A bit flip decoding method and device for polarization code

Abstract

The present invention discloses a method and device for bit flip decoding of polar codes. The method comprises the following steps: for the same code length, determining the optimal threshold of the log-likelihood ratio applicable to different code rates and signal-to-noise ratios through experiments, constructing a key set according to the optimal threshold of the LLR; and adjusting the order of the elements in the key set by using the relationship between the decoding reliability of each element in the key set and the position of the element in the key set. The present invention provides a continuous offset bit flip decoding scheme suitable for practical applications, which has relatively balanced indicators such as frame error rate and decoding complexity under the conditions of specific code length, different code rates and signal-to-noise ratios.

Description

Technical Field

[0001] The present invention belongs to the technical field of polar code decoding schemes, and in particular relates to a polar code bit flip decoding method and device. Background Art

[0002] Polar Codes Polar Codes are the first coding scheme that can be rigorously proven to reach the channel capacity of a binary discrete memoryless channel (B-DMC). It has the advantages of a fixed construction method and low decoding complexity, and has been used as the control channel coding standard for 5G mobile communications.

[0003] The decoding scheme of polar codes has always been a hot topic in the research of polar codes. Serial cancellation (SC) decoding is the first decoding scheme for polar codes. When the code length tends to infinity, this decoding method can reach the channel capacity, but when the code length is finite, its decoding performance decreases. Therefore, SC decoding is not suitable for practical applications. In order to improve the decoding performance, E. Arikan proposed a belief propagation (BP) decoding scheme, which uses iterative calculation of the log-likelihood ratio of each node to achieve good decoding performance, but the decoding complexity is very high. I. Tal and A. Vardy proposed a serial cancellation list (SCL) decoding scheme, which improves the decoding performance by searching and retaining a certain number of candidate paths. This scheme improves the parallelism of decoding, but when the number of candidate paths is large, its decoding complexity and decoding delay are high. Subsequently, in order to improve the SCL decoding performance, a cyclic redundancy check SCL decoding scheme (CA-SCL) was proposed. The efficiency of selecting the correct candidate path was improved by adding a cyclic redundancy check. The serial cancellation stack (SCS) decoding and serial cancellation hybrid (SCH) (SCH) decoding schemes reduced the complexity of SCL decoding to varying degrees while ensuring the decoding accuracy. In addition, the Viterbi decoding, BCJR decoding, and sphere decoding schemes of polar codes can all achieve decoding performance close to the maximum likelihood, but the above decoding schemes are very complex and have poor decoding effects when the code length is long.

[0004] The proposal of the continuous cancellation bit flip (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 et al. proposed an SC-Flip scheme, which arranges the absolute values ​​of the log-likelihood ratio (LLR) of the information bits in ascending order, and then performs bit flip operations in sequence until the decoding is correct or the set maximum number of flips is reached. This scheme greatly improves the performance of SC decoding, but the number of additional decoding times is large for medium and high bit rates, and the decoding performance is poor. Carlo Condo et al. proposed the bit-flip decoding schemes of FIS (Fixed index selection) and EIS (Enhanced index selection), but both schemes are based on the key set of erroneous bits selected by simulation experiments, and the relative order of elements in the set is fixed, but the decoding performance of the scheme decreases with the increase of the bit rate; based on this scheme, Furkan Ercan et al. proposed a threshold-based SC-Flip decoding scheme, which proposed a universal key set for different signal-to-noise ratios and bit rates under the same code length, and determined the thresholds for different signal-to-noise ratios under the same bit rate. This method improves the decoding performance under high bit error rates, but the number of additional decoding times is relatively large under low bit rate conditions, resulting in a slow convergence speed of the frame error rate (FER); the scheme proposed a Fast-SSC-Flip decoding method, which reduces delays without sacrificing error correction performance, but greatly increases the implementation complexity of the decoder and is difficult to apply in practice.

[0005] In summary, a lot of research results have been achieved in the research on decoding schemes for polar codes. However, different decoding methods will have different performance indicators such as frame error rate, computational complexity and decoding delay under different conditions such as code length, code rate and signal-to-noise ratio.

[0006] How to provide a continuous offset bit flipping SC-Flip solution suitable for practical applications with relatively balanced indicators such as frame error rate and decoding complexity under different conditions is an urgent problem to be solved. Summary of the invention

[0007] The main purpose of the present invention is to provide a method and device for bit flipping decoding of polar codes, so as to overcome the shortcomings of the prior art.

