Hierarchical scheduling decoding method for 5GLDPC codes

Abstract

The invention provides a 5G LDPC (Low Density Parity Check Code) hierarchical scheduling decoding method. The 5G LDPC hierarchical scheduling decoding method comprises the following steps: step 1, setting and respectively representing an ith check node and a jth variable node in a PCM (Pulse Code Modulation); sums are set as messages from transmitted verification to variables and messages from transmitted variables to verification in the t-th iteration respectively; if yes, a posterior probability message of the jth coding bit in the tth iteration is represented, and a normalized minimum sum hierarchical decoding algorithm is executed; and step 2, generating a decoding updating sequence of each layer different from a natural sequence in the check matrix by adopting a hierarchical scheduling algorithm. According to the scheme, the average number of iterations of decoding is reduced while the decoding performance is improved, and the complexity of the decoding process is almost not required to be increased in the improvement.

Description

TECHNICAL FIELD

[0001] The present application relates to a 5G LDPC code layered scheduling decoding method. BACKGROUND

[0002] Channel coding technology is one of the important supporting technologies of modern digital communication systems, which enhances the reliability of transmitted information by adding certain redundant information in the information sequence. In 1948, Shannon proposed the famous channel coding theorem: when the capacity of the channel is C, there is a channel coding scheme with infinite code length and transmission rate of C that can make the error rate of such coding in the transmission process infinitely small. After Shannon proposed the channel coding theorem, many scholars began to search for good coding schemes according to this theorem, during which some valuable code types appeared: Hamming code, Reed-Solomon (RS) code, Turbo code, Low-Density Parity-Check (LDPC) code and Polar code. LDPC code was proposed by Dr. Gallager in the 1960s, since it was rediscovered in 1995, it has received widespread attention from academia and industry because of its ability to provide near-Shannon capacity performance and easy hardware implementation, and it has become one of the research hotspots in the field of channel coding. In 2016, the Third Generation Partnership Project (3GPP) determined LDPC code as the encoding scheme for data channels in the standard of the fifth generation (5G) mobile communication system. The 5G mobile communication system has the characteristics of high rate, low latency and large connection capacity, and has become one of the core supporting technologies in application scenarios such as automatic driving, smart city, intelligent medical treatment and industrial Internet of Things, greatly changing our way of life and production.

[0003] The layered belief propagation (LBP) decoding algorithm for LDPC codes is introduced in the document “D. Hocevar, “A reduced complexity decoder architecture via layered decoding of LDPC codes,” in Proc. IEEE Workshop on Signal Process. Syst. (SiPS), Oct. 2004, pp. 107-112”. The LBP algorithm has the advantages of good decoding performance, fast decoding convergence speed, and less resource consumption in hardware implementation, and has been widely used in practice. However, the current LBP algorithm mainly schedules each layer according to the natural order of the check matrix, and does not optimize the characteristics of the check matrix of the 5G LDPC code, such as irregular row weight and the existence of punctured bits. In order to solve this problem, the document “K. Tian and H. Wang, “A novel base graph based static scheduling scheme for layered decoding of 5G LDPC codes,” IEEE Commun. Lett., vol. 26, no. 7, pp. 1450-1453, Jul. 2022” proposes a base graph based static scheduling (BGSS) scheme. The decoding priority of the BGSS scheduling algorithm is: 1) first update the layer with less punctured bits (LP). 2) secondly update the layer with lower degree (LD). 3) for those layers with the same number of punctured bits and degree, the layer that can utilize the latest information is updated first (the specific mechanism can be further referred to the document “K. Tian and H. Wang, “A novel base graph based static scheduling scheme for layered decoding of 5G LDPC codes,” IEEE Commun. Lett., vol. 26, no. 7, pp. 1450-1453, Jul. 2022”). The BGSS scheduling scheme significantly improves the decoding performance and reduces the average number of iterations of BP decoding based on the LBP algorithm. SUMMARY

[0004] The technical problem solved by the present application is to provide a 5GLDPC code hierarchical scheduling decoding method, which overcomes the shortcomings of the prior art.

[0005] Step 1, setting and respectively represent the i-th check node and the j-th variable node in the check matrix PCM ; let and be the check-to-variable messages and the variable-to-check messages from to and from to in the t-th iteration, respectively; represent the posterior probability messages of the j-th encoded bit in the t-th iteration, and the normalized min-sum hierarchical decoding algorithm is executed;

[0006] Step 2, a decoding update order of each layer different from the natural order in the check matrix is generated by using a hierarchical scheduling algorithm.

