PAC code decoding method based on path split times
By introducing a dual sorting mechanism of path split count and path metric, the PAC code decoding process is optimized, solving the problem of unbalanced decoding performance and complexity, and achieving faster decoding speed and higher decoding efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- THE 54TH RESEARCH INSTITUTE OF CHINA ELECTRONICS TECHNOLOGY GROUP CORPORATION
- Filing Date
- 2024-11-11
- Publication Date
- 2026-06-02
AI Technical Summary
Existing PAC code decoding methods struggle to balance decoding performance and complexity, lacking an effective method that comprehensively considers both.
A PAC code decoding method based on the number of path splits is adopted. By introducing a dual sorting mechanism of consecutive non-splitting counts and path metric values, the decoding process is optimized, decoding latency is reduced, and decoding efficiency is improved.
This method can find decoding paths with smaller path metrics more quickly, reduce decoding time, improve the decoding speed and efficiency of PAC codes, and enhance decoding performance.
Smart Images
Figure CN119766253B_ABST
Abstract
Description
Technical Field
[0001] This 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 splits. Background Technology
[0002] With the rapid development of wireless communication, future 6G applications are shifting from unified services to personalized services, leading to an explosive growth in the types and number of communication commands. To address this shift, new communication standards are improving overall wireless communication service capabilities by separating control signaling and data channels. Currently, Polar codes are used as the encoding method for control channels. Because Polar codes fully utilize channel characteristics, they are theoretically capable of reaching the Shannon limit. Following the introduction of Polar codes, Professor Arikan further improved upon them in 2019 with a Polar Adjusted Convolutional Code (PAC). By incorporating polarization transformations during convolutional coding, PAC codes have the potential to further enhance performance in real-world channels.
[0003] Currently, decoding methods for PAC codes include BP decoding, sequence decoding, maximum likelihood decoding, and list decoding, but there is no consensus. Therefore, it is necessary to comprehensively consider decoding performance and decoding complexity to propose a suitable decoding method 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 splits. This invention can reduce the decoding complexity and improve the performance of PAC codes when using PAC codes as the control channel coding method.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] A PAC code decoding method based on the number of path splits is used to decode N bits to be decoded. Before decoding, the method provides a set A of known information bit indices, a generator polynomial g, and a list Π of candidate paths. At the start of decoding, Π contains only one path. The method includes the following steps:
[0007] Step 1: Obtain the output values corresponding to the N bits to be decoded from the channel. Initialize the current decoded bit index t = 1;
[0008] Step 2: Determine whether the current decoded bit index t is in the index set A. If yes, proceed to step 3; otherwise, proceed to step 4.
[0009] Step 3: Traverse the candidate path list ∏, perform convolution transformation, path metric calculation and partial sum calculation for each path, and then proceed to step 5;
[0010] Step 4: Perform the candidate path list expansion operation; if the size of the resulting candidate path list is greater than the set value L, sort the paths in the candidate path list ∏ according to the number of consecutive non-splits and the path metric value, and retain the L paths with the smallest path metric values.
[0011] Step 5: Determine if the current decoding bit index t is equal to N. If it is, output the first path in the candidate path list ∏ as the decoding result and the decoding ends. Otherwise, t = t + 1 and return to step 2.
[0012] Furthermore, the specific method of the convolution transformation described in step 3 is as follows: 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 are used as inputs to the convolution transformation, and v t Convolving with the generator polynomial g yields the convolution result u of the Pi-th path at position t. t [Pi], and simultaneously obtain the new state at position t in the current path:
[0013] S t [Pi] = v t +S t-1 [1,...,|g|-2],
[0014] Where |g| is the number of coefficients of the generator polynomial g, and 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 for calculating the path metric value in step 3 is as follows:
[0016]
[0017] Among them, M t [Pi] represents the path metric value of the Pi-th decoding path at position t; This represents the information bit u at position t in the Pi-th decoding path. t The predicted value; This 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 are no connections between them, the path metric is infinite.
[0018] Furthermore, the specific method for expanding the candidate path list in step 4 is as follows:
[0019] For the current information bit u t Perform a path split or hard decision operation based on the result of the following formula:
[0020]
[0021] in, [This refers to information bits u] t The predicted value, L Pi (u t ) represents the information bit u in the Pi-th path. t The corresponding log-likelihood ratio, For bit u at position t t The probability of incorrect decoding, E(L(u) t )) is N L(u t The mathematical expectation of ), where split represents the splitting operation;
[0022] After making a decision on the information bits, if no splitting operation is performed, the number of consecutive non-split counts W will be recorded. l Add 1 to the quantity.
[0023] Furthermore, in step 4, the paths in the candidate path list Π are sorted according to the number of consecutive non-splits and the path metric, specifically as follows:
[0024] Using the number of consecutive non-splits W l The path metric is used as the first ranking factor, and the W value is used as the second ranking factor in the ranking results. l Larger ones with smaller path metrics are ranked higher.
