Low-complexity Fano decoding method for PAC code

Abstract

The invention discloses a low-complexity Fano decoding method for a PAC code, and relates to the field of wireless communication channel coding. According to the method, on the premise that the index, the log-likelihood ratio and the channel state of the received PAC code are known, the frozen bit and the information bit in the received PAC code are respectively subjected to decoding judgment, the total path metric is updated in real time, whether backtracking is carried out or not and a specific backtracking process is selected according to the total path metric, and finally a decoding result corresponding to the received PAC code is obtained. According to the method, the backtracking operation is newly optimized, the backtracking threshold is newly defined, and the complexity of the Fano decoding algorithm is effectively reduced on the premise that the error correction performance of the algorithm is not greatly reduced.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication channel coding, and in particular to a low-complexity Fano decoding method for PAC codes. Background Art

[0002] With the further development of the wireless communication field, the new communication standards improve the overall wireless communication service capabilities by processing the control channel and the data channel separately. In channel coding, short codes have many benefits for control channels. First, short codes can reduce the complexity of encoding and decoding. Secondly, the use of short codes can increase the redundancy of information and reduce the occurrence of errors. Finally, the use of short codes can also improve the security of communication. Polarization-adjusted convolutional code PAC has great application potential in the field of short codes. At present, relevant researchers are committed to exploring the optimal decoding algorithm of PAC code. Among them, the error correction performance of Fano decoding has certain advantages over list decoding, stack decoding, etc., but it still has a large room for optimization in terms of complexity, which hinders the pace of its engineering application. Summary of the invention

[0003] In view of this, the present invention proposes a low-complexity Fano decoding method for PAC codes, which effectively reduces the complexity of the Fano decoding algorithm without significantly reducing the error correction performance of the algorithm.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0005] A low-complexity Fano decoding method for PAC codes comprises the following steps:

[0006] Step 1: Receive a bit string to be decoded of a PAC code, wherein the length of the bit string to be decoded is N, and the index sets of the information bits and the frozen bits in the bit string to be decoded are A and A respectively. c , the log-likelihood ratio LLR values ​​corresponding to the N bits to be decoded are λ n , n=1,2,3,……,N, n is the index of the bit to be decoded; the channel state is y;

[0007] Step 2, set the variable current indicating the index value of the bit to be decoded, set current = 1; initialize the total path metric PM0 = 0, initialize the backtracking threshold T = 0, and set the convolution polynomial g;

[0008] Step 3: for the current bit i to be decoded current , if current belongs to the frozen bit index set A c , then execute step 4. If current belongs to the information bit index set A, then execute step 5;

[0009] Step 4: The current bit to be decoded i current The decoding result is recorded as There is only one path at this time. Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And update the total path metric PM current , if PM current If it is greater than the backtracking threshold T, execute step 7, otherwise execute step 8;

[0010] Step 5: Split the path to obtain two paths. The current bit i to be decoded corresponding to the two paths is current The decoding results are and

[0011] against The path will Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And calculate the corresponding total path metric under this path;

[0012] against The path will Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And calculate the corresponding total path metric under this path;

[0013] Among the total path metrics corresponding to the two paths, the maximum value is selected and recorded as PM max , select the minimum value and record it as PM min ;

[0014] If PM min If it is greater than the backtracking threshold T, execute step 6;

[0015] If PM min Less than the backtracking threshold T, and PM max If it is greater than the backtracking threshold T, PM max Denoted as the updated total path metric PM current , PM max Corresponding Denote the current bit to be decoded i current The decoding result is obtained, and then step 7 is executed;

[0016] If PM max If it is less than the backtracking threshold T, PM max Denoted as the updated total path metric PM current , PMmax Corresponding Denote the current bit to be decoded i current The decoding result is obtained, and then step 8 is executed;