[0007] In step 1, the normalized min-sum hierarchical decoding algorithm comprises the following steps:

[0008] Step 1-1, initialization: setting the channel log-likelihood ratio (LLR) of the j-th encoded bit as , setting the initial a posteriori probability (APP) message of the j-th encoded bit as , and setting the initial check-to-variable (C2V) message of the i-th check node to the j-th variable node as ;

[0009] Step 1-2, iterative decoding: setting the variable-to-check message of the j-th variable node to the i-th check node in the t-th iteration as , setting the posterior probability message of the j-th encoded bit in the t-th iteration as , setting the check-to-variable message of the i-th check node to the j-th variable node in the t-1-th iteration as , and setting the variable-to-check message of the k-th variable node to the i-th check node in the t-th iteration as ;

[0010] Step 1-3, hard decision.

[0011] In step 1-1, the decoder initializes the a posteriori probability (APP) message and the check-to-variable (C2V) message in the following manner after receiving the channel log-likelihood ratio (LLR):

[0012] (1),

[0013] (2),

[0014] in , , ; Indicates and verifies the node The set of indices of connected variable nodes, where N and M represent the number of variable nodes and check nodes, respectively.

[0015] In steps 1-2, after initialization, the iterative decoding process begins. In the t-th iteration, the variables are first updated to the verification message V2C message in the following manner:

[0016] (3),

[0017] Then update the C2V message as follows:

[0018] (4),

[0019] in It is a normalization factor used to alleviate the problem of C2V message overestimation. express Remove index j from the set;

[0020] After the C2V message is updated, update the APP message as follows:

[0021] (5).

[0022] Steps 1-3 include: setting the decision result of the j-th encoded bit in the t-th iteration as follows: The parity-check matrix of the LDPC code is set as follows: After all layers in the parity check matrix are updated using formulas (3) to (5), each bit is judged as follows:

[0023] (6),

[0024] Repeat steps 1-2 to 1-3 until the codeword for the decision is reached. satisfy Or the number of decoding iterations has reached the preset maximum number of iterations. , where T represents the matrix transpose.

[0025] Step 2 includes:

[0026] Step 2-1: Execute the delayed update strategy for the core matrix;

[0027] Step 2-2: Execute the real-time decoding information-assisted scheduling strategy.

[0028] Step 2-1 includes: using the natural order of the layers in the parity-check matrix as the basic decoding order set D, and then using the Least Degree (LD) rule to obtain another decoding order set L and the first q layers in L. , recorded as ,in This represents the q-th layer in L; the minimum row weight LD rule means that layers with smaller row weights are decoded and updated first.

[0029] The iterative process of the delayed update strategy for the core matrix is ​​divided into the following three stages:

[0030] Phase One: Before In this iteration, the layers in the core matrix of the first q layers of the basic decoding sequence set D are not updated. The layers in the core matrix of the first q layers of the basic decoding sequence set D are denoted as core layers, and their positions are sequentially determined using... Fill, in the order of the obtained set Decode and update all layers in the parity check matrix;

[0031] Phase Two: Until the In the next iteration, all layers in the parity-check matrix are decoded and updated according to the basic decoding order set D; ;

[0032] Phase Three: In the End In this iteration, the basic decoding order set will be... Remove, and then Fill in the corresponding core layers removed in the first stage at the specified positions to obtain the decoding sequence set. Then, according to the decoding order set... Perform decoding updates.

[0033] Step 2-2 includes: After each iteration, the hierarchical belief propagation decoding algorithm performs parity checking on each layer of the parity-check matrix and generates a corrector. After each iteration, it counts the number of zero elements in the region of the corrector corresponding to each layer, denoted as S. Then, it calculates a heuristic metric for each layer. :

[0034] (7),

[0035] Where W represents the row weight corresponding to each level;

[0036] After the calculation is completed, apply the following to each layer: The sizes are sorted in ascending order to obtain the decoding update order (decoding order set) for the next iteration process;

[0037] Set the basic decoding order set D in step 2-1 to the decoding order set generated by the strategy in step 2-2.

[0038] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0039] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0040] Beneficial effects: This scheme introduces two new technical strategies while continuing to use the LD rules of existing schemes: a delayed update strategy for the core matrix and a real-time decoding state information assistance strategy. Compared with existing schemes, this scheme improves decoding performance while reducing the average number of decoding iterations, and this improvement requires almost no increase in the complexity of the decoding process. Attached Figure Description

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0042] Figure 1 This is a schematic diagram of the decoding sequence generated by the existing scheme.

[0043] Figure 2 This is a schematic diagram of the decoding sequence generated by this scheme.

[0044] Figure 3 This is a diagram comparing the frame error rates of the existing scheme and this scheme.