[0025] By adopting the above technical solutions, the present invention has the following beneficial effects:
[0026] 1. In the PAC decoding algorithm process adopted in this invention, a specific splitting condition is introduced for the PAC code information node to be decoded, which can find the decoding path with smaller path metric more quickly, save decoding time, thereby reducing PAC code decoding delay and improving PAC code decoding speed.
[0027] 2. In the process of adopting the SCL decoding algorithm for PAC codes, this invention introduces a method for counting the number of consecutive non-splitting steps in a single decoding path and a dual-factor sorting path deletion method. The number of consecutive non-splitting steps is used as the first sorting factor for the final decoding path selection, which can effectively improve the decoding performance of information nodes and thus improve the decoding efficiency of PAC codes. Attached Figure Description
[0028] Figure 1 This is a flowchart of the present invention.
[0029] Figure 2 This is a comparison chart of the decoding error rates of the method of this invention and the classical decoding algorithm. Detailed Implementation
[0030] To clearly illustrate the technical features of this solution, the invention will be 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 splits is proposed. This method calculates the error decoding probability of the bit sequence to be decoded obtained from a Gaussian white noise channel, which serves as the criterion for determining whether a node splits during the decoding process. It records the number of consecutive non-splits for each candidate decoding path as an important criterion for deciding the decoding result. The method calculates the path metric based on the current position state and the next position state of the decoding path. Finally, when selecting the decoding path, the method uses both the number of consecutive non-splits and the path metric to perform a double sorting to obtain the optimal decoding path.
[0032] This method is used to decode N bits to be decoded from source data encoded by PAC polarization-adjusted convolutional codes after passing through a Gaussian white noise channel. The set of indexes of known information bits A before decoding, the convolution generator polynomial g, and the list of candidate paths Π are provided. At the beginning of decoding, there is only one path in Π.
[0033] Figure 1 The decoding process, starting from the decoding bit position, specifically includes the following steps:
[0034] Step 1: Obtain the output values corresponding to the N bits to be decoded from the channel. Initialize the current decoded bit index t = 1;
[0035] Step 2: Determine whether the current decoded bit index t is in the index set A. If yes, proceed to step 3; otherwise, proceed to step 4. The information bit index set A is determined by the channel reliability ranking. Specific channel reliability metrics include Barthelite parameter, Gaussian approximation, density evolution, etc. Barthelite parameter is used as a sub-channel reliability evaluation standard. It uses maximum likelihood decision to derive the upper limit of the error probability of each sub-channel. This evaluation standard is also commonly used in Gaussian channels.
[0036] Step 3: Traverse the candidate path list Π, perform convolution transformation, path metric calculation, and partial sum calculation for each path, then proceed to step 5; the specific method of convolution transformation is as follows:
[0037] Set the current decoded bit value v t The state S at position t in the current path and the generator polynomial g are used as inputs to the convolution transformation, and v t Convolving with the generator polynomial g yields the convolution result u of the Pi-th path at position t. t[Pi], and simultaneously obtain the new state at position t in the current path:
[0038] S t [Pi] = v t +S t-1 [1,...,|g|-2],
[0039] Where |g| is the number of coefficients of the generator polynomial g, and 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 each state are also pre-designed. A relatively mature state transition diagram is the state transition diagram for convolutional codes in the Viterbi decoding algorithm, which can effectively determine the transition relationship between decoded bits and bits to be decoded during sequential decoding, and can make the decoding process smoother.
[0041] The specific method for calculating path metrics is as follows:
[0042]
[0043] Among them, M t [Pi] represents the path metric value of the Pi-th decoding path at position t; This represents the information bit u at position t in the Pi-th decoding path. t The predicted value is calculated as shown in step 4; This represents the output value corresponding to the bit at position t obtained from the channel. The state S at position t-1... t-1 and the state S at position t t When there are no connections between paths, the path metric is infinite, indicating that the current decoding path is blocked. This path can be removed from the candidate paths for decoding. Due to the pre-defined state transition diagram, some paths can be eliminated in a timely manner during the decoding process, thereby speeding up the decoding flow and saving decoding time.
[0044] The partial sum calculation method in this step is the same as that proposed by Arikan for SC decoding.
[0045] Step 4, perform the expansion operation of the candidate path list, specifically as follows:
[0046] For the current information bit u t Perform a path split or hard decision operation based on the result of the following formula:
[0047]
[0048] in, [This refers to information bits u]t The predicted value, L Pi (u t ) represents the information bit u in the Pi-th path. t The corresponding log-likelihood ratio is calculated using the same iterative method as the SC decoding process proposed by Arikan. For bit u at position t t The probability of incorrect decoding, E(L(u) t )) is N L(u t The mathematical expectation of ), where split represents the splitting operation;
[0049] After making a decision on the information bits, if no splitting operation is performed, the number of consecutive non-split counts W will be recorded. l Add 1 to the quantity.