[0017] Step 6: PM max Denoted as the updated total path metric PM current , PM max Corresponding Denote the current bit to be decoded i current Decoding result; determine whether current = N. If current = N, complete the low-complexity Fano decoding for the PAC code; otherwise, set current = current + 1, and return to continue to execute step 3;

[0018] Step 7, determine whether current = N is true. If current = N is true, then complete the low-complexity Fano decoding of the PAC code; if current = N is not true, then continue to determine whether it is the first time to access the current bit to be decoded i current , if it is the first time to access the current decoded bit i current , then update the threshold T so that Δ is the threshold update step size, and Δ is a positive integer. Indicates rounding down, then set current = current + 1, and return to step 3; if it is not the first time to access the current decoded bit i current , then directly set current = current + 1, and return to step 3;

[0019] Step 8: Determine the current bit i to be decoded current Is it the first bit to be decoded or the first information bit in the bit string to be decoded, or is it the current bit to be decoded i current All previously decoded bits are frozen bits;

[0020] If so, iterate and perform T=T-Δ operation according to the threshold update step size Δ until PM max >T, then go to step 7;

[0021] Otherwise, at the current bit i to be decoded current Among all the previously decoded bits, find the bit i that is closest to the current bit to be decoded. current The most recent information bit is denoted as i back , back belongs to the information bit index set A; judge i current with i back Is the backtracking length between the two greater than the backtracking length threshold BT? currentIf so, continue to determine whether current = N is true. If current = N is true, complete the low-complexity Fano decoding for the PAC code; if current = N is not true, directly set current = current + 1 and return to step 3; if i current with i back The backtracking length between the two is not greater than the backtracking length threshold BT current Then start backtracking;

[0022] Specifically, the backtracking process is:

[0023] Step 801, let T = T-Δ;

[0024] Step 802: From the current bit to be decoded i current Start reverse iteration and get the total path metric PM back-1 The value of

[0025] Step 803: Based on the total path metric PM back-1 Combined with step 5, we can get the values ​​of i back The total path metric of the two corresponding paths;

[0026] Step 804: Select the i before this backtracking process back Another path other than the selected path, and its corresponding total path metric is recorded as PM back ;

[0027] Step 805, according to PM back The value of i back Start forward iteration and get i current-1 The corresponding total path metric PM current-1 The value of the current bit to be decoded is then returned to step 3. current Make a new decoding decision.

[0028] Furthermore, the current path metric is calculated in steps 4 and 5. And calculate the current path metric The way is as follows:

[0029]

[0030] The superscript (0) or (1) indicates the current bit to be decoded i. current The decoding results are and ln represents the logarithmic function with base e.

[0031] Further, in step 4, the total path metric is updated, in step 5, the total path metric corresponding to this path is calculated, and in step 805, the total path metric corresponding to this path is calculated.back Start forward iteration and get i current-1 The corresponding total path metric PM current-1 The value of is as follows:

[0032] PM current =PM current-1 +m current -α q ×ln(1-p e,current );

[0033] Among them, m current for or p e,current Indicates the current bit to be decoded i current The probability of error decoding is obtained from the channel noise distribution; Δ q Update the adjustment factor for the total path metric, Indicates rounding up.

[0034]

[0035] It means that based on the decoded j-1 bits, given the known channel state y, the j-th bit is estimated to be The probability of is obtained according to the channel transfer probability; the superscript l indicates the path, represents the decoded j-1 bit string, represents the decoding estimation result of the j-th bit, The value of is 1 or 0; when j = 1, It means that under the premise of known channel state y, the first bit is estimated to be The probability of

[0036] P(u j |U j-1 ,y) means that based on the decoded j-1 bits, given the known channel state y, the jth bit is estimated to be u j The probability of is obtained according to the probability distribution of channel noise; U j-1 represents the decoded j-1 bit string, u j represents the decoding estimation result of the jth bit, u j The value of is 1 or 0; when j = 1, P(u j |U j-1 ,y)=P(u j |y), which means that under the premise of known channel state y, the first bit is estimated to be u j The probability of E y () represents mathematical expectation;

[0037] Correspondingly, in step 802, from the current bit to be decoded i current Start reverse iteration and get the total path metric PM back-1 The value of is as follows:

[0038] PM current-1 =PM current -m current +α q ×log(1-p e,current ).