[0045] Figure 4 This is a diagram comparing the average number of decoding iterations between existing and proposed solutions.

[0046] Figure 5 This is a flowchart illustrating the method of this solution. Detailed Implementation

[0047] This invention provides a hierarchical scheduling decoding method for 5GLDPC codes. This scheme employs a hierarchical decoding algorithm based on Normalized Min-Sum (NMS). The hierarchical decoding algorithm updates each layer of the parity-check matrix in a specific order, utilizing the latest information from the previous layer to update the next layer, resulting in faster convergence. Assuming... and Represented as PCM Let the i-th check node and the j-th variable node be defined. and From the t-th iteration respectively Passed to The check-to-variable (C2V) message and from Passed to The variable-to-check (V2C) message. This represents the j-th encoded bit in the t-th iteration. The posterior probability (APP) message. The implementation process of the normalized minimum and hierarchical decoding algorithm is shown below.

[0048] (A) Initialization: Set the channel log-likelihood ratio (LLR) of the j-th coded bit to 1. After receiving the LLR channel, the decoder initializes the APP message and C2V message as follows:

[0049] (1),

[0050] (2),

[0051] in , , , Indicates and verifies the node The set of indices of connected variable nodes, where N and M represent the number of variable nodes and check nodes, respectively.

[0052] (B) Iterative Decoding: After initialization, the iterative decoding process begins. In the t-th iteration, the V2C message is first updated in the following way:

[0053] (3),

[0054] Then update the C2V message as follows:

[0055] (4),

[0056] in It is a normalization factor used to alleviate the problem of C2V message overestimation. express Remove index from collection After the C2V message is updated, update the APP message as follows:

[0057] (5),

[0058] (C) Hard decision: After all layers have been updated using formulas (3) to (5), each bit is decided as follows:

[0059] (6),

[0060] Steps (B) and (C) above are executed repeatedly until the codeword of the decision is reached. Meets the verification conditions Or the number of decoding iterations has reached the preset maximum number of iterations. .

[0061] 3. High-performance hierarchical scheduling algorithm

[0062] This scheme, based on the normalized minimum and hierarchical decoding algorithms, employs a high-performance hierarchical scheduling algorithm to generate a decoding update order for each layer that differs from the natural order in the parity-check matrix. This scheduling algorithm mainly includes the following two strategies.

[0063] (A) Delayed update strategy for the core matrix

[0064] This strategy first uses the natural order of the layers in the parity-check matrix (or the decoding order generated by other scheduling schemes) as the basic decoding order set D, and then uses the LD rule (layers with smaller row weights are decoded and updated first) to obtain another decoding order set L and the first q layers in it. ), denoted as The iterative process of this strategy consists of three stages: 1) in the initial stage... In this iteration, the layers in the core matrix of the first q layers of the basic decoding sequence set D (hereafter referred to as the core layers) are not updated, and their order positions are sequentially updated using... Fill, in this order of the obtained set Decode and update each layer. 2) Then, until the... ( In the next iteration, each layer is decoded and updated according to the basic decoding order set. 3) In the final... In this iteration, the basic decoding order set will be... These layers are removed and then replaced with the corresponding core layers removed in the first stage, and assembled in this order. Perform decoding updates. All of the above operations can be completed offline, so they do not introduce additional decoding complexity during actual decoding.

[0065] It is worth noting the parameters in the above process. , , Rough optimization can be performed by comparing decoding performance through simulation experiments. The optimization method is as follows. Initially, simply set q to 4. Subsequently, simulation can determine ( , The optimal combination of ). Obviously, if If it is 10, then It can be set to 1, 2, 3, 4, 5, corresponding to The values ​​are 9, 8, 7, 6, and 5 respectively. Assume the simulation results show that ( , The best combination is () , Then the next step can be () , With q fixed at 2 and 8, the values ​​of q (1~4) are adjusted to further simulate and compare decoding performance. Finally, a set of superior ( , , ) Parameter combination.

[0066] The core principle of the delayed update strategy of the core matrix is ​​that the degree distribution of nodes in 5G LDPC codes is extremely irregular. In BG1 (BG2), the degree of variable nodes ranges from 1 to 30 (23), with core variable nodes having a higher degree and extended variable nodes having a degree of 1. According to the hierarchical scheduling decoding, core variable nodes with higher degrees have more adjacent check nodes, so they are updated more frequently in one iteration. Therefore, these variable nodes usually exhibit a large posterior probability message, which can be called a strong message. When a strong message is wrong and its magnitude is too high, it will seriously hinder the correction of other variable nodes, resulting in a slower convergence speed. In the first few iterations, this scheme replaces some layers (with higher node degrees) in the core matrix with layers with lower degrees. Due to the inherently highly dense core matrix of 5G LDPC codes, a large number of core variable nodes are associated with layers in the core matrix. And the core variable nodes with low degree layer associations used for replacement are much fewer. Therefore, when the layers in these core matrices are replaced with low-degree layers, the update frequency of posterior probability messages corresponding to a large number of core variable nodes is significantly reduced, thus suppressing the growth of strong messages in the initial iterations. When erroneous strong messages are effectively suppressed, their negative impact on the correction of other variable nodes is weakened, thereby accelerating overall convergence.

