A high-performance decoding method for shortening three-dimensional TPC

Abstract

The present invention discloses a high-performance decoding method for shortening three-dimensional time-dependent per-process (TPC). This method, based on the chase II algorithm, performs iterative decoding by combining the external information generated by the other two-dimensional decoders during the iterative process with the original received information as correction information for each of the soft information input to each SISO decoder during the serial iterative decoding process. Simultaneously, the soft information received by each dimensional decoder on the shortened bit is always [‑p‑1, ‑1]. Finally, hard-decision iterative decoding is performed to output the final decoding result. The improved decoder structure used in the present invention improves decoding performance by approximately 0.6 dB compared to an unimproved general structure, providing an effective decoding solution for shortening three-dimensional time-dependent per-process (TPC).

Description

Technical Field

[0001] The present invention belongs to the field of digital communication technology, and in particular relates to a high-performance decoding method for shortening three-dimensional TPC. Background Art

[0002] In digital communication systems, error probability is often used to measure system reliability. Information transmitted over wireless channels can be affected by interference such as noise, leading to transmission errors. Error control coding techniques can detect and even correct these errors, reducing the error probability of the entire system. Turbo Product Codes (TPC) have excellent error correction capabilities, making them a popular research area in the field of error-correcting codes.

[0003] TPC codes have a natural interleaving property. By encoding each row and column of the original information using a sub-error-correcting code, and then combining them by row-column interleaving, a two-dimensional TPC code can be created. Common sub-error-correcting codes include RS codes and Hamming codes. Three-dimensional TPC codes employ the same method, adding an additional dimension of information. While retaining the advantages of two-dimensional TPC, they also offer improved performance under low signal-to-noise ratio conditions. Shortening TPC codes can be achieved by shortening the information bits in each row or column before encoding.

[0004] TPC decoding algorithms can be categorized as hard-decision decoding and soft-decision decoding. Hard-decision algorithms feed the symbol's sign bit into the decoder for algebraic decoding. While this method is simple to implement and offers high decoding speeds, it is subject to some uncorrectable errors, limiting its decoding performance. Soft-decision decoding primarily involves the chase algorithm, which generates a test pattern by finding the unreliable bit with the smallest absolute value in the received sequence. This test sequence is then algebraically decoded, and the decoded result with the closest Euclidean distance to the received sequence is selected. Existing serial architectures fail to fully utilize the extrinsic information in each output dimension, thus underperforming TPC performance. Summary of the Invention

[0005] The object of the present invention is to provide an improved high-performance decoding method for shortening three-dimensional TPC codes.

[0006] The technical solution for achieving the purpose of the present invention is: a high-performance decoding method for shortening three-dimensional TPC, comprising the following steps:

[0007] Step 1: The first-dimensional decoder performs hard decision on the received corrected soft information to obtain a hard decision sequence;

[0008] Step 2: Generate a test pattern based on the unreliable bits generated by the modified soft information sequence;

[0009] Step 3: Add the test pattern and the hard decision sequence to obtain the test sequence;

[0010] Step 4: Obtain the decoding result of the test sequence and determine the reliability of the decoding result;

[0011] Step 5: Determine the best codeword in the decoding result based on the reliability of the decoding result, and determine the competitors of the best codeword;

[0012] Step 6: Obtain the extrinsic information of the first-dimensional decoder based on the best codeword and its competitors;

[0013] Step 7: Determine the corrected soft information received by the second-dimensional decoder based on the original information and the extrinsic information of the other two-dimensional decoders;

[0014] Step 8: Obtain the extrinsic information of the second-dimensional decoder according to the method of steps 1 to 6, and determine the corrected soft information received by the third-dimensional decoder;

[0015] Step 9: Obtain the extrinsic information of the third-dimensional decoder according to the method of steps 1 to 6, and determine the corrected soft information received by the first-dimensional decoder;

[0016] Step 10: Repeat steps 1 to 9 until the maximum number of iterations is reached, and output the final information result to perform hard decision to obtain the decoding result.

[0017] Preferably, a hard decision is performed on the received modified soft information to obtain a hard decision sequence Y = (y1, y2, ..y n The judgment rules are:

[0018]

[0019] Among them, r i is an element in the modified soft information vector, i=1,2,3…n, and n is the component code length.