[0039] Furthermore, in step 8, the backtracking length threshold BT current The specific values ​​are:

[0040] BT current =ffs(bin(current));

[0041] Specifically, bin(current) represents the binary representation of current, and ffs(bin(current)) represents the position of the first '1' in the binary number of current.

[0042] Due to the adoption of the above technical solution, the beneficial effects of the present invention compared with the prior art are:

[0043] 1. In the low-complexity Fano decoding algorithm process adopted by the present invention, the backtracking operation is completely optimized and the backtracking threshold is newly defined, which can greatly reduce the algorithm complexity and has little impact on the error correction performance.

[0044] 2. The present invention introduces an adjustment factor for path metric value update and a backtracking length calculation rule into the path metric value update process of the low-complexity Fano decoding algorithm, and combines this with a rounding-up operation, thereby ensuring the error correction performance of the algorithm and reducing the computational complexity of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of a backtracking process of a low-complexity Fano decoding method for PAC code when N=4 in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0047] A low-complexity Fano decoding method for PAC codes comprises the following steps:

[0048] Step 1: Receive a bit string to be decoded of a PAC code, wherein the length of the bit string to be decoded is N, and the index sets of the information bits and the frozen bits in the bit string to be decoded are A and A respectively.c , the log-likelihood ratio LLR values ​​corresponding to the N bits to be decoded are λ n , n=1,2,3,……,N, n is the index of the bit to be decoded; the channel state is y;

[0049] Step 2, set the variable current indicating the index value of the bit to be decoded, set current = 1; initialize the total path metric PM0 = 0, initialize the backtracking threshold T = 0, and set the convolution polynomial g;

[0050] Specifically, in this embodiment, the convolution polynomial g is 1011011.

[0051] Step 3: for the current bit i to be decoded current , if current belongs to the frozen bit index set A c , then execute step 4. If current belongs to the information bit index set A, then execute step 5;

[0052] Step 4: The current bit to be decoded i current The decoding result is recorded as There is only one path at this time. Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And update the total path metric PM current , if PM current If it is greater than the backtracking threshold T, execute step 7, otherwise execute step 8;

[0053] Step 5: Split the path to obtain two paths. The current bit i to be decoded corresponding to the two paths is current The decoding results are and

[0054] against The path will Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And calculate the corresponding total path metric under this path;

[0055] against The path will Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And calculate the corresponding total path metric under this path;

[0056] Among the total path metrics corresponding to the two paths, the maximum value is selected and recorded as PMmax , select the minimum value and record it as PM min ;

[0057] If PM min If it is greater than the backtracking threshold T, execute step 6;

[0058] If PM min Less than the backtracking threshold T, and PM max If it is greater than the backtracking threshold T, PM max Denoted as the updated total path metric PM current , PM max Corresponding Denote the current bit to be decoded i current The decoding result is obtained, and then step 7 is executed;

[0059] If PM max If it is less than the backtracking threshold T, PM max Denoted as the updated total path metric PM current , PM max Corresponding Denote the current bit to be decoded i current The decoding result is obtained, and then step 8 is executed;

[0060] Step 6: PM max Denoted as the updated total path metric PM current , PM max Corresponding Denote the current bit to be decoded i current Decoding result; determine whether current = N. If current = N, complete the low-complexity Fano decoding for the PAC code; otherwise, set current = current + 1, and return to continue to execute step 3;

[0061] Step 7, determine whether current = N is true. If current = N is true, then complete the low-complexity Fano decoding of the PAC code; if current = N is not true, then continue to determine whether it is the first time to access the current bit to be decoded i current , if it is the first time to access the current decoded bit i current , then update the threshold T so that Δ is the threshold update step size, and Δ is a positive integer. Indicates rounding down, then set current = current + 1, and return to step 3; if it is not the first time to access the current decoded bit i current , then directly set current = current + 1, and return to step 3;

[0062] Specifically, in this embodiment, the value of the threshold update step length Δ is any one of 1, 2, 3 or 4. In this embodiment, the value of Δ is 2.

