CN114584153A - Bit flipping decoding method and device for polarization code - Google Patents
Bit flipping decoding method and device for polarization code Download PDFInfo
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- 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
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Abstract
The invention discloses a bit flipping decoding method and device of a polarization code. The method comprises the steps of determining the optimal threshold of the log-likelihood ratio suitable for different code rates and signal-to-noise ratios through experiments aiming at the same code length, and constructing a key set according to the optimal threshold of LLR; and adjusting the ordering of the elements in the key set by using the relation between the decoding reliability of each element in the key set and the positions of the elements in the key set. The invention provides a continuous offset bit flipping decoding scheme which is relatively balanced in indexes such as frame error rate, decoding complexity and the like under the conditions of specific code length, different code rates and signal to noise ratios and is suitable for practical application.
Description
Technical Field
The invention belongs to the technical field of a decoding scheme of a polarization code, and particularly relates to a bit flipping decoding method and device of the polarization code.
Background
Polar Codes (Polar Codes) Polar Codes are the first coding scheme that can be strictly proven to reach the capacity of a binary discrete memoryless channel (B-DMC), have the advantages of fixed construction method, low decoding complexity and the like, and have been used as the control channel coding standard of 5G mobile communication.
The decoding scheme of the polarization code has been the research hotspot of the polarization code. Serial Cancellation (SC) decoding is the first scheme of polar code decoding, and when the code length tends to infinity, the decoding performance is degraded when the code length is limited, so SC decoding is not suitable for practical application. In order to improve decoding performance, the e.arika proposes a Belief Propagation (BP) decoding scheme, which obtains good decoding performance by iteratively calculating the log-likelihood ratio of each node, but the decoding complexity is very high. I.tal and a.vardy also propose a Serial Cancellation List (SCL) decoding scheme, which improves decoding performance by searching and retaining a certain number of candidate paths, and improves decoding parallelism, but when the number of candidate paths is large, decoding complexity and decoding delay are high. Then, in order to improve the SCL decoding performance, a cyclic redundancy check SCL decoding scheme (CA-SCL) is proposed, and the selection efficiency of a correct candidate path is improved by adding the cyclic redundancy check; while Serial Cancellation Stack (SCS) coding and Serial Cancellation Hybrid (SCH) coding schemes reduce SCL coding complexity to different degrees under the condition of ensuring coding accuracy; in addition, all schemes such as viterbi decoding, BCJR decoding, and Sphere (Sphere) decoding of polar codes can achieve decoding performance approaching maximum likelihood, but the above decoding schemes are very complex and have poor decoding effect when the code length is long.
And the proposal of the continuous cancellation bit flipping (SC-Flip) decoding scheme provides a new idea for improving the SC decoding performance. The core of the SC-Flip scheme is to find the first erroneous information bit and Flip it in the additional SC decoding to improve the decoding performance. Afisiadis and the like propose an SC-Flip scheme, absolute values of Log-likelihood ratios (LLRs) of information bits are arranged in an ascending order, and then bit flipping operation is performed in sequence until decoding is correct or a set maximum flipping number is reached. Carlo Condo et al propose FIS (Fixed index selection) and EIS (Enhanced index selection) bit flipping decoding schemes, but both schemes are key sets for selecting error bits based on simulation experiments, and the relative order of elements in the sets is Fixed, but the decoding performance of the scheme decreases with the increase of the code rate; based on the scheme, Furkan Ercan and the like also provide an SC-Flip decoding scheme based on a threshold, a general key set is provided for different signal-to-noise ratios and code rates under the same code length, and the thresholds of the same code rate and different signal-to-noise ratios are determined, so that the decoding performance under a high bit error rate is improved by the method, but the additional decoding times are relatively more under the condition of low code rate, and the convergence rate of Frame Error Rate (FER) is slower; the scheme provides a Fast-SSC-Flip decoding method, reduces delay on the basis of not sacrificing error correction performance, greatly increases implementation complexity of a decoder, and is difficult to be applied to practice.
In summary, many research results have been obtained in the research on the decoding scheme of the polar code, but different decoding methods have different performance indexes such as frame error rate, computational complexity, decoding delay and the like under different conditions such as code length, code rate, signal to noise ratio and the like.
How to provide a continuous offset bit flipping SC-Flip scheme which is relatively balanced in indexes such as frame error rate and decoding complexity and is suitable for practical application under different conditions is a problem which needs to be solved urgently.
