Polar Code Serial Cancellation Decoding Algorithm Modified by Simulated Annealing Algorithm

Abstract

The present invention discloses a polar code serial offset decoding algorithm modified by a simulated annealing algorithm. The specific technical scheme is as follows: first, SC decoding is performed in units of frames, and the decoding result is subjected to CRC detection. If the detection is passed, the next frame is decoded, otherwise, it is handed over to the simulated annealing algorithm for correction; the simulated annealing algorithm calculates the corresponding initial likelihood value for the bit in a frame, and arranges the absolute value of the likelihood value corresponding to the information bit part in ascending order, and executes the simulated annealing algorithm; the result of the simulated annealing algorithm is subjected to CRC detection. If the detection is passed, the next frame is decoded, otherwise the decoding is declared to have failed. The present invention enhances the error correction capability of the polar code when the code is short, improves its reliability and maintains a low decoding delay.

Description

Technical Field

[0001] The invention belongs to the technical field of communication and relates to a polar code serial cancellation decoding algorithm modified by a simulated annealing algorithm. Background Art

[0002] Polar codes are the first coding technology that can be mathematically proven to reach the capacity limit of a binary discrete memoryless channel. Due to its low complexity in both coding and decoding, it has been a research hotspot in the industry for the past decade and was successfully selected as the coding standard for the control channel in the 5G enhanced mobile broadband (eMBB) scenario in 2016.

[0003] Although the performance of polar codes under the SCL (Successive Cancellation list, SCL) decoding algorithm with cyclic redundancy check (CRC) and large list width can reach the performance of some optimized LDPC codes, the serial mechanism will lead to high latency and high complexity of hardware implementation. With the development of Internet of Things technology and blockchain technology, a large number of IoT devices require an effective transmission mechanism, and these devices require low-power, low-cost, and low-complexity hardware implementation. Obviously, SCL-CRC cannot meet the needs of this scenario.

[0004] Current hot AI technologies such as autonomous driving and telemedicine require ultra-high reliability and ultra-low latency for transmission, so the transmitted code length is short. However, various improved algorithms based on SC decoding have poor performance when the code length is too short due to the unclear channel polarization effect, and the high latency and low output caused by the serial decoding mechanism cannot meet the needs of high reliability and low latency scenarios, and need further optimization.

[0005] The Belief Propagation (BP) decoding algorithm is another basic decoding algorithm for polar codes. This algorithm is a soft output decoding and can decode in parallel. Compared with other decoding algorithms, it is more reliable and stable than the SCL algorithm, and is more conducive to the application of polar codes in turbo equalization of channels with internal symbol interference. However, soft decision decoding algorithms generally obtain the optimal solution through exhaustive search, which is difficult to apply to occasions with a large solution space.

[0006] In response to the above problems, scholars have used some intelligent optimization algorithms such as generalized minimum distance decoding, genetic algorithm, Chase-2 and neural network algorithms for decoding. Among them, the simulated annealing algorithm is also used to find reasonable solutions in large-scale combinatorial optimization problems. Because it can converge to the global optimal solution in theory, the present invention uses it in the correction process of polar code SC decoding results to improve the performance of polar code SC decoding while maintaining low decoding complexity and delay. Summary of the invention

[0007] The object of the present invention is to provide a polar code serial cancellation decoding algorithm modified by a simulated annealing algorithm.

[0008] The technical solution adopted by the present invention is:

[0009] The polar code serial cancellation decoding algorithm modified by simulated annealing algorithm comprises the following steps:

[0010] Step 1: The sender sends the information sequence u=(u0,u1,...,u N-1 ) is polarized and encoded. After the receiving end receives the sequence stream transmitted from the channel, it decodes it in units of frames. First, a frame y=(y0,y1,...y N-1 ) Use SC to decode, the decoding result Submit it to CRC for detection. If the detection passes, the decoding of the frame is completed and the decoding of the next frame is carried out. Otherwise, it is submitted to the simulated annealing algorithm for correction;

[0011] Step 2: Receive the decoding result After that, for y=(y0,y1,...y N-1 ) in the bit calculation corresponding to the initial likelihood value and sorting, and executing the simulated annealing algorithm;

[0012] Step 3: Take the output of the simulated annealing algorithm as u = (u0, u1, ..., u N-1 ) is sent to the CRC detector for detection. If it passes, the decoding of the frame is completed and the decoding of the next frame is carried out. Otherwise, the decoding is declared a failure.

[0013] The specific process of step 2 is as follows:

[0014] (1) For y=(y0,y1,...y N-1 ) and arrange the absolute values ​​of the likelihood values ​​corresponding to the information bits in ascending order to obtain the vector LLR_I. The subscripts corresponding to the information bits arranged in this order form the vector A.

