An iterative detection and decoding method based on tree search

Abstract

The present invention discloses an iterative detection decoding method based on tree search, comprising: initializing a K-Best detector; obtaining a priori message L through a FastSOL decoder; A1 (s i ); perform the K-Best detector with the prior message L A1 (s i ) to obtain a symbol estimate sequence; the symbol estimate sequence is converted into a bit estimate sequence, which is output to the FastSOL decoder for FastSOL decoding to obtain a decoded result sequence; a determination is made as to whether the maximum number of iterations has been reached. If not, the decoded result sequence is output to the K-Best detector as a priori information; otherwise, detection and decoding are completed, and the corresponding FER performance data is output. This invention utilizes soft information exchange between the detection and decoding modules to achieve better reliability than separate detection and decoding (SDD). This solution is optimized to meet the requirements of error rate performance and complexity, achieving better error rate performance and lower complexity by adjusting the layer width and message exchange.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to an iterative detection decoding method based on tree search. Background Art

[0002] Future 6G scenarios place even higher demands on receiver reliability. Polar codes have been proven to reach channel capacity, enabling polar-coded multiple-input multiple-output (MIMO) systems to achieve superior frame error rate (FER) performance. Polar-coded iterative detection and decoding (IDD) receivers offer particularly impressive performance, primarily due to the message exchange between the detector and decoder.

[0003] The performance advantages of IDD receivers can be further enhanced by using high-performance detectors and decoders:

[0004] (1) For MIMO detectors, maximum likelihood detection is considered the optimal detection algorithm, but the complexity required is too high and difficult to implement. Tree-search-based detectors, such as sphere decoding (SD) detectors and K-Best detectors, can achieve a trade-off between performance and complexity through parameter tuning.

[0005] (2) For polar code decoders, the cyclic redundancy check aided successive cancellation list (CA-SCL) decoder is widely used due to its superior performance. However, it cannot iteratively provide soft messages, which makes it unsuitable for direct application in IDD receivers. To address this issue, researchers have proposed soft cancellation (SCAN) decoders and soft-output list (SOL) decoders, which can provide soft messages and thus serve as decoder modules for IDD receivers.

[0006] Existing polar code MIMO systems have the following problems:

[0007] 1) In traditional separate detection and decoding (SDD) receivers, the results of the detection module are unidirectionally input to the decoding module, while ignoring the message interaction between the two modules, which cannot ensure the high reliability of the system.

[0008] 2) Among existing IDD receivers, no polar code IDD receiver based on serial cancellation decoding (which fully complies with polar code encoding rules) has been implemented. This makes it difficult to achieve satisfactory high performance, and an effective trade-off between performance and complexity cannot be achieved by simply adjusting parameters, which makes hardware implementation difficult.

[0009] In existing IDD receivers, there is no solution that uses machine learning to optimize parameters. Existing solutions rely on the designer's expertise, and the empirical values ​​provided lack adaptability to different environments. The method is not universal and cannot achieve a more efficient "performance-complexity" trade-off.

[0010] Although tree search algorithms have shown excellent error rate performance in both detectors and decoders, their high complexity makes them difficult to be widely used. Previous studies have shown that one solution is to use empirical methods to reduce the layer width, such as non-constant K-Best (NC K-Best) detection and adaptive SCL (adaptive SCL) decoding. Another approach is to use neural networks for adaptive SCL decoding. In addition, segmented CA-SCL (SCA-SCL) reduces computational complexity by verifying the correctness of the path in the middle of the decoding process. Researchers have also proposed a scheme for designing the adaptive SCL decoding layer width using a genetic algorithm.

[0011] Currently, there are no polar-coded IDD receivers based entirely on a tree search module. Furthermore, for the two adjustable parameters mentioned above, layer width and message interaction, there is currently no machine learning optimization work to further explore the optimal performance-complexity trade-off. Summary of the Invention

[0012] Purpose of the invention: In order to overcome the shortcomings of the existing technology, an iterative detection and decoding method based on tree search is provided. Through the soft information exchange between the detection and decoding modules, iterative detection and decoding (IDD) can achieve better reliability than separate detection and decoding (SDD). The scheme is optimized, starting from the requirements of error rate performance and complexity, and achieving better error rate performance and lower complexity by adjusting the layer width and message interaction.

