as list L increases, but at the same time decoding complexity and resource consumption also increase.
Since the rayleigh fading channel is more in line with the real communication system, the performance of the polarization code is reduced under the rayleigh fading channel, and the polarization code cannot be constructed by gaussian approximation for SC decoding under the fading channel, the polarization code is generally constructed by monte carlo method. The method of acquiring a reliable channel by monte carlo simulation is complicated and takes a long time to calculate, which is not acceptable in real communication. Therefore, in order to balance the complexity and frame error rate, niu Kai teaches et al that the rayleigh channel is equivalent to a gaussian channel by using KL (Kullback-Leibler) divergence, and further, the polarization code is constructed by using a gaussian approximation, and the decoding performance of the method is better than that of the monte carlo construction method, and the complexity is lower. Considering that the channel equivalent method can be further optimized, the invention calculates the receiving vector distribution difference of the additive white gaussian noise (Additive White Gaussian Noise, AWGN) channel and the rayleigh fading channel (Rayleigh Fading Channel, RFC) based on the maximized mean difference (Maximum Mean Discrepancy, MMD), and the channel equivalent index thereof is measured by the maximized mean difference value. The minimum value that maximizes the mean difference exists in the measurement distribution difference interval, and the noise standard deviation at this point is considered to be the noise standard deviation of the two channel equivalents. And constructing the polarization code by using the Gaussian approximation construction method by taking the standard deviation of the noise as an initial value, and directly transmitting the constructed polarization code into a Rayleigh fading channel for encoding and decoding without regenerating the polarization code in the Rayleigh fading channel. Finally, simulation data show that the construction method improves SC decoding performance in a fading channel, and in addition, the Gaussian approximation construction after channel equivalence and the derivative method thereof can be applied in the fading channel.
Disclosure of Invention
In order to solve the problems that the Gaussian approximation structure polarization code is not suitable for the traditional fading channel and the continuous elimination decoding performance is poor in the Rayleigh fading channel, the invention provides a fading channel polarization code structure based on the maximized mean value difference, the whole system block diagram of the fading channel polarization code structure is shown in figure 1, and the whole system block diagram is composed of an initial receiving vector module, a measurement distribution difference module, a noise standard deviation calculating module and a polarization code generating module. The statistical method used in the distribution difference measuring module is used for maximizing the mean difference, so that the reliable channel distribution under the fading channel can be obtained more accurately. The construction polarization code scheme of equivalent Rayleigh fading channel as Gaussian channel does not need a large number of samples to calculate like Monte Carlo simulation method, and Gaussian approximation construction and derivative method thereof can be applied to construction polarization code in fading channel after equivalent of channel.
The basic idea of the invention is as follows: the Gaussian approximation construction polarization code method is proposed based on Gaussian channels, the Gaussian approximation construction polarization code cannot be directly used in fading channels, the complexity of constructing the polarization code by using a Monte Carlo simulation method in Rayleigh fading channels is high, and therefore the maximum mean difference is proposed to be used for measuring the distribution difference of receiving vectors of RFC and AWGN channels. And obtaining noise variance when the RFC is equivalent to an AWGN channel. Because the equivalent channel can use Gaussian approximation to construct the polarization code, the noise variance is used as the initial value of the Gaussian approximation to construct the polarization code, and the problem that the fading channel cannot directly use the Gaussian approximation is solved.
Based on the technical problems, the technical method adopted by the invention comprises the following steps: the invention provides a polarization code construction scheme, which firstly processes the polarization code to generate a receiving vector y of an AWGN channel a Received vector y of RFC r . The distribution difference module is used for measuring the received vector y a And y r And carrying out maximum mean difference operation, and obtaining a distribution relation diagram of the noise variance and the maximum mean difference distance d in the measurement distribution difference interval. And acquiring the corresponding noise variance when the d value is minimum in the generated distribution relation diagram. The polarization code is constructed using a gaussian approximation method with the noise standard deviation as an initial value.
