Polarization code blind frame synchronization method assisted by auxiliary bits

Abstract

The invention provides an auxiliary bit assisted polar code blind frame synchronization method, which comprises the following steps of: S1, before polar coding, inserting set A auxiliary bits [a0, a1,..., aA-1] at the foremost ends of original K information bits [m0, m1, m2,..., mK-1] to form a K + A bit sequence to be coded, and then performing polar coding on the sequence; s2, at a receiving end, N-length candidate sequences are intercepted bit by bit on the receiving sequence through an N-length sliding window, and N candidate sequences are synchronously intercepted in one blind frame; all the intercepted candidate sequences are decoded through an SC or SCL decoder; s3, continuing to decode to obtain estimation of an original information bit, and calculating to obtain a synchronization metric of the candidate sequence; the synchronization measurement is used for representing the similarity between one sequence and the permitted code word of the polarization code; and S4, selecting the position of the first bit of the sequence with the minimum synchronization metric SMt [N] from the candidate sequences which are not stopped early as an estimated synchronization position.

Description

Technical Field

[0001] The present invention belongs to the field of communications, and particularly relates to a blind frame synchronization method for polar codes assisted by auxiliary bits. Background Art

[0002] In digital communication systems, data is usually transmitted in the form of "frames". Frame synchronization is an essential step at the receiving end, and its function is to accurately find the start and end positions of a frame in the received bit stream, so that the subsequent decoder can correctly decode the information contained in the frame. Traditional frame synchronization is completed by inserting a pilot sequence or a frame synchronization word into the transmission sequence and detecting it at the receiving end. To improve the synchronization performance, one method is to increase the length of the pilot sequence or the frame synchronization word. The disadvantage of this method is that it will lead to an increase in overhead, which may offset part of the gain brought by channel coding; another method is to use the error correction performance of channel coding to assist frame synchronization. This method does not require inserting a pilot sequence or a frame synchronization word, so it is also called blind frame synchronization. Although the blind frame synchronization method can reduce the spectral overhead, it comes at the cost of higher complexity.

[0003] Currently, the research on blind frame synchronization combining Turbo codes and LDPC codes has been very extensive, while the research on combining polar codes is very few. In the literature [1] (Feng Z, Liu Y, Zhang S, et al. Polar-Coding-Assisted Blind Frame Synchronization Based on Soft Information of Frozen Bits. IEEE Commun. Letters, 2023, 27(10): 2563-2567.), a blind frame synchronization method for polar codes was first proposed, which calculates the probability that the current position is the frame start position by using the information of the frozen bits of the polar code, and a synchronization metric was proposed. However, this method requires a large number of polar code decoders for decoding, and there is a problem of high complexity. Therefore, it is meaningful to optimize the existing blind frame synchronization algorithm for polar codes. Summary of the Invention

[0004] The present invention proposes a blind frame synchronization method for polar codes assisted by auxiliary bits. This method replaces some of the frozen bits of the polar code with specific auxiliary bits, detects the decoding results of these bits during decoding, and directly eliminates the candidate sequences whose decoding results do not match the set auxiliary bits, thereby reducing the computational complexity and improving the synchronization performance.

[0005] The blind frame synchronization method for polar codes assisted by auxiliary bits of the present invention includes the following steps:

[0006] S1. Before polar coding, insert the set A auxiliary bits [a 0 , a 1 , a 2 ,..., a K-1 at the very front of the original K-bit information bits [m 0 , m 1 , m A-1 to form a (K + A)-bit sequence to be coded, and then perform polar coding on this sequence to form a polar code of length N.