[0008] To achieve the aforementioned invention objective, the technical solution adopted by the present invention includes: a bit flip decoding method of a polar code, comprising:

[0009] S100, for the same code length, calculating the threshold of the log likelihood ratio under different code rates and signal-to-noise ratio conditions, selecting the maximum value of the LLR thresholds obtained under different combinations of code rates and signal-to-noise ratios as the optimal threshold under the code length, and constructing a key set using the optimal threshold;

[0010] S200, adjusting the order of the elements in the key set by using the relationship between the decoding reliability of each element in the key set and the position of the element in the key set.

[0011] In a preferred embodiment, in S100, a simulation experiment method is used to determine the optimal threshold of the log-likelihood ratio.

[0012] In a preferred embodiment, the S100 includes:

[0013] S101, input code length, code rate and signal-to-noise ratio parameters;

[0014] S102, setting an initial value and a step size of the LLR temporary threshold, and the number of simulations of SC decoding, and performing simulation of SC decoding;

[0015] S103, calculating the probability of the first error bit in the key set, and if the probability is greater than a set value, confirming that the temporary threshold of the current LLR is the threshold T corresponding to the code rate and signal-to-noise ratio under the current code length;

[0016] S104, under the same code length, according to S101 to S103, calculate the thresholds T corresponding to different code rates and signal-to-noise ratios, and store them in a table, and select the maximum threshold from the table as the optimal LLR threshold corresponding to the code length.

[0017] 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 increased by 1 and the process returns to S102 until the calculated probability of the first error bit in the key set is greater than the set value.

[0018] In a preferred embodiment, in S102, the process of constructing a bit flip set includes:

[0019] When a decoding error occurs, the corresponding LLR value is compared with the LLR temporary threshold in order from small to large according to the information bit index. If it is less than the temporary threshold, the index of the information bit is put into the bit flip set to construct the bit flip set.

[0020] In a preferred embodiment, the S103, the process of calculating the probability of the first error bit in the bit flip set includes: after constructing the bit flip set, recording the number of times the first error bit is included in the bit flip set and the total number of error decodings, and calculating the probability of the first error bit in the bit flip set based on the number of times the first error bit is included in the bit flip set and the total number of error decodings.

[0021] In a preferred embodiment, the S200 includes:

[0022] S201, input code length, code rate, signal-to-noise ratio and corresponding LLR optimal threshold parameters;

[0023] S202, when a decoding error occurs, the absolute 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;

[0024] S203, defining an LLR value set, wherein the elements in the LLR value set are absolute values ​​of the LLR values ​​corresponding to the indexes of the information bits in the initial key set, and arranging the constituent elements in the LLR value set in descending order according to the magnitude of the values;

[0025] S204, constructing a change position index set, where the elements in the set are the difference between the position index corresponding to each element in the initial key set in the initial key set and the position index of the absolute value of the corresponding LLR value in the LLR value set;

[0026] S205, arranging the elements in the position index change set in descending order to obtain a new change position index set, adjusting the position of the corresponding element 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.

[0027] In a preferred embodiment, S202 includes: if a serial cancellation decoding error occurs, then the corresponding |LLR| value is compared with the input optimal LLR threshold in order from small to large according to the information bit index. If it is less than the optimal threshold, the index of the information bit is placed in the initial key set.

[0028] In a preferred embodiment, in S204, the process of constructing the changed position index set specifically includes: subtracting the position index corresponding to the corresponding element in the initial key set in S202 from the new position index in step S203 to obtain the changed position index set.

[0029] An embodiment of the present invention provides a bit flip decoding device for a polar code, including:

[0030] A key set construction module is used to calculate the LLR thresholds under different code rates and signal-to-noise ratio conditions for the same code length, select 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 use the optimal threshold to construct a key set;

[0031] The element sorting adjustment module is used to adjust the sorting of the elements in the key set by utilizing the relationship between the decoding reliability of each element in the key set and the position of the element in the key set.

[0032] Compared with the prior art, the beneficial effects of the present invention are at least:

[0033] 1. The present invention proposes a new key set construction method based on LLR threshold, which uses a large number of simulation experiments to find the optimal LLR threshold suitable for different code rates and signal-to-noise ratios under a specific code length, and can effectively solve the shortcomings of high complexity in key set construction and poor decoding error correction performance under high code rate conditions.