[0050] Here, an explicit formula P is used to determine whether or not information bits are split. e (u t ) calculate, which represents the information bit u t The probability of a translation error is 1-P. e (u t This represents the probability of correct decoding, which is equivalent to having prior decoding knowledge of the codeword after polarization transformation before performing PAC code decoding, and being able to calculate P in advance before decoding. e (u t This eliminates many unnecessary decoding splitting steps. When no splitting occurs, it means that the current decision result is the correct decoding with the highest probability. As the number of consecutive no splitting increases, during the decoding process of PAC codes, as the reliability of the splitting channel increases, the correct decoding path will choose to continue without splitting to obtain the correct decoding result, and finally form a benign decoding, which maximizes the probability of obtaining the correct decoding result.
[0051] If the size of the resulting list of candidate paths exceeds a set value L, then the paths in the list ∏ are sorted according to the number of consecutive non-splits and the path metric, and the L paths with the smallest path metric are retained. The specific sorting method is as follows:
[0052] Using the number of consecutive non-splits W l The path metric is used as the first ranking factor, and the W value is used as the second ranking factor in the ranking results. l Larger ones with smaller path metrics are ranked higher.
[0053] Two sorting factors are used when sorting the decoding path list, and the condition of consecutive non-splitting number is introduced. Compared with existing decoding methods, the decoding result obtained in this way is more likely to be the correct decoding result. Although it introduces some computational resource consumption, it is completely acceptable for this sorting based on the number of splits.
[0054] Step 5: Determine if the current decoding bit index t is equal to N. If it is, output the first path in the candidate path list Π as the decoding result and the decoding ends. Otherwise, t = t + 1 and return to step 2.
[0055] Figure 2 The error rate of this method is compared with that of two other typical decoding strategies.
[0056] In summary, this invention employs a PAC code decoding method based on the number of path splits, which can effectively improve the decoding performance of PAC codes, reduce decoding latency, and provide a new decoding approach for polarization-adjusted convolutional codes.
Claims
1. A PAC code decoding method based on the number of path splits, characterized in that, This is used to decode N bits to be decoded, given the set A of indices of known information bits before decoding, the generator polynomial g, and a list of candidate paths. Decoding begins There is only one path in it; Includes the following steps: Step 1: Obtain the output values corresponding to the N bits to be decoded from the channel. Initialize the current decoded bit index t=1; Step 2: Determine whether the current decoded bit index t is in the index set A. If yes, proceed to step 3; otherwise, proceed to step 4. Step 3, iterate through the list of candidate paths For each path, perform convolution transformation, calculate path metric, and calculate partial sum, then proceed to step 5; the specific method of convolution transformation is as follows: convert the value of the current decoded bit... The state S at position t in the current path and the generator polynomial g are used as inputs to the convolution transformation. Convolving with the generator polynomial g yields the convolution result of the Pi-th path at position t. At the same time, we obtain the new state at position t in the current path: ， in, The number of coefficients for generating polynomial g, This indicates the state at position t-1, where t=1. For the specified bit width The initial state; The specific method for calculating path metrics is as follows: ， in, This represents the path metric value of the Pi-th decoding path at position t; This represents the information bit at position t in the Pi-th decoding path. The predicted value; This represents the output value corresponding to the bit at position t obtained from the channel, when the state at position t-1 is... and the state of position t When there are no connections between them, the path metric value is infinity; Step 4: Perform a candidate path list expansion operation; if the size of the resulting candidate path list is greater than the set value L, then the candidate path list is adjusted based on the number of consecutive non-splits and the path metric. Sort the paths in the list and retain the L paths with the smallest metric values; the specific method for expanding the candidate path list is as follows: For the current information bits Perform a path split or hard decision operation based on the result of the following formula: ， in, Information bits The predicted value, Indicates the information bits in the Pi-th path. The corresponding log-likelihood ratio, Bit at position t The probability of incorrect decoding, There are N The mathematical expectation of , where split represents the splitting operation; After making a decision on the information bits, if no splitting operation is performed, the number of consecutive non-splitting operations will be counted. Increase the quantity by 1; List of candidate paths based on consecutive non-split counts and path metrics The paths in the data are sorted as follows: Use consecutive non-split counts The path metric is used as the first ranking factor and as the second ranking factor in the ranking results. Larger values with smaller path metrics are listed first; Step 5: Determine if the current decoded bit index t is equal to N. If so, add the candidate path list. The path that appears first in the sequence is output as the decoding result, and the decoding ends. Otherwise, t = t + 1, and return to step 2.