[0007] S2. At the receiving end, intercept N-length candidate sequences bit by bit on the received sequence through a sliding window of length N, and a total of N candidate sequences are intercepted in one blind frame synchronization. Decode all the intercepted candidate sequences through an SC or SCL decoder. Due to the serial nature of the SC and SCL decoders, the A-bit auxiliary bits of all candidate sequences will be decoded first, and the SC decoder will obtain the estimated value of the auxiliary bits where represents the estimated value of the i-th auxiliary bit by the SC decoder, i ∈ [0, A - 1]; each decoding path of the SCL decoder will obtain an estimated value of the auxiliary bits where represents the estimated value of the i-th auxiliary bit by the k-th decoding path of the SCL decoder, k ∈ [0, l - 1], taking values of 0 or 1. For the SC decoder, if then terminate the decoding process in advance, otherwise execute step S3; for the SCL decoder, if then terminate the decoding process in advance, otherwise execute step S3.

[0008] S3. Continue decoding to obtain the estimate of the original information bits and calculate the synchronization metric of the candidate sequence. The calculation formula for the synchronization metric is:

[0009]

[0010] where SM t [i] represents the synchronization metric of the t-th candidate sequence decoded to the i-th bit, l t，i represents the log-likelihood ratio of the i-th leaf node of the t-th candidate sequence, represents the set of frozen bits of the polar code. The synchronization metric is used to characterize the similarity between a sequence and the allowed codewords of the polar code. The smaller the synchronization metric, the more likely this position is the synchronization position.

[0011] S4. Select the position of the first bit of the sequence with the smallest synchronization metric SM t [N] among the candidate sequences not prematurely stopped as the estimated synchronization position, that is

[0012] Define the early stopping performance EP = 1 - P ret , where P ret is the proportion of candidate sequences that have completed the entire decoding process among all candidate sequences. The higher the EP, the higher the proportion of candidate sequences that are early stopped, and the better the early stopping performance.

[0013] Preferably, the auxiliary bits in step S1 are selected according to the following principles:

[0014] S1.1. For two auxiliary bits at the same 2-length R1 node, set the previous auxiliary bit to 1, and the latter auxiliary bit can be arbitrarily selected as 0 or 1.

[0015] S1.2. For R1 nodes with a length greater than 2, decompose them into a series of 2-length R1 nodes, and then select the auxiliary bits according to step S1.1.

[0016] S1.3. For a single auxiliary bit, if it is not the last auxiliary bit, it must be located at a Rep node, and set it to 1.

[0017] S1.4. For the auxiliary bits on the SPC node, decompose the SPC node into a REP node and a series of R1 nodes, and then select according to steps S1.1 - S1.3.

[0018] S1.5. For the last auxiliary bit, it can be arbitrarily selected as 0 or 1.

[0019] Under the condition of auxiliary bits with the same length, steps S1.1 - S1.5 can enable step S2 to achieve the optimal early stopping performance and reduce the complexity the most.

[0020] Preferably, under a certain code length and code rate, step S1 should select the auxiliary bit length that reduces the overall complexity the most. The overall complexity reduction of blind frame synchronization is defined as C- = EP × (C o - C ep ), C o is the complexity of SC or SCL decoding the entire N-length codeword, C ep is the complexity of the decoded early stopped, which can be estimated by the total number of f operations and g operations during the decoding process. Let the last auxiliary bit be at the Dth position of the codeword, then C o and need to be calculated according to the specific code length and code rate, C ep needs to be calculated according to the code length, code rate and auxiliary bit length.

[0021] Under the principle of selecting auxiliary bits in steps S1.1 to S1.5, the above scheme for selecting the length of auxiliary bits can implement the method of the present invention with the lowest complexity.

[0022] The advantages and positive effects of the present invention are as follows:

[0023] (1) The method of the present invention greatly reduces the complexity of the existing blind frame synchronization of polar codes, which is beneficial to the implementation of the hardware platform.

[0024] (2) The method of the present invention improves the synchronization performance of the blind frame synchronization of polar codes. Description of the Drawings

[0025] Figure 1 is a schematic diagram of the way of inserting auxiliary bits in the method of the present invention.

[0026] Figure 2 is a schematic diagram of intercepting a candidate sequence on the received sequence.

[0027] Figure 3 is the complexity reduction of the method of the present invention under different lengths of auxiliary bits.

[0028] Figure 4 is a comparison of the false frame synchronization rates of the method of the present invention under different lengths of auxiliary bits. Detailed Embodiment

[0029] Next, the present invention will be further described in detail with reference to the Figures 1-4 drawings and embodiments.