[0013] Technical Solution: To achieve the above-mentioned purpose, the present invention provides an iterative detection and decoding method based on tree search, comprising the following steps:

[0014] S1: Initialize K-Best detector;

[0015] S2: Obtain the prior message L through the FastSOL decoder A1(s i );

[0016] S3: Execute the K-Best detector with the prior message L A1 (s i ) to obtain the symbol estimation sequence;

[0017] S4: Convert the symbol estimation sequence into a bit estimation sequence, output it to the FastSOL decoder for FastSOL decoding, and obtain the decoding result sequence;

[0018] S5: Determine whether the maximum number of iterations has been reached. If not, output the decoded result sequence as a priori information to the K-Best detector, and return to step S2; otherwise, proceed to step S6.

[0019] S6: Complete detection and decoding, and output corresponding FER performance data.

[0020] Furthermore, the prior message L in step S2 A1 (s i ) is obtained as follows:

[0021] The a posteriori message L output by the FastSOL decoder D2 Expressed as:

[0022] L D2 (x k |y)=L A2 (x k )+L E2 (x k |y) (1)

[0023] Among them, x k represents the kth bit; the decoder prior message L A2 (x k ) is provided by the K-Best detector; the decoding process is through the prior message L A2 (x k ) to approximate the decoder likelihood L E2 (x k |y) and output the posterior message L D2 (x k |y);

[0024] According to formula (1), L E2 (x k |y), L E2 (x k |y) as the prior message L A1 (s i ).

[0025] Furthermore, in step S3, the prior message L A1 (s i ) performs probability domain conversion, corresponding to each bit, converts them into symbol domain, and inputs the probability of the symbol domain into the K-Best detector. The probability domain conversion formula is:

[0026]

[0027] Among them, s0 represents the symbol corresponding to all bits being 0, and P(s0) is conventionally set to 1; Q represents the number of bits mapped to each modulation symbol, and x i,b =1 and x i,b =0 means that the bth bit of the i-th symbol is judged to be 1 and 0 respectively.

[0028] Furthermore, the K-Best detection method in step S3 is:

[0029] According to the prior information L A1 (s i ) to calculate the changed PED', the calculation formula is:

[0030] PED′=PED+L A1 (s i ) (3)

[0031] The symbols that minimize the PED amplitude are selected layer by layer and form a symbol estimation sequence.

[0032] Furthermore, the conversion formula for converting the symbol estimation sequence into the bit estimation sequence in step S4 is:

[0033]

[0034] in, is such that x k =1 symbol set, is such that x k =0 symbol set.

[0035] Furthermore, the scaling parameters δ, μ, and ω are introduced to the prior value L received by the K-Best detector. D1 , the a posteriori message L output by the FastSOL decoder D2 and PED' to find the best scaling ratio, specifically:

[0036] L D1 =δL A1 +L E1 (5)

[0037] L D2 =μL A2 +LE2 (6)

[0038] PED′=PED+ωL A1 (7)

[0039] Among them, {δ, μ, ω} are the three parameters introduced to adjust the external message to improve performance.

[0040] The SMS-EMOA method employed in this paper models the problem using an objective function and constraint functions, aiming to find an optimal solution that maximizes the objective function while satisfying the constraints. In the proposed problem, the goal is to find a set of {δ, μ, ω} parameters that minimizes the system's FER, all other conditions being equal. Therefore, there are no constraints on the range of parameter selection, and the objective function is:

[0041] F=FER(δ,μ,ω) (8)

[0042] Furthermore, SMS-EMOA is used to train the K-Best detector and FastSOL decoder layer-wide. The specific training process includes:

[0043] 1) Input the target performance and initial list vector into the layer-width training algorithm based on SMS-EMOA, where all components in the initial list vector are the maximum values ​​of the set training range, i.e. K i =K max ,i=1,...,N t ;L i =L max , i = 1, ..., M; the target performance is the FER performance P generated by the IDD receiver using the initial list vector target ;