[0063] Step 8: Determine the current bit i to be decoded current Is it the first bit to be decoded or the first information bit in the bit string to be decoded, or is it the current bit to be decoded i current All previously decoded bits are frozen bits;

[0064] If so, iterate and perform T=T-Δ operation according to the threshold update step size Δ until PM max >T, then go to step 7;

[0065] Otherwise, at the current bit i to be decoded current Among all the previously decoded bits, find the bit i that is closest to the current bit to be decoded. current The most recent information bit is denoted as i back , back belongs to the information bit index set A; judge i current with i back Is the backtracking length between the two greater than the backtracking length threshold BT? current If so, continue to determine whether current = N is true. If current = N is true, complete the low-complexity Fano decoding for the PAC code; if current = N is not true, directly set current = current + 1 and return to step 3; if i current with i back The backtracking length between the two is not greater than the backtracking length threshold BT current Then start backtracking;

[0066] Specifically, the backtracking process is:

[0067] Step 801, let T = T-Δ;

[0068] Step 802: From the current bit to be decoded i current Start reverse iteration and get the total path metric PM back-1 The value of

[0069] Step 803: Based on the total path metric PM back-1 Combined with step 5, we can get the values ​​of i back The total path metric of the two corresponding paths;

[0070] Step 804: Select the i before this backtracking process back Another path other than the selected path, and its corresponding total path metric is recorded as PM back ;

[0071] Step 805, according to PM back The value of i back Start forward iteration and get i current-1 The corresponding total path metric PM current-1 The value of the current bit to be decoded is then returned to step 3. current Make a new decoding decision.

[0072] Furthermore, the current path metric is calculated in steps 4 and 5. And calculate the current path metric The way is as follows:

[0073]

[0074] The superscript (0) or (1) indicates the current bit to be decoded i. current The decoding results are and ln represents the logarithmic function with base e.

[0075] Further, in step 4, the total path metric is updated, in step 5, the total path metric corresponding to this path is calculated, and in step 805, the total path metric corresponding to this path is calculated. back Start forward iteration and get i current-1 The corresponding total path metric PM current-1 The value of is as follows:

[0076] PM current =PM current-1 +m current -α q ×ln(1-p e,current );

[0077] Among them, m current for or p e,current Indicates the current bit to be decoded i current The probability of error decoding is obtained from the channel noise distribution; Δ q Update the adjustment factor for the total path metric, Indicates rounding up;

[0078] Specifically, in this embodiment, the total path metric update adjustment factor Δ q The value of is 1, 2, 3 or 4. In this embodiment, Δ q The value of is 2.

[0079]

[0080] It means that based on the decoded j-1 bits, given the known channel state y, the j-th bit is estimated to be The probability of is obtained according to the channel transfer probability; the superscript l indicates the path, represents the decoded j-1 bit string, represents the decoding estimation result of the j-th bit, The value of is 1 or 0; when j = 1, It means that under the premise of known channel state y, the first bit is estimated to be The probability of

[0081] P(u j |U j-1 ,y) means that based on the decoded j-1 bits, given the known channel state y, the jth bit is estimated to be u j The probability of is obtained according to the probability distribution of channel noise; U j-1 represents the decoded j-1 bit string, u j represents the decoding estimation result of the jth bit, u j The value of is 1 or 0; when j = 1, P(u j |U j-1 ,y)=P(u j |y), which means that under the premise of known channel state y, the first bit is estimated to be u j The probability of E y () represents mathematical expectation;

[0082] Correspondingly, in step 802, from the current bit to be decoded i current Start reverse iteration and get the total path metric PM back-1 The value of is as follows:

[0083] PM current-1 =PM current -m current +α q ×ln(1-p e,current ).