[0034] 2. This paper studies the relationship between LLR sorting and the position of key set elements, further optimizes the sorting of elements in the key set, and ensures that the average position of the first error bit is closer under different bit rates and signal-to-noise ratios, solving the shortcomings of similar continuous offset bit flipping decoding algorithms, such as large average additional decoding times, slow convergence speed of frame error rate FER, and poor practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0036] Figure 1 It is a schematic flow chart of a bit flip decoding method of a polar code in one embodiment of the present invention;

[0037] Figure 2 is a schematic diagram of the flow structure of step S100 in one embodiment of the present invention;

[0038] Figure 3 It is a schematic diagram of the flow structure of step S200 in one embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention will be more fully understood through 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 should be understood that the disclosed embodiments are only exemplary of the present invention, which can be embodied in various forms. Therefore, the specific functional details disclosed herein should not be interpreted as limiting, but only as the basis of the claims and as a representative basis for teaching those skilled in the art to adopt the present invention in different ways in virtually any appropriate detailed embodiment.

[0040] like Figure 1 As shown, the present invention discloses a polar code bit flip decoding method, the main purpose of which is to solve the disadvantage of poor decoding performance under high code rate conditions in the existing continuous cancellation bit flip (SC-Flip) decoding algorithm, and at the same time has the advantages of low complexity and strong practicality. The method mainly includes the following two steps:

[0041] S100, for the same code length, calculate the LLR thresholds under different code rates and signal-to-noise ratio conditions, select 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 use the optimal threshold to construct a key set.

[0042] Among them, the selection of key set elements directly affects whether the first error bit can be included in it. The probability that the first error bit is included in the key set is defined as accuracy. When the accuracy is large enough, the first error bit can be corrected under ideal conditions after a certain number of bit flips. Since most of the first error bits occur in a part of the information bits, a reasonable LLR threshold Ω is selected to make the generated key set cover the error-prone information bits as much as possible, which can effectively improve the performance of SC-Flip decoding. The present invention mainly uses the simulation experiment method to determine the LLR threshold, such as Figure 2 As shown, the specific process includes:

[0043] S101, input code length, code rate and signal-to-noise ratio parameters.

[0044] S102, setting the initial value and step size of the LLR temporary threshold, and the number of simulations of SC decoding, and performing simulation of SC decoding.

[0045] In this embodiment, temp_LLR_Threshold is used to represent the temporary LLR threshold. The initial value of temp_LLR_Threshold is set to 1, the step size is 1, and 5×10 5 Second SC decoding simulation.

[0046] When serially canceling SC decoding errors, the corresponding |LLR| values ​​are compared with the current temp_LLR_Threshold in ascending order according to the information bit index. If the index is i k The |LLR| value of the information bit satisfy Then the index of the information bit is sequentially put into the bit flip bit_Flip_Set to construct the bit flip set bit_Flip_Set. After all simulations are completed, the number of times the first error bit is included in the set bit_Flip_Set effective_Err and the number of error decoding frame_Err are recorded.

[0047] S103, calculating the probability of the first error bit in the key set, if the probability is greater than the set value, confirming that the temporary threshold of the current LLR is the threshold T corresponding to the code rate and signal-to-noise ratio under the current code length.

[0048] Specifically, the probability accuracy of the first error bit in the key set is calculated based on the number of times effective_Err that the first error bit is included in the key set and the total number of error decodings frame_Err. In this embodiment, accuracy = 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, confirm that the current temp_LLR_Threshold is the LLR threshold T under the current conditions, that is, let the LLR threshold T under the current code length, code rate and signal-to-noise ratio conditions = temp_LLR_Threshold, and continue to enter step S104. If accuracy is less than or equal to the set value, then set temp_LLR_Threshold = temp_LLR_Threshold+1 and return to S102, and continue to perform SC decoding simulation until the calculated probability of the first error bit in the key set is greater than the set value.

[0049] S104, under the same code length, according to S101 to S103 above, calculate the thresholds T corresponding to different code rates and signal-to-noise ratios, and store them in a table, and select the maximum threshold from the table as the optimal LLR threshold corresponding to the code length.