In order to ensure the reliability of calculating the distribution difference in the distribution difference measuring module, the number of circulation times is set to accumulate d values obtained by each calculation, and the average value of d is obtained after the circulation accumulation is completed. Since the noise variance is obtained by squaring the noise standard deviation, the noise standard deviation is used in calculating and generating the distribution in MATLAB for simplicity of calculation.
After the corresponding noise standard deviation is found under all experimental signal-to-noise ratios, a Gaussian approximation method is used for constructing a polarized code word, so that an information set of the polarized code can be constructed before an input fading channel is subjected to SC coding. The SC decoder is used in the equivalent fading channel, and the externally constructed polarization code is used in the SC decoder, so that the step of selecting information bits in the coding process of the SC decoder is reduced, and compared with the Monte Carlo simulation method, the method is simpler and more convenient. The obtained noise standard deviation is more accurate because the value with the minimum maximum mean difference distance between the Rayleigh fading channel and the additive Gaussian white noise channel is selected in the channel equivalence process. Therefore, the construction method improves the error correction performance of the method that the Rayleigh channel is equivalent to the Gaussian channel compared with the error correction performance of the method that the KL (Kullback-Leibler) divergence is used in the fading channel by using the SC decoder.
Compared with the prior art, the invention has the advantages and beneficial effects that:
1) The invention uses the maximized mean value difference to equivalent the Rayleigh fading channel to the Gaussian channel, and the constructed polarized code channel has higher reliability.
2) The polarization code constructed by the invention can be generated before SC coding is carried out on the fading channel, so that the coding steps of an SC decoder are reduced.
3) The invention can apply the Gaussian approximation structure and the derivative method thereof in the equivalent fading channel.
Drawings
Fig. 1 is a system block diagram of a fading channel polar code construction structure based on maximized mean difference;
FIG. 2 is a flow chart for measuring channel distribution differences;
FIG. 3 is a graph of the distribution of noise standard deviation and maximum mean difference distance;
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings, the following examples being preferred examples of the application of the present invention and should not be construed as limiting the invention.
As shown in fig. 1, the fading channel polarization code construction structure based on the maximized mean value difference is composed of an initial receiving vector module, a measurement distribution difference module, a noise standard deviation calculating module and a polarization code generating module. And inputting the received vectors yr and ya of the Rayleigh fading channel and the Gaussian channel output by the initial received vector module into the measurement distribution difference module to perform maximum mean value difference operation. Output in the metric distribution difference module is a distance value d of the distribution difference between the two channels and a noise standard deviation associated with d. The noise standard deviation calculating module judges the data output by the distribution difference measuring module, when d is minimum, the Rayleigh fading channel is considered to be equivalent to a Gaussian channel, and the noise standard deviation corresponding to d is taken as an initial value to be input and output to the polarization code generating module to construct a polarization code.
In the initial received vector module, the received vector y in the Rayleigh fading channel r =hs (b) +n, where h is a fading coefficient, s (b) =1-2 b, b is a source codeword and b e {0,1}, n is noise satisfying a gaussian distribution. Received vector y in gaussian channel a =h+n. Reception at the time of receiving a signal due to a rayleigh fading channelVector progressionProcessing, so the index for measuring the equivalent of the Rayleigh fading channel to the Gaussian channel in the distribution difference module is +.>Wherein->Is the noise variance of the rayleigh fading channel, +.>Is the noise variance of the gaussian channel. To reduce the amount of computation, the computed channel noise variance is reduced to the channel noise standard deviation. Defining the reduced channel equivalent index as sigma r ＝σ a . The statistical method for measuring the channel difference is to maximize the mean value difference, and the calculation formula of the maximum mean value difference value is +.>Where m is the length of the received vector, H is the Gaussian kernel function, < >>So there is a corresponding noise standard deviation sigma in calculating each d value a Calculating the distribution condition of the maximized mean difference value and the noise standard deviation between the two channels is realized in MATLAB.