[0044] 2) Calculate the current F function and generate a new list vector that makes the F function value smaller through SMS-EMOA;

[0045] 3) Substitute the new list vector into the IDD receiver to obtain the current performance FER(K,L);

[0046] 4) If the current performance FEP(K, L) satisfies the P function, proceed to step 5), otherwise return to step 2);

[0047] 5) Keep the current list vector;

[0048] 6) Determine whether the maximum number of iterations has been reached. If so, proceed to step 6; otherwise, return to step 2).

[0049] 7) Output the optimized list vectors K and L.

[0050] Furthermore, in step 2), the current F function is calculated according to formula (8), specifically:

[0051]

[0052] The P function in step 4) is:

[0053] P=FER(K,L)<(1+ε)P target , (10

[0054] Among them, N t is the number of transmitting antennas (corresponding to the number of search layers of the K-Best detection tree), M is the number of information bits (corresponding to the number of search layers of the FastSOL decoding tree), F function represents the average value of K and L in I iterations, P function represents whether the FER of the current candidate meets the constraints. This optimization problem is to find a set of layer width parameters that makes the F function as small as possible under the premise of satisfying the P function; FER(K,L) represents the FER performance under a certain set of layer width parameters {K,L}, P target represents the target FER; ε represents the allowed error range of FER, so that some candidate parameters with slight performance fluctuations due to limited training sets can be considered.

[0055] This paper proposes an iterative detection and decoding (IDD) method based on tree search. The IDD receiver employed utilizes a K-Best detector and a FastSOL decoder, fully leveraging the error rate performance advantages of the tree search algorithm. Furthermore, a scaling parameter is introduced to optimize message interaction and enhance the efficiency of the tree search. Since both algorithms employ tree search, the algorithm complexity can be controlled by adjusting the layer width parameter, K, in detection, and L, in the list size, respectively, in decoding. Through these measures, the present invention achieves a more optimal "performance-complexity" tradeoff for IDD receivers.

[0056] Beneficial effects: Compared with the prior art, the present invention proposes for the first time an IDD method receiver based entirely on tree search in order to meet the requirements of future communication systems for high reliability. The IDD receiver adopts a K-Best detector and a fast soft output list (FastSOL) decoder, fully utilizing the error rate performance advantages brought by the tree search algorithm, and introduces scaling parameters to optimize message interaction, thereby further enhancing the efficiency of the tree search. Finally, the complexity of the tree search is reduced by introducing and reducing the layer width parameter. In order to obtain a better "performance-complexity" trade-off for the IDD receiver, the present invention adopts a method based on the S metric selection evolutionary multiobjective optimization algorithms (SMS-EMOA) to reduce the layer width and optimize the scaling parameters respectively. The former aims to minimize the average layer width while maintaining the receiver error rate performance, and the latter aims to improve the receiver error rate performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Schematic diagram of a polar code MIMO system of an IDD receiver in the present invention;

[0058] Figure 2 Schematic diagram of the process of the present invention;

[0059] Figure 3 Flowchart for layer width training using SMS-EMOA;

[0060] Figure 4 Performance comparison chart. DETAILED DESCRIPTION

[0061] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0062] The present invention provides an iterative detection decoding method based on tree search. In order to implement this method, the present invention constructs the following Figure 1 The polar code coded MIMO system of the IDD receiver shown in the figure includes coding, modulation, IDD receiver and other modules. The IDD receiver adopts K-Best detector and FastSOL decoder. Based on this system, refer to Figure 2 , the method of the present invention comprises the following steps:

[0063] S1: The IDD receiver receives the signal y and the channel matrix H, and performs QR decomposition and other processing to complete the initialization of the K-Best detector;

[0064] S2: Obtain the prior message L through the FastSOL decoder A1 (s i );

[0065] Prior message L A1 (s i ) is obtained as follows:

[0066] The a posteriori message L output by the FastSOL decoder D2 Expressed as:

[0067] L D2 (x k |y)=L A2 (x k )+L E2 (x k |y) (1)

[0068] Among them, x k represents the kth bit; the decoder prior message L A2 (x k ) is provided by the K-Best detector; the decoding process is through the prior message L A2 (x k ) to approximate the decoder likelihood L E2 (x k |y) and output the posterior message L D2 (x k |y);

[0069] According to formula (1), L E2 (x k |y), L E2 (x k |y) as the prior message L A1 (s i ).