[0015] (2) Generate new neighbors: Flip each bit with a certain probability based on LLR_I and A vectors The bits in , each iteration flips one bit to get a new neighbor solution, the implementation function corresponding to this step is

[0016] (3) Accepting a new solution with a certain probability: Calculate the energy of the new solution and the current solution respectively, and then accept the new solution with a certain probability.

[0017] The beneficial effects of the present invention are:

[0018] The existing polar code SC decoding algorithm and the improved decoding algorithm based on SC currently cannot provide low-latency and high-performance error correction capabilities when the code is short. The present invention aims to enhance the error correction capability of the polar code when the code is short, improve its reliability and maintain a low decoding delay, so as to better adapt to the needs of the two major scenarios under 5G. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flow chart of the method of the present invention;

[0020] Figure 2 is an information processing process diagram of the present invention;

[0021] Figure 3 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 8 and the code rate is 0.5;

[0022] Figure 4 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 16 and the code rate is 0.5;

[0023] Figure 5 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 32 and the code rate is 0.5;

[0024] Figure 6 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 64 and the code rate is 0.5;

[0025] Figure 7 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 8 and the code rate is 0.75;

[0026] Figure 8 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 16 and the code rate is 0.75;

[0027] Fig. 9 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 32 and the code rate is 0.75;

[0028] Fig.10 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 64 and the code rate is 0.75;

[0029] Fig.11 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 8 and the code rate is 0.35;

[0030] Fig.12 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 16 and the code rate is 0.35;

[0031] Fig.13 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 32 and the code rate is 0.35;

[0032] Fig.14 This is a performance comparison chart of the present invention and other common decoding algorithms when the code length is 64 and the code rate is 0.35. DETAILED DESCRIPTION

[0033] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0034] The SC decoding algorithm is the most important and basic decoding algorithm for polar codes. Only under this decoding algorithm can polar codes reach the channel capacity limit when the code length tends to infinity. Therefore, based on the SC decoding algorithm, the simulated annealing algorithm is used to correct the decoding results of SC, thereby improving the overall error correction capability. The basic principle of the SC decoding algorithm is bit-by-bit decoding. The likelihood value of each bit is calculated from right to left according to the coding diagram. The decoding result of the current bit is used to calculate the likelihood value of the next bit. It is a serial decoding mechanism. The simulated annealing algorithm is derived from the principle of solid annealing. It is a probability-based algorithm. Its basic idea is to start from a higher initial temperature and gradually reduce the temperature until the temperature is reduced to meet the thermal equilibrium condition. At each temperature, n rounds of search are performed. In each round of search, random perturbations are added to the old solution to generate a new solution, and the new solution is received according to certain rules. Because the simulated annealing algorithm receives the old solution according to a certain probability, there is a certain probability to jump out of the local optimal solution and find the global optimal solution.

[0035] The main steps of the method of the present invention are as follows Figure 1 Shown

[0036] Step 1: The sender sends the information sequence u=(u0,u1,...,u N-1 ) is used to encode the polarization code. After the receiving end receives the sequence stream transmitted from the channel, it decodes it in units of frames. First, a frame y=(y0,y1,...y N-1 ) Use SC to decode, the decoding result It is sent to CRC for detection. If the detection passes, the decoding of the frame is completed and the decoder starts to decode the next frame. Otherwise, it is sent to the simulated annealing algorithm for correction.

[0037] The key calculation formulas involved in the SC decoding process are as follows:

[0038]

[0039] here

[0040]

[0041] If the subscript is an odd number,

[0042]

[0043] otherwise

[0044]

[0045] Step 2: The simulated annealing algorithm receives the decoding result Then, perform the following process:

[0046] (1) For y=(y0,y1,...y N-1 ) and arrange the absolute values ​​of the likelihood values ​​corresponding to the information bits in ascending order to obtain the vector LLR_I. The subscripts corresponding to the information bits arranged in this order form the vector A.

[0047] (2) Generate new neighbors: Flip each bit with a certain probability based on LLR_I and A vectors The bit in , flip one bit each iteration to get a new neighbor solution. The implementation function corresponding to this step is

[0048] (3) Accepting a new solution with a certain probability: Calculate the energy of the new solution and the current solution respectively, and then accept the new solution with a certain probability.

[0049] Step 3: Take the output of the simulated annealing algorithm as u = (u0, u1, ..., u N-1 ) is sent to the CRC detector for detection. If it passes, the decoding of the frame ends and the decoding of the next frame proceeds. Otherwise, the decoding fails.

[0050] Several key algorithm flows in the present invention are given below. First, the overall design algorithm flow of the method is shown in Algorithm 1.