[0067] All existing solutions update all layers in the verification matrix completely in each iteration, while our solution breaks this conventional thinking.

[0068] (B) Real-time decoding information-assisted scheduling strategy

[0069] The normalized minimum sum hierarchical decoding algorithm performs parity checking on each layer of the parity-check matrix after each iteration and generates a corrector. This strategy counts the number of zero elements in the region of the corrector for each layer after each iteration, denoted as S. Then, a heuristic metric is calculated for each layer. The calculation method is as follows:

[0070] (7),

[0071] Where W represents the row weight corresponding to each level. After calculation, each level is sorted by... The decoding update order for the next iteration is obtained by sorting the values ​​in ascending order. Since the decoding update order of each layer is generated online after one iteration, and the metric S, which reflects the decoding convergence of the layers in the parity-check matrix in real time, is also considered, this strategy can provide some real-time decoding information to assist in scheduling decoding. Therefore, this strategy can be understood as a semi-dynamic scheduling scheme (different from the classic dynamic scheduling decoding algorithm). Since there are punctured bits in 5G LDPC codes, the first iteration of this strategy uses the BGSS scheduling scheme to quickly recover the missing information of punctured bits. Except for the first iteration, each subsequent iteration generates the decoding order set of each layer in the above manner. Although the real-time decoding information-assisted scheduling strategy introduces additional decoding complexity, this additional complexity is negligible because the number of indicators that need to be sorted and the number of multiplication operations (which can be further simplified to addition and shift operations) are exactly equal to the number of layers (this number is much smaller than the number of operations in the normalized minimum and layered decoding algorithms).

[0072] Combining strategy (A) and strategy (B) described here constitutes the solution of this invention. Specifically, it is only necessary to set the basic decoding order set D in (A) to the decoding order set generated by strategy (B). For a detailed flowchart, please refer to [link / reference]. Figure 5 .

[0073] This embodiment considers the first 1 to 10 layers of the 5G LDPC codewords of a parity-check matrix generated from a corresponding BG1 matrix. The decoding update order of each layer in the 1st, 5th, and 8th iterations is as follows: Figure 2 As shown. Figure 1 This is the decoding update order generated by the existing BGSS scheme. Figure 2 This is the decoding update order generated by this scheme, where the parameter combination used in this scheme is ( , , ).

[0074] Figure 2The gray circles in the diagram represent decoding order changes caused by the delayed update strategy of the core matrix. From... Figure 1 , Figure 2 As can be seen, there are significant differences between the decoding scheduling order of the first, fifth, and eighth iterations generated by BGSS in this scheme and the existing scheme.

[0075] Consider a 5G LDPC codeword (corresponding to a BG2 matrix) with K=3840 and R=1 / 3. Its performance is measured using Monte Carlo simulation, where QPSK modulation is used, the transmission channel is an AWGN channel, and the normalization factor of the NMS decoding algorithm is set to... The parameter combination of the scheduling algorithm in this scheme is set as follows: , , ). Figure 3 Simulation curves of the frame error rate (FER) for the existing BGSS scheme and the scheduling algorithm of this scheme are presented. Figure 4 Simulation curves of the average number of decoding iterations (ANI) for the existing scheme BGSS and the scheduling algorithm of this scheme are presented. The calculation method of ANI is as follows.

[0076] (8),

[0077] Where F is the total number of frames (total number of codewords) in the simulation test. This represents the number of decoding iterations for the LDPC code in the i-th frame.

[0078] From Figure 3 and Figure 4 As can be seen from the data, the algorithm in this proposal is superior to existing solutions in terms of performance. There is approximately a 0.2dB performance gain at the same time. This scheme reduces the average number of decoding iterations by approximately 0.8 compared to existing schemes. This demonstrates that this scheme not only significantly improves decoding performance but also greatly reduces the average number of decoding iterations, thus helping to reduce the average decoding latency and power consumption.