Disclosure of Invention
The main objective of the present invention is to provide a bit flipping decoding method and apparatus for polarization code, so as to overcome the disadvantages of the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps: a bit flipping decoding method of a polarization code comprises the following steps:
s100, aiming at the same code length, calculating thresholds of log-likelihood ratios under different code rates and signal-to-noise ratios, selecting the maximum value of LLR thresholds obtained under different code rate and signal-to-noise ratio combinations as the optimal threshold under the code length, and constructing a key set by using the optimal threshold;
s200, adjusting the sequence of the elements in the key set by using the relation between the decoding reliability of each element in the key set and the positions of the elements in the key set.
In a preferred embodiment, in S100, a simulation experiment method is used to determine the optimal threshold of the log-likelihood ratio.
In a preferred embodiment, the S100 includes:
s101, inputting code length, code rate and signal-to-noise ratio parameters;
s102, setting an initial value and a step length of the temporary LLR threshold value and simulation times of SC decoding, and simulating the SC decoding;
s103, calculating the probability of the first error bit in the key set, and if the probability is greater than a set value, determining that the temporary threshold of the current LLR is a threshold T corresponding to the code rate and the signal-to-noise ratio under the current code length;
and S104, under the same code length, calculating threshold values T corresponding to different code rates and signal-to-noise ratios according to the S101 to S103, counting the threshold values in a table, and selecting a maximum threshold value from the table as an optimal LLR threshold value corresponding to the code length.
In a preferred embodiment, in S103, if the probability is less than or equal to a set value, the temporary threshold of the current LLR is added with 1 and then returned to S102 until the calculated probability of the first error bit in the key set is greater than the set value.
In a preferred embodiment, in S102, the process of constructing the bit flipping set includes:
and when the decoding is wrong, comparing the corresponding LLR value with the temporary LLR threshold value in sequence from small to large according to the information bit index, and if the LLR value is smaller than the temporary threshold value, putting the index of the information bit into a bit overturning set to construct the bit overturning set.
In a preferred embodiment, the step S103 of calculating the probability of the first error bit in the bit flip set includes: after a bit flipping set is constructed, the times of the first error bit contained in the bit flipping set and the total error decoding times are recorded, and the probability of the first error bit in the bit flipping set is calculated according to the times of the first error bit contained in the bit flipping set and the total error decoding times.
In a preferred embodiment, the S200 includes:
s201, inputting a code length, a code rate, a signal-to-noise ratio and a corresponding LLR optimal threshold parameter;
s202, when the decoding is wrong, comparing the absolute value of the LLR value corresponding to the information bit with the input LLR optimal threshold value, and extracting the index of the information bit smaller than the optimal threshold value to construct an initial key set;
s203, defining an LLR value set, wherein elements in the LLR value set are absolute values of LLR values corresponding to indexes of information bits in the initial key set, and arranging the elements in the LLR value set in a descending order according to the magnitude of the values;
s204, constructing a change position index set, wherein elements in the set are the difference values between the position index of each element in the initial key set, which corresponds to the element in the initial key set, and the position index of the absolute value of the LLR value, which corresponds to the element in the initial key set, in the LLR value set;
s205, arranging the elements in the position index change set in a descending order to obtain a new change position index set, and adjusting the positions of the corresponding elements in the initial key set according to the position index of each element in the new change position index set to obtain a final key set.
In a preferred embodiment, the S202 includes: and if the serial offset decoding error occurs, comparing the corresponding LLR | value with the input optimal LLR threshold value in sequence from small to large according to the index of the information bit, and if the index of the information bit is smaller than the optimal threshold value, putting the index of the information bit into an initial key set.
In a preferred embodiment, in S204, the process of constructing the change position index set specifically includes: and subtracting the position index corresponding to the element in the initial key set in the step S202 from the new position index in the step S203 to obtain a change position index set.
The embodiment of the invention provides a bit flipping decoding device of a polarization code, which comprises:
the key set construction module is used for calculating LLR thresholds under different code rates and signal-to-noise ratios according to the same code length, selecting the maximum value of the LLR thresholds obtained under different code rates and signal-to-noise ratio combinations as the optimal threshold under the code length, and constructing a key set by using the optimal threshold;
and the element sorting adjusting module is used for adjusting the sorting of the elements in the key set by utilizing the relation between the decoding reliability of each element in the key set and the positions of the elements in the key set.
Compared with the prior art, the invention has the beneficial effects that:
1. the new key set construction method based on the LLR threshold value, provided by the invention, can find out the optimal LLR threshold value suitable for different code rates and signal-to-noise ratios under a specific code length by utilizing a large number of simulation experiments, and can effectively overcome the defects of high complexity, poor decoding and error correction performance under high code rate conditions and the like in the key set construction.