[0020] Preferably, the specific method for generating a test pattern based on unreliable bits generated by the modified soft information sequence is:

[0021] By finding the p positions with the smallest absolute value of the elements in the soft information sequence after the decoder correction, p unreliable bits are generated; all elements in the hard decision sequence except the unreliable bit positions are set to 0, and the permutations of 01 are performed on the unreliable bits. One permutation is used as a test pattern to generate 2 p A test pattern of length n.

[0022] Preferably, the specific method for obtaining the decoding result of the test sequence is:

[0023] Multiply the obtained test sequence with the check matrix and perform algebraic decoding to obtain 2 p The decoding results of the test sequences n is the component code length, j=1,2,...2 p .

[0024] Preferably, the best codeword in the decoding result is the codeword with the lowest reliability in the decoding result.

[0025] Preferably, the method for determining the competitor of the best codeword is: if there is a codeword in the decoding result that is not equal to the best codeword, then it is used as the competitor of the best codeword; if more than one codeword is not equal to the best codeword, then the one with the lowest reliability is selected as the competitor.

[0026] Preferably, the calculation method of the external information is:

[0027] If there is a competitor for the best codeword, the extrinsic information is calculated as:

[0028] w i =(2D i -1)(m c -m d )-r i

[0029] Among them, r i is the element in the corrected soft information vector, D i is the element on the optimal codeword, i=1,2,3…n, n is the component code length, m c is the competitor's reliability, m d is the reliability of the best codeword;

[0030] When there are no competitors, the external information is calculated as:

[0031] w i =(2D i -1)β

[0032] β is the preset correction coefficient.

[0033] Preferably, the modified soft information received by the decoder is:

[0034] [R1(m)]=[R]+α[λ1w2(m-1)+λ2w3(m-1)]

[0035] [R2(m)]=[R]+α[λ1w1(m)+λ2w3(m-1)]

[0036] [R3(m)]=[R]+α[λ1w1(m)+λ2w2(m)]

[0037] Where R1(m), R2(m), and R3(m) are the modified soft information received by the first-dimensional decoder, the second-dimensional decoder, and the third-dimensional decoder, respectively; λ1, λ2, and α are weighting factors; w1, w2, and w3 are the extrinsic information of the three-dimensional decoders, respectively; and m is the number of iterations.

[0038] Compared with the prior art, the present invention has the following significant advantages: the performance of the present invention is improved by about 0.6dB, a new high-performance decoding scheme is provided for the shortened three-dimensional TPC code, and an improved decoding structure is provided for the three-dimensional TPC code.

[0039] The present invention will be described in further detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of three-dimensional TPC coding structure.

[0041] Figure 2 Schematic diagram of a two-dimensional shortened TPC coding matrix.

[0042] Figure 3 It is a general three-dimensional TPC decoder structure.

[0043] Figure 4 This is a structural diagram of the implementation of the present invention.

[0044] Figure 5 This is the Matlab bit error rate simulation diagram. DETAILED DESCRIPTION

[0045] An improved high-performance decoding method for shortened three-dimensional TPC codes. Figure 3 The improved decoder based on Figure 4 The specific steps are as follows:

[0046] Step 1: Figure 1 、 4 As shown, first, the X-dimensional SISO decoder receives the modified soft information R x Make a hard decision and get the hard decision sequence Y=(y1,y2,..y n ), n is the component code length.

[0047] The hard decision rules are:

[0048]

[0049] Among them, r i is an element in the modified soft information vector, i = 1, 2, 3…n, where n is the component code length. For the shortened 3D TPC code, the soft input information value of the shortened bits received by the decoder is always [-p-1, -1], where p is the number of unreliable bits.

[0050] The corrected soft information R received by the X-dimensional decoder x Specifically:

[0051] [R x (m)]=[R]+α[λ1w y (m-1)+λ2w z (m-1)]

[0052] [R] is the original information received, [W(m)] is the external information, and m is the number of iterations. λ1, λ2, and α are weighting factors. y 、w z They are the external information of Y dimension and Z dimension respectively. Initially, w y (0), w z (0)=0.