[0050] To help understand, Table 1 lists the LLR thresholds T corresponding to different bit rates and signal-to-noise ratios when N = 1024. The maximum value in Table 1 (obtained when R = 1 / 8, SNR = 1.0) is selected as the optimal threshold when N = 1024. When N = 1024, the optimal threshold is used to construct the key set under any bit rate and signal-to-noise ratio conditions.

[0051] Table 1 LLR thresholds corresponding to different bit rates and signal-to-noise ratios when N=1024

[0052]

[0053] S200, adjusting the order of the elements in the key set by using the relationship between the decoding reliability of each element in the key set and the position of the element in the key set.

[0054] Specifically, the order of the key set elements is directly related to the average position average_position of the first error bit in the key set, which in turn affects the average number of SC-Flip additional decoding. Figure 3 As shown, the process of the key set element sorting method of the present invention mainly includes:

[0055] S201, input code length, code rate, signal-to-noise ratio and corresponding LLR optimal threshold parameters;

[0056] S202, when a decoding error occurs, the absolute value of the LLR value corresponding to the information bit (|LLR| value) is compared with the input LLR optimal threshold value, and the index of the information bit smaller than the optimal threshold is extracted to construct an initial key set.

[0057] Specifically, in this embodiment, if a serial offset decoding error occurs, the corresponding |LLR| value is compared with Ω in order from small to large according to the information bit index. If it is less than Ω, the index of the information bit is put into the initial key set, that is, if the index is i k The information bit corresponding to the |LLR| value If it is less than Ω, the index value is sequentially included in the initial key set init_CS, then the initial key set:

[0058]

[0059] S203, define an LLR value set LLR_CS, where the elements in the LLR value set LLR_CS are the |LLR| values ​​corresponding to the indexes of the information bits in the initial key set init_CS. The larger the element value, the higher the reliability. Arrange the constituent elements in the set LLR_CS in descending order to obtain the position index R of the sorted LLR value set corresponding to each element in the initial key set init_CS = {r1, r2, ...r k ,...};

[0060] S204, constructing a position index change set, where the elements in the set are the differences between the position index corresponding to each element in the initial key set in the initial key set and the position index of its corresponding |LLR| value in the LLR value set;

[0061] Specifically, the new position index R in step S203 is used as R={r1, r2, ... r k ,...} minus the position index corresponding to the index value corresponding to the corresponding element in the initial key set in step S202 to obtain a change position index set, and define the change position index set as Δ, which represents the position change of each element in the LLR value set LLR_CS before and after sorting in the LLR value set. In this embodiment, Δ={r1-1,r2-2,...r k -k,r k+1 -k-1,...}, the larger the value, the greater the probability of error.

[0062] S205, arrange the elements in the change position index set Δ in descending order to obtain a new change position index set Δ1, thereby obtaining the position index of each element in the change position index set Δ in the new change position index set Δ1, and adjust 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 the final key set final_CS.

[0063] The method of traversal simulation for LLR threshold proposed in this paper is applicable to SC-Flip decoding under different code lengths, code rates and signal-to-noise ratios. This method basically ensures that the probability of including the first error element is more than 99.99% when the number of key set elements is minimized. In addition, the method of reliability sorting of key set elements proposed in this invention helps to quickly locate the first error bit during decoding, reduce the number of additional decoding times, and quickly converge the frame error rate FER to the minimum limit.

[0064] Corresponding to the above method, a bit flip decoding device of a polar code disclosed in the present invention includes:

[0065] The key set construction module is used to calculate the LLR thresholds under different code rates and signal-to-noise ratio conditions for the same code length, select 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 use the optimal threshold to construct the key set.

[0066] The element sorting adjustment module is used to adjust the sorting of the elements in the key set by utilizing the relationship between the decoding reliability of each element in the key set and the position of the element in the key set.

[0067] The workflows of the key set building module and the element sorting adjustment module may refer to the above steps S100 and S200 respectively, and will not be described in detail here.

