A key set protected CRC concatenated polar code encoding method

Abstract

The application provides a CRC concatenated Polar code encoding method for key set protection, which comprises the following steps: according to a Polar code Gaussian approximation (GA) construction algorithm, selecting reliable bit channels as information bits and unreliable bit channels as frozen bits; obtaining the information bit most likely to have the first error, i.e. the key set, through a code tree structure or Monte Carlo simulation; selecting a CRC polynomial to pre-encode the key set, and then appending the obtained CRC check vector to the end of the information bit vector; and finally encoding the pre-encoded vector by using a Polar code encoding method. The method has the following advantages: compared with a traditional CRC concatenated Polar code encoding method, the method can use a smaller CRC code length by protecting the key set, and can reduce the block error rate when applied to SC-Flip decoding.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of channel coding, and particularly relates to a CRC-cascaded Polar code encoding method for key set protection. BACKGROUND

[0002] Since 2012, the fifth generation mobile communication (5G) system has gradually become a main research hotspot in the field of mobile communication. A large number of scholars and engineers are committed to pursuing the Shannon capacity limit. Although the performance of Turbo and LDPC codes is very close to the Shannon capacity limit, the capacity limit has not been reached. Polar code is the first encoding scheme that can be strictly proved to reach the capacity limit under the binary input symmetric discrete memoryless channel (BI-BDC). Polar code is mainly based on channel polarization theory. Through channel merging and channel splitting, the split channels are divided into two levels: one part becomes a noiseless channel with a capacity close to 1, and the other part becomes a pure noise channel with a capacity close to 0. Only the data to be transmitted is loaded into the noiseless channel, and the pure noise channel is not used, so that the reliable transmission of data can be realized.

[0003] Polar code uses a serial cancellation (SC) algorithm in the decoding algorithm. When the code length tends to infinity, the SC decoding algorithm can achieve excellent performance, but when the code length is medium or short, the performance loss of the SC decoding algorithm is serious. Scholars have proposed a serial cancellation list (SCL) algorithm, and the CRC code is cascaded to achieve better performance. However, the time complexity and memory space of the SCL decoding are very high, and it is difficult to realize a high-throughput SCL decoder. Then, scholars have proposed a serial cancellation flip (SC-Flip) algorithm. The algorithm uses the CRC code to determine whether the SC decoding is correct. If it is not correct, the least reliable bit is flipped until the maximum number of flips is reached and the CRC code is successfully checked. However, the cyclic redundancy check (CRC) code has excellent burst error detection capability, but when the CRC code is too long (rate loss) or too short (cannot determine whether the decoding is correct), the performance of the SC-Flip algorithm will be lost. SUMMARY

[0004] Therefore, the application provides a CRC-cascaded Polar code encoding method for key set protection, which comprises the following steps:

[0005] S1, according to the GA construction algorithm, the reliable bit channels are selected as information bits, and the unreliable bit channels are selected as frozen bits;

[0006] S2, the key set is obtained through a code tree structure or Monte Carlo simulation;

[0007] S3, CRC pre-encoding the key set with a selected CRC polynomial, and appending the obtained CRC check vector to the end of the information bit vector;

[0008] S4, encoding the pre-encoded vector by using a Polar code encoding method.

[0009] Further, the S1 specific steps are as follows:

[0010] S11, selecting a code length N, an information bit number K+r, and constructing a signal-to-noise ratio E b N0; then according to the GA construction algorithm, it is known that the Gaussian distribution variance of the AWGN channel is:

[0011]

[0012] S12, receiving end LLR mean E is the i-th element of the N-dimensional receiving end LLR mean, i=0,1,...,N-1; wherein the initial condition is According to the recursive formula of the GA construction algorithm, each element of the receiving end LLR mean can be calculated:

[0013]

[0014] wherein

[0015]

[0016] S13, according to the Select the index value of the largest K+r bits as the information bit index, and the remaining index values as the frozen bit index.

