PAC code decoding method based on path splitting times

Abstract

The invention discloses a PAC code decoding method based on path splitting times, and belongs to the field of wireless communication channel coding. The method comprises the following steps: acquiring an output value corresponding to a bit to be decoded from a channel, and initializing a current decoding bit index; judging whether the current decoding bit index is in an index set or not, if so, traversing the to-be-selected path list, and performing convolution transformation, path metric value calculation and partial sum value calculation on each path, otherwise, executing to-be-selected path list expansion operation; and outputting the most front path in the to-be-selected path list as a decoding result, and ending the decoding. According to the invention, the decoding performance of the PAC code can be effectively improved, and the decoding time delay is reduced.

Description

Technical Field

[0001] The invention relates to the field of wireless communication channel coding, and in particular to a PAC code decoding method based on the number of path splitting times. Background Art

[0002] With the rapid development of the field of wireless communications, the future 6G application scenarios will usher in a transformation from unified services to personalized services, and the types and number of communication instructions will usher in a blowout growth. In order to cope with this new transformation, the new communication standard improves the overall wireless communication service capabilities by processing control signaling and data channels separately. At present, Polar codes are used as the coding method for control channels in communication standards. Since the coding process of Polar codes makes full use of channel characteristics, it also makes it a coding method that can reach the Shannon limit in theory. After proposing Polar codes, Professor Arikan proposed a polarization adjusted convolutional code (PAC) in 2019 to further improve Polar codes. Since polarization transformation is added in the convolutional coding process, PAC codes have the potential to further improve performance in actual channels.

[0003] At present, there are many decoding methods for PAC codes, such as BP decoding, sequence decoding, maximum likelihood decoding, list decoding, etc., and there is no consensus. Therefore, it is necessary to comprehensively consider decoding performance and decoding complexity and propose a decoding method suitable for PAC codes. Summary of the invention

[0004] In view of this, the present invention proposes a PAC code decoding method based on the number of path splitting times. The present invention can reduce the decoding complexity of the PAC code and improve the performance of the PAC code when the PAC code is used as the control channel coding mode in the control channel coding.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A PAC code decoding method based on the number of path splitting times is used to decode N bits to be decoded, wherein an index set A of information bits, a generating polynomial g, and a list of candidate paths Π are known before decoding, and there is only one path in Π when decoding starts; the method comprises the following steps:

[0007] Step 1: Get the output value corresponding to N bits to be decoded from the channel Initialize the current decoding bit index t=1;

[0008] Step 2, determine whether the current decoded bit index t is in the index set A, if so, go to step 3, otherwise go to step 4;

[0009] Step 3, traverse the list of candidate paths ∏, perform convolution transformation, path metric calculation and partial sum calculation on each path, and then go to step 5;

[0010] Step 4, perform the operation of expanding the list of candidate paths; if the size of the obtained list of candidate paths is larger than the set value L, sort the paths in the list of candidate paths ∏ according to the number of consecutive non-splits and the path metric value, and retain the L paths with the smallest path metric value;

[0011] Step 5, determine whether the current decoding bit index t is equal to N. If so, output the path ranked first in the candidate path list Π as the decoding result, and the decoding ends. Otherwise, t=t+1, return to step 2.

[0012] Furthermore, the specific method of the convolution transformation described in step 3 is: the value v of the current decoded bit is t , the state S at position t in the current path, and the generator polynomial g as the convolution transformation input, by v t Convolve with the generating polynomial g to obtain the convolution result u of the Pith path at position t t [Pi], and get the new state of position t in the current path:

[0013] S t [Pi]=v t +S t-1 [1,...,|g|-2],

[0014] Among them, |g| is the number of coefficients of the generating polynomial g, S t-1 [1,...,|g|-2] represents the state at position t-1. When t=1, S0 is the initial state with a specified bit width of |g|-2.

[0015] Furthermore, the specific method of calculating the path metric value described in step 3 is:

[0016]

[0017] Among them, M t [Pi] represents the path metric value of the Pi-th decoding path at position t; represents the information bit u at position t in the Pi-th decoding path t The predicted value of Represents the output value corresponding to the bit at position t obtained from the channel. When the state S at position t-1 t-1 and the state S at position t t When there is no connection between them, the path metric is infinite.

[0018] Furthermore, the specific method of the operation of expanding the list of candidate paths described in step 4 is:

[0019] For the current information bit u t , perform path splitting or hard decision operation according to the following result:

[0020]

[0021] in, [is the information bit u t The predicted value, L Pi (u t ) represents the information bit u in the Pith path t The corresponding log-likelihood ratio, is the bit u at position t t The probability of error decoding, E(L(u t )) is N L(u t ), split represents the split operation;

[0022] After making a decision on the information bit, if no splitting operation is performed, the number of consecutive non-splitting times W will be l The number of is increased by 1.

[0023] Furthermore, in step 4, the paths in the candidate path list Π are sorted according to the number of consecutive non-split times and the path metric value, specifically in the following manner:

[0024] Use the number of consecutive non-splits W l As the first sorting factor, the path metric value is used as the second sorting factor. In the sorting result, W l The larger ones with smaller path metrics are ranked first.