[0053] Step 2: Generate p unreliable bits by finding the p positions with the smallest absolute value of the elements in the soft information sequence after the decoder correction. p Let all elements in the hard decision sequence except the unreliable bit position be 0, and perform permutations and combinations of 01 on the unreliable bit position. One permutation is used as a test pattern, and finally 2 p A test pattern of length n.

[0054] Step 3: Add the test pattern to the hard decision sequence to obtain a test sequence.

[0055] Step 4: Multiply the obtained test sequence with the check matrix and perform algebraic decoding to obtain 2 p The decoding results of the test sequences n is the component code length, j=(1,2,...2 p ), the decoding result C j Form a candidate codeword set Ω, and each test sequence decoding result C j The reliability of the decoding result C j The Euclidean distance between the received information sequence is measured and the calculation formula is:

[0056] m j =- <C j ,R p >

[0057] m j Represents the Euclidean distance, which is the decoding result C j With R p The negative value of the inner product, R p Receive information for the decoder.

[0058] Step 5: Select the codeword with the smallest metric value in the candidate codeword set Ω as the optimal codeword D = (D1, D2, ..D n ), n is the length of the component code, and its metric value (Euclidean distance) is recorded as m d Then search for the competing codewords of D in the candidate codeword set Ω. If there are other codewords in the candidate codeword set Ω that are not equal to the best codeword D, then use them as competitors C of the best codeword D. If there are more than one such codewords, then choose the one with the smallest Euclidean distance as the competitor, and its metric value is recorded as m. c .

[0059] Step 6: Calculate the external information w=(w1,w2,..w n ), n is the component code length, if there is a competitor C of the best codeword D, then the extrinsic information is calculated as:

[0060] w i =(2D i -1)(m c -m d )-r i

[0061] where r i is the element in the corrected soft information vector, D i are the elements on the optimal codeword D, i = 1, 2, 3…n, and n is the component code length.

[0062] If the distance between the best codeword D and its competitor C is large, then w i A large value of indicates that the reliability of the optimal codeword D is high, and vice versa, it indicates that the reliability of the optimal codeword D is low.

[0063] When competitor C does not exist, it indicates that the reliability of the optimal codeword D is very high, and the external information can be directly calculated by the following approximation:

[0064] w i =(2D i -1)β

[0065] β is the preset correction coefficient. In the calculation of extrinsic information, the shortened information bit does not participate in the process, and all extrinsic information on the shortened bit is set to 0.

[0066] Step 7: Determine the corrected soft information R received by the Y-dimensional decoder during the decoding iteration based on the original information and the external information of the other two-dimensional decoders. y ;

[0067] Specifically, the modified soft information R received by the Y-dimensional decoder during the decoding iteration process is y It can be expressed as follows:

[0068] [R y(m)]=[R]+α[λ1w x (m)+λ2w z (m-1)]

[0069] [R] is the original information received, [W(m)] is the external information, and m is the number of iterations. λ1, λ2, and α are weighting factors. x 、w z is the external information of Y and Z dimensions. Initially, the external information of each dimension is 0 (i.e., w x (0), w y (0), w z (0) = 0, the information received in the Y dimension at the start of the first decoding iteration is [R] + αλ1w x (m)).

[0070] Step 8: The Y-dimensional decoder decodes the received soft information R y Perform hard decision and follow steps 1 to 6 to obtain the Y-dimensional output external information w y , and determine the corrected soft information R received by the Z-dimensional decoder during the decoding iteration process z ;

[0071] The corrected soft information R received by the Z-dimensional decoder during the decoding iteration z It can be expressed as follows:

[0072] [R z (m)]=[R]+α[λ1w x (m)+λ2w y (m)]

[0073] [R] is the original information received, [W(m)] is the external information, and m is the number of iterations. λ1, λ2, and α are weighting factors. x 、w y is the external information of Y and Z dimensions. Initially, the external information of each dimension is 0 (i.e., w x (0), w y (0), w z (0) = 0, the information received in the Z dimension at the beginning of the first decoding iteration is [R] + α [λ1w x (m)+ λ2w y (m)]).

[0074] Step 9: The Z-dimensional decoder decodes the received soft information R z Perform hard decision and follow steps 1 to 6 to obtain the Z-dimensional output external information w z , and determine X as the corrected soft information R received by the decoder x .