[0070] S3: Execute the K-Best detector with the prior message L A1 (s i ) to obtain the symbol estimation sequence;

[0071] Since the decoder outputs the a posteriori message L D2 is the bit domain log likelihood ratio (LLR), which requires the prior message L A1 (s i) performs probability domain conversion, corresponding to each bit, converts them into symbol domain, and inputs the probability of the symbol domain into the K-Best detector. The probability domain conversion formula is:

[0072]

[0073] Among them, s0 represents the symbol corresponding to all bits being 0, and P(s0) is conventionally set to 1; Q represents the number of bits mapped to each modulation symbol, and x i,b =1 and x i,b =0 means that the bth bit of the i-th symbol is judged as 1 and 0 respectively;

[0074] Due to the common characteristics of tree search algorithms, the partial Euclidean distance (PED) of K-Best detection and the path metric (PM) of FastSOL decoding both have a metric form that increases with the layer width.

[0075] Therefore, the transmission of prior information can be reflected by the change of PED. The K-Best detection method is:

[0076] According to the prior information L A1 (s i ) to calculate the changed PED', the calculation formula is:

[0077] PED′=PED+L A1 (s i ) (3)

[0078] The symbols that minimize the PED amplitude are selected layer by layer and form a symbol estimation sequence.

[0079] S4: Convert the symbol estimation sequence into a bit estimation sequence;

[0080] Since the symbol domain LLRs output by the detector correspond to each symbol, they need to be converted into the bit domain and the bit domain probabilities are input into the decoder module.

[0081] The conversion formula for converting the symbol estimation sequence into the bit estimation sequence is:

[0082]

[0083] in, is such that x k =1 symbol set, is such that x k =0 symbol set.

[0084] S5: Output the bit estimation sequence to the FastSOL decoder for FastSOL decoding to obtain a decoding result sequence;

[0085] S6: Determine whether the maximum number of iterations has been reached. If not, output the decoded result sequence as a priori information to the K-Best detector, and return to step S2; otherwise, proceed to step S6.

[0086] S7: Complete detection and decoding, and output corresponding FER performance data.

[0087] Based on the above content, it can be seen that in the IDD receiver of the present invention, the K-Best detector obtains the channel observation value y and the prior value L A1 To calculate the external message L E1 , which is then used as the prior input L of the FastSOL decoder A2 ; FastSOL decoder is based on L A2 Decode and calculate the external message L E2 , as the prior value L A1 Feedback is given to the K-Best detector to complete one iteration and realize message exchange.

[0088] Based on the iterative process of the above-mentioned IDD receiver, the present invention adopts the SMS-EMOA method to optimize the scaling parameters and layer width parameters, the purpose of which is to improve the error rate performance and reduce the complexity, as follows:

[0089] 1. Scaling parameter optimization:

[0090] In order to improve the error rate performance of the IDD receiver, the scaling parameters δ, μ, and ω are introduced to the prior value L received by the K-Best detector. D1 , the a posteriori message L output by the FastSOL decoder D2 and PED' to find the best scaling ratio, specifically:

[0091] L D1 =δL A1 +L E1 (5)

[0092] L D2 =μL A2 +L E2 (6)

[0093] PED′=PED+ωL A1 (7)

[0094] Among them, {δ, μ, ω} are three parameters introduced to adjust the external message to improve performance. In the existing IDD receiver, the values ​​of these three parameters are: 1.0, 0.0, 0.0 respectively.