[0017] Further, in S2, the specific steps of obtaining the key set through the code tree structure are as follows:

[0018] S21, obtaining the information bit index and the frozen bit index by S1 to form a set Γ in index order;

[0019] S22, the set Γ is a leaf node of a depth n=log2N binary tree, wherein the leaf node corresponding to the information bit index is assigned a value of 1, and the leaf node corresponding to the frozen bit index is assigned a value of 0;

[0020] S23, in the binary tree created in S22, the first leaf node index in the sub-binary tree with all leaf node values of 1 is selected to form a key set CS in index order.

[0021] Further, in S2, the specific steps of obtaining the key set through Monte Carlo simulation are as follows:

[0022] S201, obtaining the information bit index and the frozen bit index by S1 to form a set Γ in index order;

[0023] S202, obtaining the set Γ, assigning 0 and 1 to the information bit index in the set Γ with equal probability, and assigning 0 to the frozen bit index to form an input vector U, and performing BPSK modulation on the input vector U to obtain an output vector Y through an AWGN channel.

[0024] S203, performing SC decoding on the obtained output vector Y to obtain an output vector Y. Comparing the output vector Y with the input vector U to find the index of the first error bit, recording the index, repeating the execution m times, and arranging the indexes in order to form a key set CS.

[0025] Further, S3 specifically comprises the following steps:

[0026] S31, selecting a CRC code length r according to the code length N, the information bit number K+r and the key set size |CS|, and finally obtaining the value of the actual information bit number K to be transmitted;

[0027] S32, obtaining the set Γ from S21, and arranging the first K information bits in the set Γ to transmit the data to be sent and the frozen bits to be fixed as 0 to form an input vector Un; separating the data belonging to the key set CS in the information bits of the input vector Un and arranging them in index order as CC.

[0028] S33, performing backward extension of r bits on the CC obtained from S32 to form CR, and assigning all the extended bits to 0 and placing them at the end of CR.

[0029] S34, performing modulo 2 division of the CR obtained from S33 on the CRC polynomial to obtain r-bit remainders and sequentially placing the r-bit remainders in the last r information bits of the input vector Un.

[0030] Further, S4 is specifically:

[0031] For the generator matrix The nth Kronecker product of the polar matrix The polar code encoding can be obtained by the formula to obtain an encoding vector Xn:

[0032] The technical solution provided by the application has the following beneficial effects:

[0033] The application selects reliable bit channels as information bits and unreliable bit channels as frozen bits according to a Polar code Gaussian approximation (GA) construction algorithm; the information bit that is most likely to have the first error, i.e., a key set, is obtained through a code tree structure or Monte Carlo simulation; a CRC polynomial is selected to perform CRC precoding on the key set, and a CRC check vector obtained after the precoding is appended to the end of an information bit vector; and finally, a Polar code encoding method is used to encode the precoding vector. The performance of the SC-Flip algorithm is improved by reducing the CRC code length (without affecting the performance), and after the method is applied to SC-Flip decoding, the block error rate is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 A key set protection CRC cascaded Polar code encoding method of the application is shown in the figure.

[0035] Figure 2 A Monte Carlo simulation generated key set flowchart of the application is shown in the figure.

[0036] Figure 3 SC and SC-Oracle block error rate curves under different signal-to-noise ratios are shown in the figure.

[0037] Figure 4 SC-Flip block error rate curves under different signal-to-noise ratios using different CRC methods are shown in the figure. DETAILED DESCRIPTION

[0038] To make the purpose, technical solutions and advantages of the application clearer, the embodiments of the application will be further described below with reference to the drawings.

[0039] Please refer to Figure 1 , Figure 1 A key set protection CRC cascaded Polar code encoding method of the application is shown in the figure.

[0040] A key set protection CRC cascaded Polar code encoding method, comprising the following steps:

[0041] S1, according to the GA construction algorithm, reliable bit channels are selected as information bits, and unreliable bit channels are selected as frozen bits. Here, the reliability and unreliability refer to the transmission data, and the N-K bits with a high error probability are unreliable and are frozen bits, while the K bits with a low error probability are reliable and are information bits.