[0025] By adopting the above technical solution, the present invention has the following beneficial effects:

[0026] 1. In the PAC decoding algorithm process adopted by the present invention, a specific splitting condition is introduced for the information node to be decoded of the PAC code, which can find a decoding path with a smaller path metric more quickly, save decoding time, thereby reducing the PAC code decoding delay and improving the PAC code decoding speed.

[0027] 2. In the process of adopting the SCL decoding algorithm for PAC code, the present invention introduces the statistics of the number of consecutive unsplit times for a single decoding path and the double-factor sorting path deletion method, and uses the statistics of the number of consecutive unsplit times as the first sorting factor for the final decoding path selection, which can effectively improve the decoding performance of the information node and thus improve the decoding efficiency of the PAC code. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of the present invention.

[0029] Figure 2 The figure is a comparison chart of decoding frame error rate between the method of the present invention and the classic decoding algorithm. DETAILED DESCRIPTION

[0030] In order to clearly illustrate the technical features of the present solution, the present invention is described in detail below through specific implementation methods and in conjunction with the accompanying drawings.

[0031] A PAC code decoding method based on the number of path splittings, the method calculates the probability of erroneous decoding of a bit sequence to be decoded obtained from a Gaussian white noise channel as a condition for determining whether a node is split during the decoding process; records the number of consecutive non-splits of each selected decoding path as an important criterion for determining the decoding result; calculates the path metric value of the path according to the current position state and the next position state of the decoding path; and finally, when selecting a decoding path, uses the number of consecutive non-splits of the decoding path and the path metric value for double sorting to obtain the best decoding path.

[0032] The method is used to decode N bits to be decoded formed after the source data encoded by the PAC polarization adjustment convolution code passes through a Gaussian white noise channel. Before decoding, the index set A of the information bits, the convolution generating polynomial g, and the list of candidate paths Π are known. When decoding starts, there is only one path in Π.

[0033] Figure 1 The decoding process starts from the decoding bit position, and the method specifically includes the following steps:

[0034] Step 1: Get the output value corresponding to N bits to be decoded from the channel Initialize the current decoding bit index t=1;

[0035] Step 2, determine whether the current decoded bit index t is in the index set A, if so, go to step 3, otherwise go to step 4; the information bit index set A is determined by the channel reliability ranking, and the specific channel reliability measurement indicators include Bhattacharyya parameter, Gaussian approximation, density evolution and other methods. Among them, Bhattacharyya parameter is used as an evaluation criterion for sub-channel reliability. It uses maximum likelihood judgment to obtain the upper limit of the error probability of each sub-channel. This evaluation criterion is also commonly used in Gaussian channels.

[0036] Step 3, traverse the list of candidate paths Π, perform convolution transformation, path metric calculation and partial sum calculation on each path, and then go to step 5; the specific method of convolution transformation is:

[0037] Set the value of the current decoded bit v t , the state S at position t in the current path, and the generator polynomial g as the convolution transformation input, by v t Convolve with the generating polynomial g to obtain the convolution result u of the Pith path at position t t[Pi], and get the new state of position t in the current path:

[0038] S t [Pi]=v t +S t-1 [1,...,|g|-2],

[0039] Among them, |g| is the number of coefficients of the generating polynomial g, S t-1 [1,...,|g|-2] represents the state at position t-1. When t=1, S0 is the initial state with a specified bit width of |g|-2.

[0040] State S is set before decoding, and the transition conditions between states are also pre-designed. The more mature state transition diagram is the state transition diagram for convolutional codes in the Viterbi decoding algorithm, which can effectively determine the conversion relationship between the decoded bits and the bits to be decoded during the sequential decoding process, and can make the decoding process go more smoothly.

[0041] The specific method of calculating the path metric value is as follows:

[0042]

[0043] Among them, M t [Pi] represents the path metric value of the Pi-th decoding path at position t; represents the information bit u at position t in the Pi-th decoding path t The predicted value of is calculated as shown in step 4; Represents the output value corresponding to the bit at position t obtained from the channel. When the state S at position t-1 t-1 and the state S at position t t When there is no connection between them, the path metric is infinite, which means that the current decoding path is blocked and the current path can be deleted from the candidate paths for decoding. Due to the pre-setting of the state transition diagram, some paths can be excluded in time during the decoding process, thereby speeding up the decoding process and saving decoding time.

[0044] The partial sum calculation method of this step is the same as that of the SC decoding proposed by Arikan.

[0045] Step 4: Expand the list of candidate paths.

[0046] For the current information bit u t , perform path splitting or hard decision operation according to the following result:

[0047]

[0048] in, [is the information bit ut The predicted value, L Pi (u t ) represents the information bit u in the Pith path t The corresponding log-likelihood ratio, the calculation method of the log-likelihood ratio is the same as the iterative calculation method in the SC decoding process proposed by Arikan, is the bit u at position t t The probability of error decoding, E(L(u t )) is N L(u t ), split represents the split operation;

[0049] After making a decision on the information bit, if no splitting operation is performed, the number of consecutive non-splitting times W will be l The number of is increased by 1.