[0075] Step 10: Repeat steps 1 to 9 until the maximum number of iterations is reached, and output the final information result to perform hard decision to obtain the decoding result.

[0076] The present invention belongs to the Chase II decoding algorithm based on soft decision, and improves the decoder structure of Chase II: in the iterative process, the soft information input of each dimension is the addition of the information of the other two dimensions of the decoder except the dimension and the original received information, so that the structure can achieve better performance without increasing the complexity.

[0077] Example

[0078] This embodiment takes the BPSK signal as an example. The encoding format is: the information matrix before encoding is (22, 26, 3), and the information matrix after encoding is (28, 32, 4). Each row and column is encoded using an extended Hamming code. The primitive polynomial is x 5 +x 2 +1, each page is encoded with a parity check code. The following is just an example for simulation verification.

[0079] An improved high-performance decoding method for shortening three-dimensional TPC codes, comprising the following steps:

[0080] Step 1: Take the BPSK information received through the AWGN channel as the original information R, and combine it with Figure 1 As shown in 4, first, the X-dimensional SISO decoder receives the modified soft information R x Make a hard decision and get the hard decision sequence Y=(y1,y2,..y n ), n is the component code length, and the modified soft information R received by the X-dimensional decoder during the decoding iteration process x It can be expressed as follows:

[0081] [R x (m)]=[R]+α[λ1w y (m-1)+λ2w z (m-1)]

[0082] [R] is the original information received, [W(m)] is the external information, and m is the number of iterations. λ1, λ2, and α are weighting factors. y 、w z is the external information of Y and Z dimensions. Initially, the external information of each dimension is 0. When the first decoding iteration begins, the information received in the X dimension is [R].

[0083] The hard decision rules are:

[0084]

[0085] where r i, where \(i = 1, 2, 3, \cdots, n\), are the elements in the corrected soft information vector received by the decoder, and \(n\) is the code length of the component code. For the shortened three-dimensional TPC code, the soft input information values of the shortened bits received by the decoder are always in the range of \([-p - 1, -1]\), where \(p\) is the number of unreliable bits.

[0086] Step 2: Find \(p\) unreliable bits with the smallest absolute values in the hard decision sequence (\(p < k\), where \(k\) is the information bit length). Generate 1 or 0 at the unreliable bits and set the remaining positions to 0, generating 2 p test patterns of length \(n\) (\(n\) is the code length of the component code). The unreliable bits can be obtained by finding the positions with the smallest absolute values in \(Y\).

[0087] Step 3: Add the test pattern to the hard decision sequence to obtain 2 p test sequences.

[0088] Step 4: Multiply each of the obtained 2 p test sequences by the parity-check matrix for algebraic decoding to obtain 2 p decoding results of the test sequences where \(n\) is the code length of the component code, \(j=(1, 2, \cdots, 2 p ). The algebraic decoding process of the Hamming code is as follows:

[0089] If the sequence after hard decision is \(Y\), then \(Y = C j + e i

[0090] where \(e i is the error pattern;

[0091] If \(H\) is the parity-check matrix, then the syndrome \(S = Y\times H T = C j \times H T + e i \times H T = e i \times H <s T

[0092] Therefore, when \(e i = 0\), \(S = 0\), indicating no error at this time. If \(e i \neq 0\), then \(S\neq 0\), and the valid codeword \(C j = Y - e i .

[0093] After algebraic decoding, put each decoding result \(C j of the test sequences into the candidate codeword set \(\Omega\). The reliability of \(C j can be measured by the Euclidean distance between \(C j and the received information sequence. The calculation formula is:

[0094] m j =- <C j ,R p >

[0095] m j Represents the Euclidean distance, C j With R p The negative value of the inner product of R. p Receive information for the decoder.

[0096] Step 5. Select m j The smallest codeword is taken as the optimal codeword D, and its metric value (Euclidean distance) is recorded as m d Then search for the competing codeword of D in the candidate codeword set Ω. If there are other codewords in Ω that are not equal to D, then use them as the competitor C of the best codeword D. If there is more than one such codeword, then choose the one with the smallest Euclidean distance as the competing codeword, and its metric value is recorded as m. c To save computation time, the space of candidate codewords can be reduced, which has little impact on the final performance.