[0042] S11, the code length N is selected, the information bit number is K+r, and the signal-to-noise ratio E b N0; then according to the GA construction algorithm, the Gaussian distribution variance of the additive white Gaussian noise (AWGN) channel is:

[0043]

[0044] S12, receive end LLR mean in AWGN channel is the i-th element of N-dimensional receive end LLR mean, i = 0, 1, …, N-1; wherein the initial condition is According to the recursive formula, each element of the receive end LLR mean is calculated:

[0045]

[0046] wherein

[0047]

[0048] S13, according to the S12 The index value of the largest K+r bits is selected as the information bit index, and the remaining index values are frozen bit indexes.

[0049] S2, the information bit most likely to occur the first error, i.e. the critical set, is obtained through code tree structure or Monte Carlo simulation;

[0050] (1) The information bit most likely to occur the first error, i.e. the critical set, is obtained through code tree structure, and the specific steps are as follows:

[0051] S21, the information bit index and the frozen bit index obtained by S1 are arranged in index order to form a set Γ;

[0052] S22, the set Γ is a leaf node of a depth n = log2N binary tree, wherein the leaf node corresponding to the information bit index is assigned a value of 1, and the leaf node corresponding to the frozen bit index is assigned a value of 0;

[0053] S23, in the binary tree created in S22, the first leaf node index in the sub-binary tree with all leaf node values of 1 is selected to form a critical set CS in index order.

[0054] (2) The information bit most likely to occur the first error, i.e. the critical set, is obtained through Monte Carlo simulation, and the specific steps are as follows:

[0055] Refer to Figure 2 , Figure 2 The process diagram for generating the critical set by Monte Carlo simulation is shown in the figure.

[0056] S201, the information bit index and the frozen bit index obtained by S1 are arranged in index order to form a set Γ;

[0057] S202, the information bit index in the set Γ is assigned values of 0 and 1 with equal probability, and the frozen bit index is assigned a value of 0 to form an input vector U, and the input vector U is BPSK modulated to obtain an output vector

[0058] S203, serial cancellation (SC) decoding is performed on the obtained output vector The index of the first error bit is found by comparing the input vector U, the index is recorded, and the index is repeatedly executed m (m is the number of Monte Carlo simulation times) times, and the index is sequentially composed into a key set CS.

[0059] S3, the CRC polynomial is selected for the key set, and the obtained CRC check vector is appended to the end of the information bit vector.

[0060] S31, according to the code length N, the information bit number K+r and the key set size |CS|, the CRC code length r is selected, and finally the value of the actual information bit number K to be transmitted is obtained, and in general case, the CRC length protected by the key set is smaller than the conventional CRC length.

[0061] S32, the set Γ obtained from S21 is composed, the first K information bits in the set Γ are transmitted to the data (0 or 1) to be sent, and the frozen bits are fixed as 0, and the input vector Un is composed; the data in the input vector Un information bit belonging to the key set CS is arranged in the index order as CC.

[0062] S33, the CC obtained by S32 is extended by r bits to CR, the extended bits are all assigned as 0, and are placed at the end of CR.

[0063] S34, the CR obtained by S33 is subjected to modulo 2 division with the CRC polynomial, and the r-bit remainder is sequentially placed in the last r information bits of the input vector Un.

[0064] In the embodiment, N=1024, K=512, for SC-Oracle decoding, CRC16 is a postfixed CRC code length r=16; CS-CRC8 is a CRC code length r=8 protected by the key set of the application.

[0065] S4, a Polar code encoding method is used to encode the pre-encoded vector. For the generator matrix The nth Kronecker product of the polarization matrix The Polar code encoding can be obtained by the formula to obtain the encoding vector Xn:

[0066] The effect of the application is as follows Figure 3 And Figure 4 .

[0067] Figure 3Fig. 2 is a graph of the block error rate curves of SC and SC-Oracle under different signal-to-noise ratios, wherein w is the number of error correction bits of SC-Oracle decoding, w = 1 represents the lower bound of the block error rate of SC-Flip-1, the code length N = 1024, the actual number of information bits K = 512, and the CRC code length r = 8. As shown in the figure, SC-Oracle decoding can know the position of the error, then correct the corresponding w bits, and the lower bound of the block error rate of SC-Flip-w can be obtained through Monte Carlo simulation. When w = 0 in the figure, it is actually equivalent to SC decoding of information bits K + r. It can be seen that when the number of information bits is increased, the corresponding block error rate will be reduced. When one bit of error needs to be corrected in the figure, the theoretical value that can be achieved by using the present application is shown.