[0095] The SMS-EMOA method employed in this paper models the problem using an objective function and constraint functions, aiming to find an optimal solution that maximizes the objective function while satisfying the constraints. In the proposed problem, the goal is to find a set of {δ, μ, ω} parameters that minimizes the system's FER, all other conditions being equal. Therefore, there are no constraints on the range of parameter selection, and the objective function is:

[0096] F=FER(δ,μ,ω) (8)

[0097] Finally, the set of parameters that can improve the error rate performance most significantly is selected as the final result of training and used in the proposed IDD receiver.

[0098] 2. Layer width parameter optimization:

[0099] In order to reduce the complexity, SMS-EMOA is used to optimize the layer width training of K-Best detector and FastSOL decoder. In this optimization problem, the objective function and constraint function are as follows:

[0100]

[0101] P=FER(K,L)<(1+ε)P target , (10)

[0102] Among them, N t is the number of transmitting antennas (corresponding to the number of search layers in the K-Best detection tree), M is the number of information bits (corresponding to the number of search layers in the FastSOL decoding tree), F function represents the average value of K and L in I iterations, and P function represents whether the FER of the current candidate meets the constraints. This optimization problem is to find a set of layer width parameters that can minimize the F function under the premise of satisfying the P function; FER(K,K) represents the FER performance under a certain set of layer width parameters {K,L}, and P target represents the target FER; ε represents the allowed error range of FER, so that some candidate parameters with slight performance fluctuations due to limited training sets can be considered.

[0103] Reference Figure 3 , the specific training optimization process includes:

[0104] 1) Input the target performance and initial list vector into the layer-width training algorithm based on SMS-EMOA, where all components in the initial list vector are the maximum values ​​of the set training range, i.e. K i=K max , i=1,...,N t ;L i =L max , i = 1, ..., M; the target performance is the FER performance P generated by the IDD receiver using the initial list vector target ;

[0105] 2) Calculate the current F function according to formula (8), and generate a new list vector that makes the F function value smaller through SMS-EMOA;

[0106] 3) Substitute the new list vector into the IDD receiver to obtain the current performance FER(K,L);

[0107] 4) According to the P function of formula (9), if the current performance FER(K, L) satisfies the P function, then go to step 5), otherwise go back to step 2);

[0108] 5) Keep the current list vector;

[0109] 6) Determine whether the maximum number of iterations has been reached. If so, proceed to step 6; otherwise, return to step 2).

[0110] 7) Output the optimized list vectors K and L.

[0111] Finally, under the premise of keeping the performance almost unchanged, a set of layer width parameters that minimizes the average layer width is used as the final result of training and is used in the proposed IDD receiver.

[0112] In order to verify the effectiveness and effect of the solution of the present invention, the performance of the IDD receiver provided by the present invention is compared with the existing SDD receiver in this embodiment, as follows:

[0113] Figure 4 The parameters and complexity are provided for N = 256. When N = 512, the fine-tuning parameters {δ, μ, ω} = {0.0, 2.0, 0.1} are used. In addition, the KBest-FastSOL SDD receiver is used as a complexity benchmark. Figure 4 As shown, the IDD receiver of the present invention has a frame error rate of 10 -3 The algorithm achieves up to 1.38dB of gain over SDD. By adjusting the external message parameters, the error rate performance can be further improved by up to 0.68dB. By adjusting the layer width, the complexity of the detector and decoder can be reduced by up to 56.3% and 37.8%, respectively, while maintaining the error rate performance.

Claims

1. An iterative detection and decoding method based on tree search, characterized in that: The steps include: S1: Initialize K-Best detector; S2: Obtain the prior message L through the FastSOL decoder A1 (s i ); S3: Execute the K-Best detector with the prior message L A1 (s i ) to obtain the symbol estimation sequence; S4: Convert the symbol estimation sequence into a bit estimation sequence, output it to the FastSOL decoder for FastSOL decoding, and obtain the decoding result sequence; S5: Determine whether the maximum number of iterations has been reached. If not, output the decoded result sequence as a priori information to the K-Best detector, and return to step S2; otherwise, proceed to step S6. S6: Complete detection and decoding, and output corresponding FER performance data.

