Finite-precision quantization hierarchical nonsurjective finite character set decoding method applicable to 5G LDPC codes

Abstract

The application provides a limited-precision quantization layered non-surjective finite alphabet (NS-FAID) decoding method suitable for 5G LDPC codes.Under the condition of limited-precision quantization, especially limited-precision quantization less than or equal to 4 bits, the bit width of soft quantity information in the general quantization decoding algorithm is generally consistent with the bit width of input channel information, while the layered NS-FAID decoding method designed for 5G LDPC codes provided by the application can further reduce the bit width of soft quantity information used in the check node update process in the iterative decoding process by using the lookup table mapping mode, so that the complexity of the check node internal calculation is further reduced, thereby saving hardware resources, reducing power consumption, and the performance loss is smaller compared with the standard decoding algorithm.

Description

Technical Field

[0001] This invention belongs to the field of decoding technology, and particularly relates to a finite-precision quantization layered non-surjective finite character set decoding method applicable to 5G LDPC codes. Background Technology

[0002] Low-density parity-check (LDPC) codes were first proposed by Dr. Gallager in 1962 as linear block codes that approximate the Shannon limit. Davey and Mackay first studied multi-ary LDPC codes in 1998. Compared with binary LDPC codes, multi-ary LDPC codes with medium to short code lengths have better decoding performance and are more effective in high-order modulation and burst error correction. They are widely used in storage, large-scale mobile communication and other scenarios.

[0003] For LDPC code decoding, the backpropagation (BP) and minima (MS) algorithms are commonly used. However, in practical applications, considering limited hardware resources, reducing the bit width of the information is one of the most common methods to achieve low power consumption and low complexity. Therefore, the performance of finite-precision quantization decoders is crucial in the hardware implementation of LDPC codes. However, if a simple uniform quantization is performed while using the MS algorithm, the performance of the decoder under finite-precision quantization will be significantly degraded. Therefore, in recent years, more and more researchers have focused on decoding algorithms with low complexity and finite-precision quantization.

[0004] Researchers have found that by using non-uniform quantization for the soft information used in decoding, the performance loss of LDPC decoders under finite precision quantization is relatively small. Researchers have proposed various decoding algorithms for non-uniform quantization LDPC decoders, such as MIM-LUT and Min-IB algorithms, but in fact, they can all be summarized as: using lookup tables (LUTs) to replace the internal mathematical calculations for updating variable nodes or check nodes in the MS algorithm. SK Planjery et al. proposed the Finite Alphabet Iterative Decoding (FAID) algorithm based on this idea (see: Planjery SK, Declercq D, Danjean L, et al. Finite alphabet iterative decoders-Part I: Decoding beyond belief propagation on the binary symmetric channel[J].IEEE Transactions on Communications, 2013, 61(10): 4033-4045.). However, the FAID algorithm described in the aforementioned literature is difficult to design for its LUT when dealing with irregular matrices with large node weights. The LUT has high dimensionality and high complexity. Summary of the Invention

[0005] The purpose of this invention is to provide a finite-precision quantization layered non-surjective finite character set decoding method suitable for 5G LDPC codes. The entire decoding process is divided into multiple stages according to the number of iterations. At each stage of decoding, the bit width of soft information is limited, and the bit width is further reduced in the more complex check node update unit. This reduces the hardware resources required for decoding and effectively reduces decoding latency with minimal performance loss, making it more suitable for decoding scenarios under finite-precision quantization.

[0006] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0007] A finite-precision quantization hierarchical non-surjective finite character set (FAID) decoding method applicable to 5G LDPC codes is proposed. Let H be the parity-check matrix corresponding to the 5G LDPC code base matrix BG1, with M = 4, ..., 24 rows and N = 26, ..., 46 columns in its base matrix form, and Z = 384 spread factor. The decoder uses soft information bit widths a > b > c, where the bit width of each piece of information is reflected in its superscripts a, b, and c. The soft information y received from the channel is quantized as... The bit width is b bits, and the soft information passed from the variable node to the check node in the iterative decoding is L. v2cThe bit widths before and after compression via lookup table (LUT) mapping are respectively 'a' bits of information. and c-bit information In iterative decoding, the soft information passed from the check node to the variable node is L. c2v The bit widths before and after the inverse mapping are c bits of information. and b-bit information In iterative decoding, the soft information used for each probe output is LLR, with a bit width of a bits, i.e., LLR a All the above information is represented in two's complement; let the trial decoding output sequence be D, the number of iterations be k, the current layer number be m, and the maximum number of iterations be K. max .