2. The relation between LLR sequencing and key set element positions is researched, sequencing of elements in a key set is further optimized, the average position of a first error bit is enabled to be more advanced under different code rates and signal-to-noise ratios, and the defects that the average additional decoding times of similar continuous offset bit flipping decoding algorithms are large, the frame error rate FER convergence rate is low and the practicability is poor are overcome.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flowchart of a bit flipping decoding method for a polar code according to an embodiment of the present invention;
FIG. 2 is a schematic view of the flow structure of step S100 according to an embodiment of the present invention;
fig. 3 is a schematic flow chart of step S200 according to an embodiment of the present invention.
Detailed Description
The present invention will be more fully understood from the following detailed description, which should be read in conjunction with the accompanying drawings. Detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention, which can be embodied in various forms. Therefore, specific functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention in virtually any appropriately detailed embodiment.
As shown in fig. 1, the bit flipping decoding method for polar code disclosed by the present invention mainly aims to solve the disadvantage of poor decoding performance under the condition of high code rate in the existing continuous cancellation bit flipping (SC-Flip) decoding algorithm, and has the advantages of low complexity and strong practicability. The method mainly comprises the following two steps:
s100, calculating LLR threshold values under different code rates and signal-to-noise ratios according to the same code length, selecting the maximum value of the LLR threshold values obtained under different code rate and signal-to-noise ratio combinations as the optimal threshold value under the code length, and constructing a key set by using the optimal threshold value.
The selection of the key set element directly influences whether the first error bit can be contained, the probability that the first error bit is contained in the key set is defined as accuracy, and when the accuracy is large enough, the first error bit can be corrected under an ideal condition through a certain number of bit inversions. Since most of the first error bits occur in a part of information bits in a concentrated manner, a reasonable LLR threshold value omega is selected to enable the generated key set to cover the error-prone information bits as much as possible, and therefore the performance of SC-Flip decoding can be effectively improved. The present invention mainly adopts a simulation experiment method to determine the LLR threshold, as shown in FIG. 2, the specific process includes:
s101, inputting a code length, a code rate and a signal-to-noise ratio parameter.
S102, setting an initial value and a step length of the temporary LLR threshold value and simulation times of SC decoding, and carrying out simulation of SC decoding.
In this embodiment, temp _ LLR _ Threshold is used to represent the LLR temporary Threshold, the initial value of temp _ LLR _ Threshold is set to 1, the step size is set to 1, and 5 × 10 is performed for the current value of temp _ LLR _ Threshold5And secondary SC decoding simulation.
When serial cancellation SC decoding errors occur, comparing the corresponding LLR | value with the current temp _ LLR _ Threshold in sequence from small to large according to the information bit index, and if the index is ikOf information bits of (2) | LLR | value
Satisfy the requirement of
Then the indexes of the information bits are sequentially put into the bit Flip bit _ Flip _ Set to construct a bit Flip Set bit _ Flip _ Set. Recording the first error bit contained in the set bit \uafter all simulation is finishedThe number of effective _ Err times and the number of error decoding frame _ Err times in the Flip _ Set.
S103, calculating the probability of the first error bit in the key set, and if the probability is greater than a set value, determining that the temporary threshold of the current LLR is a threshold T corresponding to the code rate and the signal-to-noise ratio under the current code length.
Specifically, the probability accuracy of the first error bit in the critical set is calculated according to the number of times effective _ Err that the first error bit is included in the critical set and the total error decoding number of times frame _ Err. In this embodiment, effective _ Err/frame _ Err. If the probability accuracy is greater than the set value, in this embodiment, the set value is 0.9999, that is, if accuracy > 0.9999, it is determined that the current temp _ LLR _ Threshold is the LLR Threshold T under the current condition, that is, the LLR Threshold T under the conditions of the current code length, the current code rate, and the signal-to-noise ratio is equal to temp _ LLR _ Threshold, and the process continues to step S104. If the accurve is smaller than or equal to the set value, returning to S102 after the temp _ LLR _ Threshold +1, and continuing SC decoding simulation until the calculated probability of the first error bit in the key set is greater than the set value.
And S104, under the same code length, calculating threshold values T corresponding to different code rates and signal-to-noise ratios according to the steps S101 to S103, counting the threshold values in a table, and selecting the maximum threshold value from the table as the optimal LLR threshold value corresponding to the code length.