[0084] Furthermore, in step 8, the backtracking length threshold BT current The specific values ​​are:

[0085] BT current =ffs(bin(current));

[0086] Specifically, bin(current) represents the binary representation of current, and ffs(bin(current)) represents the position of the first '1' in the binary number of current.

[0087] Specifically, the position of the first bit in the binary number of current is recorded as 1.

[0088] Specifically, Figure 1 , which is a schematic diagram of the backtracking process of this embodiment when N=4; this embodiment effectively reduces the complexity of the Fano decoding algorithm without significantly reducing the error correction performance of the algorithm.

[0089] In summary, the present invention has made a completely new optimization of the backtracking operation and has made a new definition of the backtracking threshold, which can greatly reduce the complexity of the algorithm and has little impact on the error correction performance. In addition, the introduction of the adjustment factor for updating the path metric value and the backtracking length calculation rule, combined with the rounding-up operation, not only ensures the error correction performance of the algorithm, but also reduces the computational complexity of the algorithm.

[0090] Those skilled in the art will appreciate that the embodiments described are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to the embodiments described. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A low-complexity Fano decoding method for PAC codes, characterized in that: The following steps are involved: Step 1: Receive a bit string to be decoded of a PAC code, wherein the length of the bit string to be decoded is N, and the index sets of the information bits and the frozen bits in the bit string to be decoded are A and A respectively. c , the log-likelihood ratio LLR values ​​corresponding to the N bits to be decoded are λ n , n=1,2,3,……,N, n is the index of the bit to be decoded; The channel state is y; Step 2, set the variable current indicating the index value of the bit to be decoded, and set current=1; Initialize the total path metric PM0 = 0, initialize the backtracking threshold T = 0, and set the convolution polynomial g; Step 3: for the current bit i to be decoded current , if current belongs to the frozen bit index set A c , then execute step 4. If current belongs to the information bit index set A, then execute step 5; Step 4: The current bit to be decoded i current The decoding result is recorded as There is only one path at this time. Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And update the total path metric PM current , if PM current If it is greater than the backtracking threshold T, execute step 7, otherwise execute step 8; Step 5: Split the path to obtain two paths. The current bit i to be decoded corresponding to the two paths is current The decoding results are and against The path will Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And calculate the corresponding total path metric under this path; against The path will Perform convolution transformation with the convolution polynomial g to obtain the corresponding convolution transformation value Calculate the current path metric And calculate the corresponding total path metric under this path; Among the total path metrics corresponding to the two paths, the maximum value is selected and recorded as PM max , select the minimum value and record it as PM min ; If PM min If it is greater than the backtracking threshold T, execute step 6; If PM min Less than the backtracking threshold T, and PM max If it is greater than the backtracking threshold T, PM max Denoted as the updated total path metric PM current , PM max Corresponding The current bit to be decoded is i current The decoding result is obtained, and then step 7 is executed; If PM max If it is less than the backtracking threshold T, PM max Denoted as the updated total path metric PM current , PM max Corresponding The current bit to be decoded is i current The decoding result is obtained, and then step 8 is executed; Step 6: PM max Denoted as the updated total path metric PM current , PM max Corresponding The current bit to be decoded is i current Decoding result; determine whether current = N. If current = N, complete the low-complexity Fano decoding for the PAC code; otherwise, set current = current + 1, and return to continue to execute step 3; Step 7, determine whether current = N is true. If current = N is true, then complete the low-complexity Fano decoding of the PAC code; if current = N is not true, then continue to determine whether it is the first time to access the current bit to be decoded i current , if it is the first time to access the current decoded bit i current , then update the threshold T so that Δ is the threshold update step size, and Δ is a positive integer. Indicates rounding down, then set current = current + 1, and return to step 3; if it is not the first time to access the current decoded bit i current , then directly set current = current + 1, and return to step 3; Step 8: Determine the current bit i to be decoded current Is it the first bit to be decoded or the first information bit in the bit string to be decoded, or is it the current bit to be decoded i current All previously decoded bits are frozen bits; If so, iterate and execute T=T-Δ operation according to the threshold update step size Δ until PM max >T, then go to step 7; Otherwise, at the current bit i to be decoded current Among all the previously decoded bits, find the bit i that is closest to the current bit to be decoded. current The most recent information bit is denoted as i back , back belongs to the information bit index set A; judge i current with i abck Is the backtracking length between the two greater than the backtracking length threshold BT? current If so, continue to determine whether current = N is true. If current = N is true, complete the low-complexity Fano decoding for the PAC code; if current = N is not true, directly set current = current + 1 and return to step 3; if i current with i back The backtracking length between the two is not greater than the backtracking length threshold BT current Then start backtracking; Specifically, the backtracking process is: Step 801, let T = T-Δ; Step 802: From the current bit to be decoded i current Start reverse iteration and get the total path metric PM back-1 The value of Step 803: Based on the total path metric PM back-1 Combined with step 5, we can get the values ​​of i back The total path metric of the two corresponding paths; Step 804: Select the i before this backtracking process back Another path other than the selected path, and its corresponding total path metric is recorded as PM back ; Step 805, according to PM back The value of i back Start forward iteration and get i current-1 The corresponding total path metric PM current-1 The value of the current bit to be decoded is then returned to step 3. mcuuent Make a new decoding decision.