2. The iterative detection and decoding method based on tree search according to claim 1, characterized in that: The prior message L in step S2 A1 (s i ) is obtained as follows: The a posteriori message L output by the FastSOL decoder D2 Expressed as: L D2 (x k |y)=L A2 (x k )+L E2 (x k |y) (1) Among them, x k represents the kth bit; the decoder prior message L A2 (x k ) is provided by the K-Best detector; the decoding process is through the prior message L A2 (x k ) to approximate the decoder likelihood L E2 (x k |y) and output the posterior message L D2 (x k |y); According to formula (1), L E2 (x k |y), L E2 (x k |y) as the prior message L A1 (s i ).

3. The iterative detection and decoding method based on tree search according to claim 2, characterized in that: In step S3, the prior message L A1 (s i ) performs probability domain conversion, corresponding to each bit, converts them into symbol domain, and inputs the probability of the symbol domain into the K-Best detector. The probability domain conversion formula is: Among them, s0 represents the symbol corresponding to all bits being 0, and P(s0) is conventionally set to 1; Q represents the number of bits mapped to each modulation symbol, and x i,b =1 and x i,b =0 means that the bth bit of the i-th symbol is judged to be 1 and 0 respectively.

4. The iterative detection and decoding method based on tree search according to claim 2, characterized in that: The K-Best detection method in step S3 is: According to the prior information L A1 (s i ) to calculate the changed PED', the calculation formula is: PED′=PED+L A1 (s i ) (3) The symbols that minimize the PED amplitude are selected layer by layer and form a symbol estimation sequence.

5. The iterative detection and decoding method based on tree search according to claim 4, characterized in that: The conversion formula for converting the symbol estimation sequence into the bit estimation sequence in step S4 is: in, is such that x k =1 symbol set, is such that x k =0 symbol set.

6. The iterative detection and decoding method based on tree search according to claim 4, characterized in that: Introduce scaling parameters δ, μ, ω to the prior value L received by the K-Best detector D1 , the a posteriori message L output by the FastSOL decoder D2 and PED' to find the best scaling ratio, specifically: L D1 =δL A1 +L E1 (5) L D2 =μL A2 +L E2 (6) PED′=PED+ωL A1 (7) Among them, {δ, μ, ω} are the three parameters introduced, L E1 is the external message of the channel observation value y.

7. The iterative detection and decoding method based on tree search according to claim 6, characterized in that: The SMS-EMOA method is used to find the optimal scaling ratio, and the objective function is: F = FER(δ,μ,ω) (8).

8. The iterative detection and decoding method based on tree search according to claim 1, characterized in that: SMS-EMOA is used to train the K-Best detector and FastSOL decoder layer-wide. The specific training process includes: 1) Input the target performance and initial list vector into the layer-width training algorithm based on SMS-EMOA, where all components in the initial list vector are the maximum values ​​of the set training range, i.e. K i =K max , i=1,...,N t ;L i =L max , i = 1, ..., M; the target performance is the FER performance P generated by the IDD receiver using the initial list vector target ; 2) Calculate the current F function and generate a new list vector that makes the F function value smaller through SMS-EMOA; 3) Substitute the new list vector into the IDD receiver to obtain the current performance FER(K,L); 4) If the current performance FER(K, L) satisfies the P function, proceed to step 5), otherwise return to step 2); 5) Keep the current list vector; 6) Determine whether the maximum number of iterations has been reached. If so, proceed to step 6; otherwise, return to step 2). 7) Output the optimized list vectors K and L.

9. The iterative detection and decoding method based on tree search according to claim 8, characterized in that: In step 2), the current F function is calculated according to formula (8), specifically: The P function in step 4) is: P=FER(K,L)<(1+ε)P target , (10) Among them, N t is the number of transmitting antennas, M is the number of information bits, the F function represents the average value of K and L in I iterations, and the P function represents whether the FER of the current candidate meets the constraints; FER(K,L) represents the FER performance under a certain set of layer width parameters {K,L}, and P target represents the FER of the target; ε represents the allowable error range of FER.

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