[0030] Taking a polar code with a code length N = 512, K = 170 and A = 6 auxiliary bits as an example, the execution process of the auxiliary bits assisting the blind frame synchronization of the polar code is described. The frozen set is determined according to the reliability sequence table of the 5G control channel polar code provided by 3GPP.

[0031] Step 1: As Figure 1 shown, before channel coding, set 6 auxiliary bits are inserted at the very front of the 170 - bit information bits to form a total of 176 new information bits, which are mapped to a 512 - bit input vector u through the reliability sequence table, and then polar - coded into a 512 - bit codeword x, which is transmitted through the channel after modulation.

[0032] Step 2: As Figure 2 shown, [..., x m-1，1 ,x m-1，2 ,…,x m-1，N ,x m，1 ,...] is the codeword sequence to be transmitted, where x m，k represents the k - th bit in the m - th codeword transmitted. After the receiving end completes carrier synchronization and demodulation, the received sequence [..., y m-1，1, y m-1，2 ,..., y m-1，N , y m，1 ,...]. On the received sequence, a total of 512 candidate sequences are intercepted through a sliding window of N-bit length represents the i-th candidate sequence of length N that is intercepted.

[0033] Step 3: Perform SCL2 decoding and synchronization metric calculation on all candidate sequences. When the 192nd bit of each candidate sequence is decoded, it can be known from the encoding method in Step 1 that the decoding of 6 auxiliary bits has been completed at this time. Compare these 6 auxiliary bits with the set value [1 0 1 1 1 0]. If they are the same as the set value, the candidate sequence continues the decoding and synchronization metric calculation until the decoding of the sequence is completed; otherwise, stop the decoding of the candidate sequence and set the synchronization metric of the sequence to the maximum value that can be quantified.

[0034] Step 4: Take the position of the sequence with the minimum synchronization metric among the 512 candidate sequences as the estimated synchronization position to complete the blind frame synchronization of the polar code.

[0035] Table 1 shows the situation of the nodes where the 6 auxiliary bits are located under the conditions of N = 512, K = 170, and A = 6.

[0036] Table 1 Auxiliary Bit Distribution

[0037] Auxiliary bit number Node 1～2 Two-length R1 node 3 Four-length Rep node 4～6 Four-length SPC node

[0038] According to the preferred embodiment of the present invention, the 1st, 3rd, 4th, and 5th auxiliary bits are selected as 1, and the other auxiliary bits can be arbitrarily selected, that is, the 6 auxiliary bits are selected as [1 0 1 1 1 0], [1 1 1 1 1 0], [1 0 1 1 1 1], or [1 1 1 1 1 1] to achieve the optimal early stopping performance under 6 auxiliary bits.

[0039] Figure 3 shows the results of the total complexity reduction of each decoder in a single blind frame synchronization through early stopping under the conditions of N = 512, K = 170, and different auxiliary bit lengths when achieving their respective optimal early stopping performances. The vertical axis represents the total number of f and g operations reduced, the horizontal axis represents the length of the auxiliary bits, and the upper red line is the number of f and g operations of each decoder when the method of the present invention is not adopted. The results show that under the selected polar code, the scheme with an auxiliary bit length of 6 can achieve the blind frame synchronization of the polar code with the lowest complexity.

[0040] Figure 4Under the conditions of N = 512 and K = 170, the comparison of the false synchronization rate of the method of the present invention with that of the existing polarization code blind frame synchronization method at different auxiliary bit lengths is given. The comparison results show that the false synchronization rate of the method of the present invention is lower than that of the existing polarization code blind frame synchronization method when the auxiliary bit length is less than or equal to 7, and it has better synchronization performance.