[0051] Algorithm 1 Overall algorithm flow

[0052]

[0053] The overall algorithm process involves two key algorithms: SC decoding algorithm and simulated annealing algorithm

[0054] The SC algorithm is a conventional implementation and will not be introduced here. In the simulated annealing algorithm, a double loop is still used. The outer loop controls the temperature from high to low according to the attenuation coefficient; the temperature in the inner loop is fixed, random perturbations are added to the old solution to obtain a new solution, and the new solution is accepted according to certain rules. The number of iterations of the inner loop is called the Markov chain length.

[0055] The execution flow of the simulated annealing algorithm is as follows:

[0056]

[0057] However, unlike the neighbor generation method of the conventional simulation algorithm, the present invention does not simply perform bit flipping. The specific new neighbor generation process is shown in the algorithm new neighbor generation function Generate_neighbour(LLR_I,A) as follows:

[0058]

[0059] Evaluate(S n ,y)The algorithm is as follows:

[0060]

[0061] According to Evaluate(S n ,y) is used as the estimated energy. The algorithm then calculates the difference between the current solution and the new solution based on the Euclidean distance to measure which one is closer to the sequence before encoding, and selects it, which drives convergence to the global optimal solution.

[0062] In the above process, the entire information flow from the sender to the receiver is as follows: Figure 2 shown.

[0063] The data in Table 3 mainly count the number of incorrect results of SC results corrected by this method under different code lengths and different signal-to-noise ratios. These data show that this method has a good correction effect on improving SC decoding results.

[0064] Table 3.Number of refined results for SC decoder by SA

[0065]

[0066] The simulation results of this method are based on a binary additive white noise Gaussian channel as the experimental channel. Figures 3 to 6The performance comparison diagrams are respectively for code lengths of 8, 16, 32, 64 and code rates of 0.5, and for this method and other common decoding algorithms such as the BP algorithm and the SCL-CRC algorithm. It can be seen that this method has better performance, and the length of the least reliable information bit setting of this method is 4 or 8. Figures 7 to 10 The bit rate is 0.75. Figures 11 to 14 This is a performance comparison under a bit rate of 0.35, which shows that this method has better error correction capability regardless of high or low bit rates.

[0067]

[0068] The performance parameters of this method have been optimized and set, and the main parameters involved are shown in the table above.

[0069] These parameters can be tuned according to the experimental results. In short, it is ensured that the number of iterations is small, the convergence speed is fast, and the complexity is low on the basis of good performance. The complexity of this method is O(NlogN)+O(N i N c mN), where N i The number of iterations of the simulated annealing algorithm is a constant. N c is the number of iterations from the initial temperature to the final temperature. In order to compare the complexity of this method with other schemes, we counted the time it takes for the decoder to decode one frame. When the polar code is (8, 0.75), the decoding time of this method and the SC decoder are 1.84ms and 2ms respectively; when the polar code is (8, 0.35), the decoding time of the two decoders are 0.6ms and 1.6ms respectively. When the polar code is (32, 0.35), the decoding time of the two decoders is 1.9ms and 1.7ms respectively. Therefore, this method can achieve better decoding performance with lower complexity in short codes.

Claims

1. Polar code serial cancellation decoding algorithm modified by simulated annealing algorithm, characterized in that: The following steps are involved: Step 1: The sender sends the information sequence u=(u0,u1,...,u N-1 ) is polar code encoded. After the receiving end receives the sequence stream transmitted from the channel, it decodes it in units of frames. First, a frame y=(y0,y1,…y N-1 ) Use SC to decode, the decoding result Submit it to CRC for detection. If the detection passes, the decoding of the frame is completed and the decoding of the next frame is carried out. Otherwise, it is submitted to the simulated annealing algorithm for correction; Step 2: Receive the decoding result After that, for y=(y0,y1,…y N-1 ) in the bit calculation corresponding to the initial likelihood value and sorting, and executing the simulated annealing algorithm; Step 3: Take the output of the simulated annealing algorithm as u = (u0, u1, ..., u N-1 ) is sent to the CRC detector for detection. If it passes, the decoding of the frame is completed and the decoding of the next frame is carried out. Otherwise, the decoding is declared a failure.

2. The polar code serial cancellation decoding algorithm modified by simulated annealing algorithm according to claim 1, characterized in that: The specific process of step 2 is as follows: (1) For y=(y0,y1,…y N-1 ) and arrange the absolute values ​​of the likelihood values ​​corresponding to the information bits in ascending order to obtain a vector LLR_I. The subscripts corresponding to the information bits arranged in this order form a vector A. (2) Generate new neighbors: Flip each bit with a certain probability based on LLR_I and A vectors The bits in , each iteration flips one bit to get a new neighbor solution, the implementation function corresponding to this step is (3) Accepting a new solution with a certain probability: Calculate the energy of the new solution and the current solution respectively, and then accept the new solution with a certain probability.

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