[0068] Figure 4 Fig. 3 is a graph of the block error rate curves of SC-Flip under different CRC methods under different signal-to-noise ratios, wherein the number of attempts of SC-Flip decoding is T = 10, and SC-Flip-1 is a decoding algorithm for correcting one error. As shown in the figure, the method of the present application is 0.1 dB better than the conventional CRC cascade method in SC-Flip-1.

[0069] The above description of disclosed embodiments enables one of ordinary skill in the art to make or use the application. Various modifications to these embodiments will be readily apparent to those of ordinary skill in the art, and the generic principles defined herein can be applied to other embodiments without departing from the spirit or scope of the application. Accordingly, the application is not to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for encoding a CRC concatenated Polar code with key-set protection, characterized in that, The method comprises the following steps: S1, selecting reliable bit channels as information bits and unreliable bit channels as frozen bits according to a GA construction algorithm; S2, obtaining a key set by using a code tree structure or Monte Carlo simulation according to the obtained information bits and frozen bits; the specific steps of obtaining the key set by using the code tree structure are as follows: S21, obtaining the information bit index and the frozen bit index by S1 to form a set in index order ; S22, the set for depth Leaf nodes of the binary tree, N being the code length, wherein the leaf node corresponding to the information bit index is assigned a value of 1 and the leaf node corresponding to the frozen bit index is assigned a value of 0; S23, in the binary tree created in S22, the first leaf node index in all the sub-binary trees whose leaf node values are all 1 is selected to form a key set in index order ; S3, selecting a CRC polynomial to perform CRC precoding on the key set, and appending a CRC check vector obtained to the end of an information bit vector; the specific steps include the following steps: S31, according to the code length , the number of information bits and the size of the key set selected CRC code length , finally get the actual information bits to be transmitted the number of bits value; S32, the set middle front Information bits to send data, frozen bits fixed to 0, the input vector ; the input vector Information bits belong to the key set Data is arranged in index order as ; S33, the obtained backwards expansion is performed bit is , the expanded bits are all assigned 0, and placed at the end; S34, the obtained modular 2 division with CRC polynomial, obtaining bit remainder is placed in the input vector end bit information bit; S4, encoding the precoding vector by using a Polar code encoding method.

2. The CRC concatenated Polar code encoding method of key set protection according to claim 1, characterized in that, The specific steps of S1 are as follows: S11, selected code length , information bit number , construct signal-to-noise ratio ; then according to the GA construction algorithm, the Gaussian distribution variance of the AWGN channel is: S12, receiving end LLR mean value in AWGN channel For the first element of the receiving end LLR mean value, ; wherein the initial condition is ; the recursive formula of the algorithm according to GA can calculate each element of the receiving end LLR mean value: Wherein ； S13, derived from S12 Select the largest The index value for the first bit is the information bit index, and the index values ​​for the remaining bits are the freeze bit indexes.

3. The CRC concatenated Polar code encoding method of key set protection according to claim 2, characterized in that, The specific steps of obtaining the key set by using Monte Carlo simulation in S2 are as follows: S201, obtaining the information bit index and the frozen bit index by S1 to form a set in index order ; S202、by the resulting set , the information bit index is assigned 0 and 1 with equal probability, while the frozen bit index is assigned 0, to form an input vector , and it is BPSK modulated to get the output vector ;​ S203, SC decoding is performed, and the obtained output vector is compared with the input vector to find the index of the first error bit, record the index, and repeat the execution , and the index is sequentially composed into a key set .

4. The CRC concatenated Polar code encoding method of key set protection according to claim 1, characterized in that, S4 is specifically: for a generator matrix is a polarizing matrix the first kronecker product; Polar code encoding can be derived from the formula to encode the vector : .

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