[0008] Because this decoding method involves operations between multiple quantized bit information points, it is necessary to define some operators for bit width conversion. Define {x a y b The symbol} represents the concatenation of 'x' bits of information into the high-order bits of 'y' bits of information, forming a (a+b)-bit information. Define a′b0 and a′b1 to represent 'a' bits of all 0s and 'a' bits of all 1s, respectively. Define x... a [b] represents the b-th bit of the a-bit information x, with the least significant bit being the first bit. a [b] refers to the b-th bit of x from the least significant bit to the most significant bit. Define x. a [b:c] represents bits c to b of information in bit x, which is (b-c+1) bits of information. Therefore, for example... This indicates that (ab) bits The b-th bit of the information, i.e., the most significant bit, is related to b bits. Information is concatenated to form a bit of information; Indicates will The a-th position and The first to the (b-1)th bits are combined to form a b-bit information.

[0009] The decoding method includes the following steps:

[0010] Step 1: Initialize the iteration count k = 0, the current layer number m = 0, and perform finite-precision quantization on the soft information received from the channel. Uniform quantization is used, and the function Q(x) is the uniform quantization function. floor(x) is the floor function. Q max As a quantization threshold, Q max =2 t-1 -1, where t is the number of quantization bits. (Using the formula...) Where α is the quantization factor, thus... The bit width is limited to b bits; then, L needs to be further modified. v2c L c2v Information such as LLR is also initialized, that is...

[0011] Step 2: This decoding method calculates layer by layer according to the steps of layered decoding. Subtract the b-bit expanded to a-bit LLR information from the a-bit LLR information. Calculate in sequence all the resources needed for this layer Information, with a bit width of a bits.

[0012] Step 3: First, use the 'a' bits obtained in step S2 that this layer needs. Truncation is performed to b bits; that is, anything exceeding the b-bit representation range is truncated to the upper or lower limit of the b-bit representation range. Then according to For L v2c Perform bit-width conversion, where the function F(x) is a mapping from b bits to c bits, such that the b bits... Reduced to c bits

[0013] This decoding method, targeting 5G LDPC codes with BG1 as the base matrix, column block number N = 26–46, row block number M = 4–24, spread factor of 384, and covering code rate range [1 / 2, 11 / 12], designs three mapping schemes as shown in Table 1, completing a 4-bit (-7 to 7, 15 states) to 3-bit (-3 to 3, 7 states) mapping, and realizing L v2c Compression of soft quantity information. Different F(m) mapping schemes are selected for different situations. For example, the following five cases:

[0014] For 5G LDPC codes with 46 column blocks, 24 row blocks, and a code rate of 1 / 2, this decoding method uses F1(m) as the mapping scheme.

[0015] For 5G LDPC codes with 35 column blocks, 13 row blocks, and a code rate of 2 / 3, this decoding method uses F1(m) as the mapping scheme.

[0016] For 5G LDPC codes with 32 column blocks, 10 row blocks, and a code rate of 11 / 15, this decoding method uses F2(m) as the mapping scheme.

[0017] For 5G LDPC codes with 29 column blocks, 7 row blocks, and a code rate of 22 / 27, this decoding method uses F2(m) as the mapping scheme.

[0018] For 5G LDPC codes with 26 column blocks, 4 row blocks, and a code rate of 11 / 12, this decoding method uses F3(m) as the mapping scheme.

[0019] m 0 1 2 3 4 5 6 7 <![CDATA[F1(m)]]> 0 0 1 2 2 2 3 3 <![CDATA[F2(m)]]> 0 1 1 2 2 2 3 3 <![CDATA[F3(m)]]> 0 1 1 2 2 3 3 3

[0020] Table 1 shows the 4-bit to 3-bit mapping for 5G LDPC design.

[0021] Then, the L-bits that have been reduced to a width of c bits will be... v2c The information is sent to the verification node and calculated using the same formula as the minimum sum algorithm, i.e. Get c bits of L c2v Soft quantity information.

[0022] Finally, according to the formula For L c2v Perform bit-width conversion, where function F -1 Function (x) is the inverse mapping of c bits to b bits, transforming c bits... Reconstruct the data to restore it to b bits.

[0023] This decoding method, targeting 5G LDPC codes with BG1 as the base matrix, column block number N = 26–46, row block number M = 4–24, spread factor 384, and covering code rate range [1 / 2, 11 / 12], designs reconstruction schemes corresponding to the three mapping schemes in Table 1 (Table 2). This results in lower performance loss during the decoding process, reconstructing 3 bits (-3 to 3, 7 states) of information into 4 bits (-7 to 7, 15 states), providing higher bit width information for LLR and variable node updates in the next iteration. Different F values ​​are selected for different situations. -1 (m) is used as a reconstruction scheme. For example, the following five cases:

[0024] For 5G LDPC codes with 46 column blocks, 24 row blocks, and a code rate of 1 / 2, this decoding method adopts... As a restructuring solution.

[0025] For 5G LDPC codes with 35 column blocks, 13 row blocks, and a code rate of 2 / 3, this decoding method adopts... As a restructuring solution.

[0026] For 5G LDPC codes with 32 column blocks, 10 row blocks, and a code rate of 11 / 15, this decoding method uses... As a restructuring solution.