The flow chart for measuring the channel distribution difference is shown in fig. 2, by using the received vector between two channels obtained in the initial received vector module, the maximum mean value difference value between two channels is calculated by using the noise standard deviation of the Gaussian channel as the channel equivalent index, and when the maximum mean value difference value is minimum, the sigma at the received vector is considered r ＝σ a I.e. the rayleigh fading channel is equivalently a gaussian channel. Obtaining the noise standard deviation sigma at this time a The polarization code is constructed using gaussian approximation with the noise standard deviation as an initial value.The generated polarization code is directly input into the Rayleigh fading channel for SC coding and decoding, and the code word is constructed by the polarization code before being input into the Rayleigh fading channel for SC decoding, so that the method reduces a certain coding step compared with the SC coding and decoding method under the traditional fading channel. The polarization code can not be constructed by using a Gaussian approximation construction method in the traditional Rayleigh fading channel, but the Rayleigh fading channel is equivalent to the Gaussian channel by adopting the maximized mean value difference, so that the Gaussian approximation construction method and the polarization code construction method derived from the Gaussian approximation construction method are also applicable to the equivalent Rayleigh fading channel.
Fig. 3 is a graph of the distribution of the standard deviation of noise and the distance of the maximized mean difference, the experimental condition is that the code length n=128, the code rate r=1/2, and the signal to noise ratio range is 1-5dB. The MATLAB outputs a subsection relation diagram of the noise standard deviation and the maximized mean value difference value after measuring the channel distribution difference, and it can be seen from the diagram that a minimum maximized mean value difference value d exists under each signal-to-noise ratio curve, and each d value has a noise standard deviation corresponding to the minimum maximized mean value difference value d. The data generated by the distribution map is transmitted to a module for calculating the standard deviation of noise, and the standard deviation of noise when the channel is equivalent under each signal-to-noise ratio is found and output in the module.
Performance simulation of a polarization code construction structure based on maximized mean difference is performed in a rayleigh fading channel environment, and meanwhile, comparison includes a method of constructing a polarization code (RFC-SC) by using monte carlo simulation and a method of equivalent a rayleigh channel to a gaussian channel by using KL divergence, and then constructing the polarization code (KL-SC) by using gaussian approximation. The method of constructing polarization codes using the method proposed by the present invention and employing an SC decoder is simply referred to as MMD-SC. Under the experimental condition of the code length N=128 and the code rate R=0.5, when the error rate is 10 -3 When the MMD-SC method reaches the error rate, the signal to noise ratio is approximately 3.85dB, the required signal to noise ratio of the KL-SC method is approximately 4.15dB, and the required signal to noise ratio of the RFC-SC method is approximately 4.4dB. The performance of the MMD-SC decoding algorithm is about 0.3dB better than the KL-SC decoding algorithm, while the performance of the KL-SC decoding algorithm is about 0.25dB better than the RFC-SC decoding algorithm. Performance of SC decoder after using polarization code constructed by the invention and KL divergence equivalent method in RFCCompared with the two methods of SC decoding after polarization code generation, the method provided by the invention has the advantage of improving the performance under the condition of high signal-to-noise ratio. The above data shows that the KL divergence equivalent method is better than the monte carlo simulation method under high signal-to-noise ratio, but the decoding performance of the structural polarization code scheme provided by the invention is better than that of the other two methods.
The above embodiments are not intended to limit the present invention in any way, and all technical methods obtained by using the similar structures, methods and similar variations of the present invention are within the scope of the present invention.
Claims (2)
1. The fading channel polarization code construction structure based on the maximized mean difference is characterized in that the difference of the distribution of the receiving vectors of the Rayleigh fading channel and the Gaussian channel is measured, and the Rayleigh fading channel is equivalent to the Gaussian channel. The statistical method used in the distribution difference measuring module is to maximize the mean difference, so that the reliable channel distribution under the fading channel can be obtained more accurately.
2. The channel approximation method of claim 1 wherein the noise standard deviation used in constructing the polarization code is obtained by measuring the channel distribution difference, and the polarization code is constructed using the noise standard deviation as an initial value of the gaussian approximation. The constructed polarization code can be directly used in the Rayleigh fading channel, and the polarization code is not regenerated during encoding and decoding, so that the complexity of constructing the polarization code in the original Rayleigh fading channel is reduced.
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