Claims

1. A polar code blind frame synchronization method assisted by auxiliary bits, characterized in that: The following steps are involved: S1. Before polarization coding, the original K information bits [m0,m1,m2,…,m K-1 ] is inserted at the front end of the set A auxiliary bits [a0, a1, ..., a A-1 ], forming a K+A-bit sequence to be encoded, and then polarization encoding is performed on the sequence to form a polar code of length N; S2. At the receiving end, a candidate sequence of length N is intercepted bit by bit on the receiving sequence through an N-length sliding window, and a total of N candidate sequences are intercepted in one blind frame synchronization; all intercepted candidate sequences are decoded through an SC or SCL decoder; S3. Continue decoding to obtain an estimate of the original information bit The synchronization metric of the candidate sequence is calculated; the synchronization metric is used to characterize the similarity between a sequence and the permitted codeword of the polar code. The smaller the synchronization metric, the more likely the position is to be a synchronization position. S4. Select the synchronization metric SM from the candidate sequence that has not been stopped early t The position of the first bit of the sequence with the smallest [N] is taken as the estimated synchronization position, that is, Define early stopping performance EP = 1-P ret , where P ret The ratio of candidate sequences that have completed the entire decoding process to all candidate sequences. The higher the EP, the higher the ratio of candidate sequences that have been stopped early, and the better the early stopping performance.

2. The method for polar code blind frame synchronization with auxiliary bits according to claim 1, characterized in that: The auxiliary bits in step S1 are selected according to the following principles: S1.

1. For two auxiliary bits in the same 2-length R1 node, the first auxiliary bit is set to 1, and the second auxiliary bit can be arbitrarily selected to 0 or 1; S1.

2. For R1 nodes with a length greater than 2, decompose them into a series of R1 nodes with a length of 2, and then select auxiliary bits according to step S1.1; S1.

3. For a single auxiliary bit, if it is not the last auxiliary bit, it must be located at the Rep node and is set to 1; S1.

4. For the auxiliary bit located on the SPC node, the SPC node is decomposed into a REP node and a series of R1 nodes, and then selected according to steps S1.1 to S1.3; S1.

5. For the last auxiliary bit, it can be arbitrarily selected as 0 or 1.

3. The method for polar code blind frame synchronization with auxiliary bits according to claim 1 or 2, characterized in that: Under a certain code length and code rate, step S1 should select the auxiliary bit length that reduces the overall complexity the most; the overall reduced complexity of blind frame synchronization is defined as C - =EP×(C o -C ep ), C o The complexity of decoding the entire N-length codeword for SC or SCL, C ep The complexity of the early-stopped decoding is estimated by the total number of f operations and g operations in the decoding process. Assuming that the last auxiliary bit is at the Dth position of the codeword, then C o and need to be calculated based on the specific code length and code rate, C ep It needs to be calculated based on the code length, code rate and auxiliary bit length.

4. The method for polar code blind frame synchronization with auxiliary bits according to claim 1, characterized in that: In step S2, the A-bit auxiliary bits of all candidate sequences will be decoded first, and the SC decoder will obtain the estimated value of the auxiliary bit. in, Represents the estimated value of the SC decoder for the i-th auxiliary bit, i∈[0,A-1].

5. The method for polar code blind frame synchronization with auxiliary bits according to claim 1, characterized in that: Each decoding path of the SCL decoder will obtain an estimate of the auxiliary bit in, represents the estimated value of the kth decoding path of the SCL decoder for the i-th auxiliary bit, k∈[0,l-1], The value is 0 or 1.

6. The method for polar code blind frame synchronization with auxiliary bits according to claim 4, characterized in that: For the SC decoder, if The decoding process is terminated in advance, otherwise, step S3 is executed.

7. The method for polar code blind frame synchronization with auxiliary bits according to claim 5, characterized in that: For the SCL decoder, if The decoding process is terminated in advance, otherwise, step S3 is executed.

8. The method for polar code blind frame synchronization with auxiliary bits according to claim 1, characterized in that: In step S3, the calculation formula of the synchronization metric is: Among them, SM t [i] represents the synchronization metric of decoding the t-th candidate sequence to the i-th bit, l t,i represents the log-likelihood ratio of the ith leaf node of the tth candidate sequence, Represents the set of frozen bits of the polar code.

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