2. A low-complexity Fano decoding method for PAC code according to claim 1, characterized in that: Calculate the current path metric in steps 4 and 5 And calculate the current path metric The way is as follows: The superscript (0) or (1) indicates the current bit to be decoded i. current The decoding results are and ln() represents the logarithmic function with base e.

3. A low-complexity Fano decoding method for PAC code according to claim 2, characterized in that: In step 4, the total path metric is updated, in step 5, the total path metric corresponding to this path is calculated, and in step 805, the total path metric corresponding to this path is calculated from i back Start forward iteration and get i current-1 The corresponding total path metric PM current-1 The value of is as follows: PM current =PM current-1 +m current -α q ×ln(1-p e,current ); Among them, m current for or p e,current Indicates the current bit to be decoded i current The probability of error decoding is obtained from the channel noise distribution; Δ q Update the adjustment factor for the total path metric, Indicates rounding up; It means that based on the decoded j-1 bits, given the known channel state y, the j-th bit is estimated to be The probability of is obtained according to the channel transfer probability; the superscript l indicates the path, represents the decoded j-1 bit string, represents the decoding estimation result of the j-th bit, The value of is 1 or 0; when j = 1, It means that under the premise of known channel state y, the first bit is estimated to be probability; P(u j |U j-1 ,y) means that based on the decoded j-1 bits, given the known channel state y, the jth bit is estimated to be u j The probability of is obtained according to the probability distribution of channel noise; U j-1 represents the decoded j-1 bit string, u j represents the decoding estimation result of the jth bit, u j The value of is 1 or 0; when j = 1, P(u j |U j-1 ,y)=P(u j |y), which means that under the premise of known channel state y, the first bit is estimated to be u j The probability of E y () represents mathematical expectation; Correspondingly, in step 802, from the current bit to be decoded i current Start reverse iteration and get the total path metric PM back-1 The value of is as follows: PM current-1 =PM current -m current +α q ×ln(1-p e,current )。 4. The low-complexity Fano decoding method for PAC code according to claim 1, characterized in that: The backtracking length threshold BT in step 8 current The specific values ​​are: BT current =ffs(bin(current)); Specifically, bin(current) represents the binary representation of current, and ffs(bin(current)) represents the position of the first '1' in the binary number of current.

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