[0097] Step 6: Calculate the external information w=(w1,w2,..w n ), n is the component code length, if there is a competitor C of the best codeword D, then the extrinsic information is calculated as:

[0098] w i =(2D i -1)(m c -m d )-r i

[0099] where r i is the element in the corrected soft information vector, D i are the elements on the optimal codeword D, i=(1,2,3…n), and n is the component code length.

[0100] If the distance between the best codeword D and its competitor C is large, then w i A large value of indicates that the reliability of the optimal codeword D is high, and vice versa. When competitor C does not exist, it indicates that the reliability of the optimal codeword D is very high. At this time, the external information at position i can be directly calculated by the following approximation:

[0101] w i =(2D i -1)β

[0102] β is the preset correction coefficient. In the calculation of extrinsic information, the shortened information bit does not participate in the process, and all extrinsic information on the shortened bit is set to 0.

[0103] Step 7: Determine the corrected soft information R received by the Y-dimensional decoder during the decoding iteration based on the original information and the external information of the other two-dimensional decoders. y ;

[0104] Specifically, the modified soft information R received by the Y-dimensional decoder during the decoding iteration process is y It can be expressed as follows:

[0105] [R y (m)]=[R]+α[λ1w x (m)+λ2w z (m-1)]

[0106] [R] is the original information received, [W(m)] is the external information, and m is the number of iterations. λ1, λ2, and α are weighting factors. x 、w z is the external information of Y and Z dimensions. Initially, the external information of each dimension is 0 (i.e., w x (0), w y (0), w z (0) = 0, the information received in the Y dimension at the start of the first decoding iteration is [R] + αλ1w x (m)).

[0107] Step 8: The Y-dimensional decoder decodes the received soft information R y Perform hard decision and follow steps 1 to 6 to obtain the Y-dimensional output external information w y , and determine the corrected soft information R received by the Z-dimensional decoder during the decoding iteration process z ;

[0108] The corrected soft information R received by the Z-dimensional decoder during the decoding iteration z It can be expressed as follows:

[0109] [R z (m)]=[R]+α[λ1w x (m)+λ2w y (m)]

[0110] [R] is the original information received, [W(m)] is the external information, and m is the number of iterations. λ1, λ2, and α are weighting factors. x 、w y is the external information of Y and Z dimensions. Initially, the external information of each dimension is 0 (i.e., w x (0), w y (0), w z (0) = 0, the information received in the Z dimension at the beginning of the first decoding iteration is [R] + α [λ1w x (m)+ λ2wy (m)]).

[0111] Step 9: The Z-dimensional decoder decodes the received soft information R z Perform hard decision and follow steps 1 to 6 to obtain the Z-dimensional output external information w z , and determine X as the corrected soft information R received by the decoder x .

[0112] Step 10: Repeat steps 1 to 9 until the maximum number of iterations is reached, and output the final information result to perform hard decision to obtain the decoding result.

[0113] To verify the effectiveness of the scheme, the number of iterations is set to 5, the number of input information frames each time is 500 frames, α = 0.5, λ1, λ2 = 1, β = 1, the soft input information value of the shortened bit on the original received sequence is set to -3, the number of unreliable bits p = 4, and to reduce the simulation time, the size of the candidate codeword space is reduced to 4. Matlab software is used for simulation verification.

[0114] According to the simulation results Figure 5 It can be seen that the improved decoding structure improves performance by approximately 0.6dB compared to the unimproved structure, indicating that in the three-dimensional TPC serial iterative decoding process, the SISO decoder in each dimension adopts the method of combining the external information generated in the other two dimensions except the dimension during the iteration process and then adding it to the original received information to correct the soft information input in the current dimension. This method is effective in improving bit error performance.

[0115] The present invention is a communication technology for three-dimensional TPC decoding. Compared with the common decoder structure ( Figure 3 ) Only when decoding in the Z dimension, the extrinsic information of the other two dimensions is used to correct the input soft information of the Z dimension. A new decoder structure is proposed. For any current dimension, the extrinsic information output by the other two dimensions during the iteration process is combined to correct the input soft information of the current dimension. At the same time, the soft information on the shortened bit received by each dimension decoder is always set to [-p-1, -1]. These measures improve the decoding performance of the decoder and provide a new decoding scheme for shortening three-dimensional TPC.