To help understand, table one lists the LLR thresholds T for different code rates and snr conditions when N is 1024. The maximum value (R: 1/8, obtained when SNR is 1.0) in table one is selected as the optimum threshold value when N is 1024. The optimal threshold is used to construct the critical set under any code rate and signal-to-noise ratio condition when N is 1024.
When table N is 1024, the corresponding LLR threshold values under different code rates and signal-to-noise ratios
S200, adjusting the sequence of the elements in the key set by using the relationship between the decoding reliability of each element in the key set and the positions of the elements in the key set.
Specifically, the sorting of the key set elements directly relates to the average position average _ position of the first error bit in the key set, thereby affecting the average number of additional SC-Flip decoding. As shown in fig. 3, the process of the method for sorting key set elements of the present invention mainly includes:
s201, inputting a code length, a code rate, a signal-to-noise ratio and a corresponding LLR optimal threshold parameter;
s202, when the decoding is wrong, the absolute value (| LLR | value) of the LLR value corresponding to the information bit is compared with the input LLR optimal threshold value, and the index of the information bit smaller than the optimal threshold value is extracted to construct an initial key set.
Specifically, in this embodiment, if the serial cancellation decoding error occurs, the corresponding LLR | values are sequentially compared with Ω from small to large according to the information bit index, and if the information bit index is smaller than Ω, the information bit index is put into the initial key set, that is, if the index is ikThe information bit of (a) corresponds to the LLR value
If the index value is less than omega, the index value is sequentially listed in the initial key set init _ CS, and then the initial key set:
s203, defining an LLR value set LLR _ CS, wherein the elements in the LLR value set LLR _ CS are LLR | values corresponding to the indexes of the information bits in the initial key set init _ CS, and then the LLR value set LLR _ CS
A larger element value indicates a higher reliability. And arranging the constituent elements in the set LLR _ CS in a descending order manner to obtain a position index R ═ R of an LLR value set after the LLR value corresponding to each element in the initial key set init _ CS is ordered1,r2,...rk,...}；
S204, constructing a position index change set, wherein elements in the set are the difference values between the position index of each element in the initial key set, which corresponds to the element in the initial key set, and the position index of the corresponding LLR value in the LLR value set;
specifically, the new position index R in step S203 is used as { R ═ R1,r2,...rk,., subtracting the corresponding position index in the initial key set in step S202 from the index value corresponding to the corresponding element to obtain a change position index set, defining a change position index set as Δ, which indicates a position change in the LLR value set before and after each element in the LLR value set LLR _ CS is sorted, where Δ ═ r in this embodiment1-1,r2-2,...rk-k,rk+1K-1, a larger value indicates a higher probability of being erroneous.
S205, arranging the elements in the change position index set Δ in a descending order to obtain a new change position index set Δ 1, thereby obtaining a position index of each element in the change position index set Δ in the new change position index set Δ 1, and adjusting the position of the corresponding element in the initial key set init _ CS according to the position index of each element in the new change position index set to obtain a final key set final _ CS.
The method for performing traversal simulation on the LLR threshold value is suitable for SC-Flip decoding under the conditions of different code lengths, code rates and signal-to-noise ratios, and basically ensures that more than 99.99% of probability contains a first error element under the condition of minimum number of key set elements. In addition, the method for sorting the reliability of the key set elements is beneficial to quickly positioning the first error bit during decoding, reducing the additional decoding times and quickly converging the frame error rate FER to the lowest limit.
Corresponding to the above method, the present invention discloses a bit flipping decoding apparatus for polarization code, comprising:
and the key set construction module is used for calculating LLR thresholds under different code rates and signal-to-noise ratios according to the same code length, selecting the maximum value of the LLR thresholds obtained under different code rate and signal-to-noise ratio combinations as the optimal threshold under the code length, and constructing a key set by using the optimal threshold.
And the element sorting adjusting module is used for adjusting the sorting of the elements in the key set by utilizing the relation between the decoding reliability of each element in the key set and the positions of the elements in the key set.
The working flows of the key set building module and the element sorting adjustment module may refer to the above steps S100 and S200, respectively, which are not described herein again.
The aspects, embodiments, features and examples of the present invention should be considered as illustrative in all respects and not intended to be limiting of the invention, the scope of which is defined only by the claims. Other embodiments, modifications, and uses will be apparent to those skilled in the art without departing from the spirit and scope of the claimed invention.