[0068] The various aspects, embodiments, features and examples of the present invention should be considered as illustrative in all aspects and are not intended to limit the present invention, the scope of the present invention 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

1. A bit flip decoding method for polar codes, characterized in that: The method comprises: S100, for the same code length, calculating the threshold of the log likelihood ratio under different code rates and signal-to-noise ratio conditions, selecting the maximum value of the LLR thresholds obtained under different combinations of code rates and signal-to-noise ratios as the optimal threshold under the code length, and constructing a key set using the optimal threshold; S200, adjusting the order of the elements in the key set by using the relationship between the decoding reliability of each element in the key set and the position of the element in the key set; Wherein, the S200 includes: S201, input code length, code rate, signal-to-noise ratio and corresponding LLR optimal threshold parameters; S202, when a decoding error occurs, the absolute 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; S203, defining an LLR value set, wherein the elements in the LLR value set are absolute values ​​of the LLR values ​​corresponding to the indexes of the information bits in the initial key set, and arranging the constituent elements in the LLR value set in descending order according to the magnitude of the values; S204, constructing a change position index set, where the elements in the set are the difference between the position index corresponding to each element in the initial key set in the initial key set and the position index of the absolute value of the corresponding LLR value in the LLR value set; S205, arranging the elements in the position index change set in descending order to obtain a new change position index set, adjusting the position of the corresponding element 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.

2. The bit flipping decoding method of polar code according to claim 1, characterized in that: 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 polar code according to claim 1 or 2, characterized in that: The S100 includes: S101, input code length, code rate and signal-to-noise ratio parameters; S102, setting an initial value and a step size of the LLR temporary threshold, and the number of simulations of SC decoding, and performing simulation of 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, confirming that the temporary threshold of the current LLR is the threshold T corresponding to the code rate and signal-to-noise ratio under the current code length; S104, under the same code length, according to S101 to S103, calculate the thresholds T corresponding to different code rates and signal-to-noise ratios, and count them in a table, and select the maximum threshold from the table as the optimal LLR threshold corresponding to the code length.

4. The bit flipping decoding method of polar code according to claim 3, characterized in that: In S103, if the probability is less than or equal to the set value, the temporary threshold of the current LLR is increased by 1 and the process returns 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 polar code according to claim 3, characterized in that: In S102, the process of constructing a bit flip set includes: When a decoding error occurs, the corresponding LLR value is compared with the LLR temporary threshold in order from small to large according to the information bit index. If it is less than the temporary threshold, the index of the information bit is put into the bit flip set to construct the bit flip set.

6. The bit-flipping decoding method of polar code according to claim 5, characterized in that: The S103, the process of calculating the probability of the first error bit in the bit flip set includes: after constructing the bit flip set, recording the number of times the first error bit is included in the bit flip set and the total number of error decodings, and calculating the probability of the first error bit in the bit flip set based on the number of times the first error bit is included in the bit flip set and the total number of error decodings.

7. The bit-flipping decoding method of polar code according to claim 1, characterized in that: The S202 includes: if a serial cancellation decoding error occurs, then comparing the corresponding |LLR| values ​​with the input optimal LLR threshold in order from small to large according to the information bit index, and if it is less than the optimal threshold, putting the index of the information bit into the initial key set.

8. The bit flipping decoding method of polar code according to claim 1, characterized in that: In S204, the process of constructing the changed position index set specifically includes: subtracting the position index corresponding to the corresponding element in the initial key set in S202 from the new position index in step S203 to obtain the changed position index set.

9. A bit flip decoding device for polar code, characterized in that: The device comprises: A key set construction module is used to calculate the LLR thresholds under different code rates and signal-to-noise ratio conditions for the same code length, select 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 use the optimal threshold to construct a key set; An element sorting adjustment module, used to adjust the sorting of the elements in the key set by using the relationship between the decoding reliability of each element in the key set and the position of the element in the key set; Among them, the method of adjusting the element sorting is: S201, input code length, code rate, signal-to-noise ratio and corresponding LLR optimal threshold parameters; S202, when a decoding error occurs, the absolute 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; S203, defining an LLR value set, wherein the elements in the LLR value set are absolute values ​​of the LLR values ​​corresponding to the indexes of the information bits in the initial key set, and arranging the constituent elements in the LLR value set in descending order according to the magnitude of the values; S204, constructing a change position index set, where the elements in the set are the difference between the position index corresponding to each element in the initial key set in the initial key set and the position index of the absolute value of the corresponding LLR value in the LLR value set; S205, arranging the elements in the position index change set in descending order to obtain a new change position index set, adjusting the position of the corresponding element 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.

Images