Claims

1. A high-performance decoding method for shortening three-dimensional TPC, characterized in that: The steps include: Step 1: The first-dimensional decoder performs hard decision on the received corrected soft information to obtain a hard decision sequence; Step 2: Generate a test pattern based on the unreliable bits generated by the modified soft information sequence; Step 3: Add the test pattern and the hard decision sequence to obtain the test sequence; Step 4: Obtain the decoding result of the test sequence and determine the reliability of the decoding result; Step 5: Determine the best codeword in the decoding result based on the reliability of the decoding result, and determine the competitors of the best codeword; Step 6: Based on the best codeword and its competitors, obtain the extrinsic information of the first-dimensional decoder. The calculation method of the extrinsic information is: If there is a competitor for the best codeword, the extrinsic information is calculated as: w i =(2D i -1)(m c -m d )-r i Among them, r i is the element in the modified soft information vector, D i is the element on the optimal codeword, i=1,2,3…n, n is the component code length, m c is the competitor's reliability, m d is the reliability of the best codeword; When there are no competitors, the external information is calculated as: w i =(2D i -1)β β is the preset correction coefficient; Step 7: Determine the corrected soft information received by the second-dimensional decoder based on the original information and the extrinsic information of the other two-dimensional decoders; Step 8: Obtain the extrinsic information of the second-dimensional decoder according to the method of steps 1 to 6, and determine the corrected soft information received by the third-dimensional decoder; Step 9: Obtain the extrinsic information of the third-dimensional decoder according to the method of steps 1 to 6, and determine the corrected soft information received by the first-dimensional decoder; Step 10: Repeat steps 1 to 9 until the maximum number of iterations is reached, and output the final information result to perform hard decision to obtain the decoding result.

2. The high-performance decoding method with shortened 3D TPC according to claim 1, characterized in that: Perform hard decision on the received corrected soft information to obtain the hard decision sequence Y=(y1,y2,..y n ) is as follows: Among them, r i is an element in the modified soft information vector, i=1,2,3…n, and n is the component code length.

3. The high-performance decoding method for shortening 3D TPC according to claim 1, characterized in that: The specific method for generating a test pattern based on the unreliable bits generated by the modified soft information sequence is as follows: By finding the p positions with the smallest absolute value of the elements in the soft information sequence after the decoder correction, p unreliable bits are generated; all elements in the hard decision sequence except the unreliable bit positions are set to 0, and the permutations of 01 are performed on the unreliable bits. One permutation is used as a test pattern to generate 2 p A test pattern of length n.

4. The high-performance decoding method with shortened 3D TPC according to claim 1, wherein: The specific method for obtaining the decoding result of the test sequence is: Multiply the obtained test sequence with the check matrix and perform algebraic decoding to obtain 2 p The decoding results of the test sequences n is the component code length, j=1,2,...2 p .

5. The high-performance decoding method with shortened three-dimensional TPC according to claim 1, characterized in that: The best codeword in the decoding result is the codeword with the lowest reliability in the decoding result.

6. The high-performance decoding method with shortened three-dimensional TPC according to claim 1, characterized in that: The method for determining the competitors of the best codeword is as follows: if there is a codeword in the decoding result that is not equal to the best codeword, it is used as a competitor of the best codeword; if more than one codeword is not equal to the best codeword, the one with the lowest reliability is selected as the competitor.

7. The high-performance decoding method with shortened three-dimensional TPC according to claim 1, characterized in that: The corrected soft information received by the decoder is: [R1(m)]=[R]+α[λ1w2(m-1)+λ2w3(m-1)] [R2(m)]=[R]+α[λ1w1(m)+λ2w3(m-1)] [R3(m)]=[R]+α[λ1w1(m)+λ2w2(m)] Where R1(m), R2(m), and R3(m) are the modified soft information received by the first-dimensional decoder, the second-dimensional decoder, and the third-dimensional decoder, respectively; λ1, λ2, and α are weighting factors; w1, w2, and w3 are the extrinsic information of the three-dimensional decoders, respectively; and m is the number of iterations.

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