Claims (10)
1. A bit flipping decoding method of polarization code is characterized in that: the method comprises the following steps:
s100, calculating thresholds of log-likelihood ratios under different code rates and signal-to-noise ratios according to the same code length, selecting the maximum value of LLR thresholds obtained under different code rate and signal-to-noise ratio combinations as the optimal threshold under the code length, and constructing a key set by using the optimal threshold;
s200, adjusting the sequence of the elements in the key set by using the relation between the decoding reliability of each element in the key set and the positions of the elements in the key set.
2. The bit flipping decoding method of polarization code according to claim 1, wherein: in S100, a simulation experiment method is used to determine the optimal threshold of the log-likelihood ratio.
3. The bit flipping decoding method of polarization code according to claim 1 or 2, wherein: the S100 includes:
s101, inputting code length, code rate and signal-to-noise ratio parameters;
s102, setting an initial value and a step length of the temporary LLR threshold value and simulation times of SC decoding, and simulating the SC decoding;
s103, calculating the probability of a first error bit in the key set, and if the probability is greater than a set value, determining that the temporary threshold of the current LLR is a threshold T corresponding to the code rate and the signal-to-noise ratio under the current code length;
and S104, under the same code length, calculating threshold values T corresponding to different code rates and signal-to-noise ratios according to the S101-S103, counting the threshold values in a table, and selecting a maximum threshold value from the table as an optimal LLR threshold value corresponding to the code length.
4. The bit flipping decoding method of polarization code according to claim 3, wherein: in S103, if the probability is less than or equal to the set value, the temporary threshold of the current LLR is added with 1 and then returned to S102 until the calculated probability of the first error bit in the key set is greater than the set value.
5. The bit flipping decoding method of polarization code according to claim 3, wherein: in S102, the process of constructing the bit flipping set includes:
and when the decoding is wrong, comparing the LLR value corresponding to the information bit index with the temporary LLR threshold value in sequence from small to large according to the information bit index, and if the LLR value is smaller than the temporary threshold value, putting the information bit index into a bit reversal set to construct the bit reversal set.
6. The bit flipping decoding method of polarization code according to claim 5, wherein: the step S103 of calculating the probability of the first error bit in the bit flipping set includes: after a bit flipping set is constructed, the times of the first error bit contained in the bit flipping set and the total error decoding times are recorded, and the probability of the first error bit in the bit flipping set is calculated according to the times of the first error bit contained in the bit flipping set and the total error decoding times.
7. The bit flipping decoding method of polarization code according to claim 1, wherein: the S200 includes:
s201, inputting a code length, a code rate, a signal-to-noise ratio and a corresponding LLR optimal threshold parameter;
s202, when the decoding is wrong, comparing the absolute value of the LLR value corresponding to the information bit with the input LLR optimal threshold value, and extracting the index of the information bit smaller than the optimal threshold value to construct an initial key set;
s203, defining an LLR value set, wherein elements in the LLR value set are absolute values of LLR values corresponding to indexes of information bits in the initial key set, and arranging the elements in the LLR value set in a descending order according to the magnitude of the values;
s204, constructing a change position index set, wherein elements in the set are the difference values between the position index of each element in the initial key set, which corresponds to the element in the initial key set, and the position index of the absolute value of the LLR value, which corresponds to the element in the initial key set, in the LLR value set;
s205, arranging the elements in the position index change set in a descending order to obtain a new change position index set, and adjusting the positions of the corresponding elements in the initial key set according to the position index of each element in the new change position index set to obtain a final key set.
8. The bit-flipping decoding method of polarization code according to claim 7, wherein: the S202 includes: and if the serial offset decoding error occurs, comparing the corresponding LLR | value with the input optimal LLR threshold value in sequence from small to large according to the index of the information bit, and if the index of the information bit is smaller than the optimal threshold value, putting the index of the information bit into an initial key set.
9. The bit flipping decoding method of polarization code according to claim 7, wherein: in S204, the process of constructing the change position index set specifically includes: and subtracting the position index corresponding to the element in the initial key set in the step S202 from the new position index in the step S203 to obtain a change position index set.
10. An apparatus for bit flipping decoding of a polarization code, the apparatus comprising:
the key set construction module is used for calculating LLR thresholds under different code rates and signal-to-noise ratios according to the same code length, selecting the maximum value of the LLR thresholds obtained under different code rates and signal-to-noise ratio combinations as the optimal threshold under the code length, and constructing a key set by using the optimal threshold;
and the element sorting adjusting module is used for adjusting the sorting of the elements in the key set by utilizing the relation between the decoding reliability of each element in the key set and the positions of the elements in the key set.
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