[0050] Here, an explicit formula P is given for whether the information bit is split or not. e (u t ) calculation, which represents the information bit u t The probability of mistranslation is 1-P e (u t ) represents the probability of correct decoding, which is equivalent to having prior decoding knowledge of the codeword after polarization transformation before decoding the PAC code, and P can be calculated in advance before decoding. e (u t ), so that many unnecessary decoding splitting steps can be saved, and when not splitting, it means that the current decision result is the correct decoding with the highest probability, and as the number of consecutive non-splitting increases, in the decoding process of the PAC code, as the reliability of the split channel increases, the correct decoding path will choose to continue not splitting to obtain the correct decoding result, and finally form a benign decoding, with the greatest possibility of obtaining the correct decoding result.

[0051] If the size of the candidate path list is larger than the set value L, the paths in the candidate path list ∏ are sorted according to the number of consecutive non-splits and the path metric value, and the L paths with the smallest path metric value are retained. The specific sorting method is:

[0052] Use the number of consecutive non-splits W l As the first sorting factor, the path metric value is used as the second sorting factor. In the sorting result, W l The larger ones with smaller path metrics are ranked first.

[0053] Two sorting factors are used when sorting the decoding path list, and the condition of the number of consecutive non-split times is introduced. Compared with the existing decoding method, the decoding result obtained in this way can be closer to the correct decoding result. Although a certain amount of computing resource consumption is introduced, it is completely acceptable for the sorting of the number of split times.

[0054] Step 5, determine whether the current decoding bit index t is equal to N. If so, output the first path in the candidate path list Π as the decoding result, and the decoding ends. Otherwise, t=t+1, return to step 2.

[0055] Figure 2 The frame error rate comparison between this method and two other typical decoding strategies is shown.

[0056] In summary, the present invention adopts a PAC code decoding method based on the number of path splitting times, which can effectively improve the decoding performance of the PAC code, reduce the decoding delay, and provide a new decoding idea for polarization adjustment convolutional codes.

Claims

1. A PAC code decoding method based on the number of path splitting times, characterized in that: Used to decode N bits to be decoded, with an index set A of known information bits before decoding, a generating polynomial g, a list of candidate paths Π, and only one path in Π when decoding starts; comprising the following steps: Step 1: Get the output value corresponding to N bits to be decoded from the channel Initialize the current decoding bit index t=1; Step 2, determine whether the current decoded bit index t is in the index set A, if so, go to step 3, otherwise go to step 4; Step 3, traverse the candidate path list Π, perform convolution transformation, path metric value calculation and partial sum value calculation on each path, and then go to step 5; Step 4, perform the expansion operation of the candidate path list; if the size of the obtained candidate path list is greater than the set value L, sort the paths in the candidate path list Π according to the number of consecutive non-splits and the path metric value, and retain L paths with the smallest path metric values; Step 5, determine whether the current decoding bit index t is equal to N. If so, output the first path in the candidate path list Π as the decoding result, and the decoding ends. Otherwise, t=t+1, return to step 2.

2. A PAC code decoding method based on the number of path splitting times according to claim 1, characterized in that: The specific method of the convolution transformation described in step 3 is: the value v of the current decoded bit t , the state S at position t in the current path, and the generator polynomial g as the convolution transformation input, by v t Convolve with the generating polynomial g to obtain the convolution result u of the Pith path at position t t [Pi], and get the new state of position t in the current path: S t [Pi]=v t +S t-1 [1,...,|g|-2] Among them, |g| is the number of coefficients of the generating polynomial g, S t-1 [1,...,|g|-2] represents the state at position t-1. When t=1, S0 is the initial state with a specified bit width of |g|-2.

3. A PAC code decoding method based on the number of path splitting times according to claim 1, characterized in that: The specific method of calculating the path metric value described in step 3 is: Among them, M t [Pi] represents the path metric value of the Pi-th decoding path at position t; represents the information bit u at position t in the Pi-th decoding path t The predicted value of Represents the output value corresponding to the bit at position t obtained from the channel. When the state S at position t-1 t-1 and the state S at position t t When there is no connection between them, the path metric is infinite.

4. A PAC code decoding method based on the number of path splitting times according to claim 1, characterized in that: The specific method of expanding the candidate path list described in step 4 is: For the current information bit u t , perform path splitting or hard decision operation according to the following result: in, [is the information bit u t The predicted value, L Pi (u t ) represents the information bit u in the Pith path t The corresponding log-likelihood ratio, is the bit u at position t t The probability of error decoding, E(L(u t )) is N L(u t ), split represents the split operation; After making a decision on the information bit, if no splitting operation is performed, the number of consecutive non-splitting times W will be l The number of is increased by 1.

5. A PAC code decoding method based on the number of path splitting times according to claim 4, characterized in that: In step 4, the paths in the candidate path list Π are sorted according to the number of consecutive non-split times and the path metric value, and the specific method is as follows: Use the number of consecutive non-splits W l As the first sorting factor, the path metric value is used as the second sorting factor. In the sorting result, W l The larger ones with smaller path metrics are ranked first.

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