[0079] This invention provides a hierarchical scheduling decoding method for 5GLDPC codes. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A hierarchical scheduling decoding method for 5GLDPC codes, characterized in that, Includes the following steps: Step 1, Setting and These are represented as checksum matrices PCM. The i-th check node and the j-th variable node in the array; let and From the t-th iteration respectively Passed to Validation of variable messages and from Passed to The variable is sent to the verification message; This represents the j-th encoded bit in the t-th iteration. The posterior probability message is used to perform a normalized minimum sum hierarchical decoding algorithm; Step 2: A hierarchical scheduling algorithm is used to generate a decoding update order for each layer that is different from the natural order in the parity check matrix.

2. The method according to claim 1, characterized in that, In step 1, the normalized minimum sum hierarchical decoding algorithm includes the following steps: Step 1-1, Initialization: Set the channel log-likelihood ratio (LLR) of the j-th coded bit to 1. Let the initial posterior probability of the j-th encoded bit be the APP message. Set the initial verification to variable C2V message from the i-th verification node to the j-th variable node as follows: ; Step 1-2, Iterative Decoding: Set the variable to verification message from the j-th variable node to the i-th verification node in the t-th iteration as... Let the posterior probability message of the j-th encoded bit in the t-th iteration be... Let the verification-to-variable message from the i-th verification node to the j-th variable node in the (t-1)-th iteration be... Let the variable to check message in the k-th variable node to the i-th check node in the t-th iteration be... ; Steps 1-3, hard decision.

3. The method according to claim 2, characterized in that, In step 1-1, after receiving the channel log-likelihood ratio (LLR), the decoder initializes the posterior probability (APP) message and the check to variable (C2V) message as follows: （1）， （2）， in , , ; Indicates and verifies the node The set of indices of connected variable nodes, where N and M represent the number of variable nodes and check nodes, respectively.

4. The method according to claim 3, characterized in that, In steps 1-2, after initialization, the iterative decoding process begins. In the t-th iteration, the variables are first updated to the verification message V2C message in the following manner: （3）， Then update the C2V message as follows: （4）， in It is a normalization factor used to alleviate the problem of C2V message overestimation. express Remove index j from the set; After the C2V message is updated, update the APP message as follows: （5）。 5. The method according to claim 4, characterized in that, Steps 1-3 include: setting the decision result of the j-th encoded bit in the t-th iteration as follows: The parity-check matrix of the LDPC code is set as follows: After all layers in the parity check matrix are updated using formulas (3) to (5), each bit is judged as follows: （6）， Repeat steps 1-2 to 1-3 until the codeword for the decision is reached. satisfy Or the number of decoding iterations has reached the preset maximum number of iterations. , where T represents the matrix transpose.

6. The method according to claim 5, characterized in that, Step 2 includes: Step 2-1: Execute the delayed update strategy for the core matrix; Step 2-2: Execute the real-time decoding information-assisted scheduling strategy.

7. The method according to claim 6, characterized in that, Step 2-1 includes: using the natural order of the layers in the parity-check matrix as the basic decoding order set D, and then using the minimum row weight LD rule to obtain another decoding order set L and the first q layers in L. , recorded as ,in This represents the q-th layer in L; the minimum row weight LD rule means that layers with smaller row weights are decoded and updated first. The iterative process of the delayed update strategy for the core matrix is ​​divided into the following three stages: Phase One: Before In this iteration, the layers in the core matrix of the first q layers of the basic decoding sequence set D are not updated. The layers in the core matrix of the first q layers of the basic decoding sequence set D are denoted as core layers, and their positions are sequentially determined using... Fill, in the order of the obtained set Decode and update all layers in the parity check matrix; Phase Two: Until the In the next iteration, all layers in the parity-check matrix are decoded and updated according to the basic decoding order set D; ; Phase Three: In the end In this iteration, the basic decoding order set will be... Remove, and then Fill in the corresponding core layers removed in the first stage at the specified positions to obtain the decoding sequence set. Then, according to the decoding order set Perform decoding updates.

8. The method according to claim 7, characterized in that, Step 2-2 includes: After each iteration, the hierarchical belief propagation decoding algorithm performs parity checking on each layer of the parity-check matrix and generates a corrector. After each iteration, it counts the number of zero elements in the region of the corrector corresponding to each layer, denoted as S. Then, it calculates a heuristic metric for each layer. : （7）， Where W represents the row weight corresponding to each level; After the calculation is completed, apply the following to each layer: The sizes are sorted in ascending order to obtain the decoding update order for the next iteration. Set the basic decoding order set D in step 2-1 to the decoding order set generated by the strategy in step 2-2.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, It stores a computer program or instructions that, when run on a computer, perform the steps of the method as described in any one of claims 1 to 8.

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