[0027] For 5G LDPC codes with 29 column blocks, 7 row blocks, and a code rate of 22 / 27, this decoding method adopts... As a restructuring solution.

[0028] For 5G LDPC codes with 26 column blocks, 4 row blocks, and a code rate of 11 / 12, this decoding method uses... As a restructuring solution.

[0029]

[0030]

[0031] Table 2 shows the 3-bit to 4-bit inverse mapping for 5G LDPC design.

[0032] Step 4: Based on the b-bit L obtained from the check node update in step S3 c2v Information and step S2, the variable node update obtains the L bit of a. v2c Information, and formulas The LLR can be updated with a bit width of a bits. Next, it is determined whether this layer is the last layer. If m = M, it means that it is the last layer, the update of this iteration ends, and step S5 is entered; if m < M, it returns to step S2 and continues to update the information of the next layer.

[0033] Step 5: First, based on the LLR updated in step S4, perform a hard decision, determining 0 or 1 based on whether the LLR is greater than 0, resulting in a codeword sequence for decoding. Then, multiply this codeword sequence by the parity check matrix. If the codeword sequence satisfies the parity check matrix (i.e., the multiplication result is 0), decoding is successful, and the codeword sequence is output. If it does not satisfy the parity check matrix (i.e., the multiplication result is not 0), compare the current iteration count with the maximum iteration count. If k < K... max In step S2, the iteration count k = k + 1, the current layer number m = 0, and the next round of decoding continues; otherwise, decoding fails within the maximum number of iterations.

[0034] The finite-precision quantization layered nonsurjective finite character set decoding method for 5G LDPC codes of the present invention has the following advantages:

[0035] This invention divides the entire decoding process into multiple stages based on the number of iterations. Compared to traditional LDPC decoding algorithms, such as the BP algorithm or the minimum sum algorithm, this decoding algorithm strictly implements the limitation on the bit width of soft information at each stage of decoding, and uses the mapping function F(x) and reconstruction function F as described in the claims. -1(x) further reduces the bit width in the more complex check node update unit, thereby reducing the hardware resources required for decoding. It also effectively reduces decoding latency with less loss of decoding performance, making it more suitable for decoding scenarios with finite precision quantization.

[0036] The decoding methods proposed in this invention are all based on the decoding algorithm for non-surjective finite character sets, and have fast iterative convergence, low latency, and good error correction performance. Attached Figure Description

[0037] Figure 1 This is a flowchart of the decoding method of the present invention.

[0038] Figure 2 The simulation verification diagram for this invention is: the frame error rate and bit error rate curves of the 5G matrix BG1_46_24_384.

[0039] Figure 3 The simulation verification diagram for this invention is: the frame error rate and bit error rate curves of the 5G matrix BG1_35_13_384.

[0040] Figure 4 The simulation verification diagram for this invention is: the frame error rate and bit error rate curves of the 5G matrix BG1_32_10_384.

[0041] Figure 5 The simulation verification diagram for this invention is: the frame error rate and bit error rate curves of the 5G matrix BG1_29_7_384.

[0042] Figure 6 The simulation verification diagram for this invention is: the frame error rate and bit error rate curves of the 5G matrix BG1_26_4_384. Detailed Implementation

[0043] To better understand the purpose, structure, and function of this invention, the following description, in conjunction with the accompanying drawings, provides a more detailed explanation of a finite-precision quantization layered non-surjective finite character set decoding method applicable to 5G LDPC codes.

[0044] This invention relates to a finite-precision quantization layered non-surjective finite character set (FAID) decoding method for 5G LDPC codes. The method is characterized by: Let H be the parity-check matrix corresponding to the 5G LDPC code base matrix BG1; its base matrix form has M = 4, ..., 24 rows, N = 26, ..., 46 columns, and a spread factor Z = 384; the decoder uses soft information bit widths a > b > c, with the bit width of each piece of information reflected in its superscripts a, b, and c; the soft information y received from the channel is quantized as... The bit width is b bits, and the soft information passed from the variable node to the check node in the iterative decoding is L.v2c The bit widths before and after compression via lookup table (LUT) mapping are respectively 'a' bits of information. and c-bit information In iterative decoding, the soft information passed from the check node to the variable node is L. c2v The bit widths before and after the inverse mapping are c bits of information. and b-bit information In iterative decoding, the soft information used for each probe output is LLR, with a bit width of a bits, i.e., LLR a All the above information is represented in two's complement; let the trial decoding output sequence be D, the number of iterations be k, the current layer number be m, and the maximum number of iterations be K. max .

[0045] Because this decoding method involves operations between multiple quantized bit information points, it is necessary to define some operators for bit width conversion. Define {x a y b The symbol} represents the concatenation of 'x' bits of information into the high-order bits of 'y' bits of information, forming a (a+b)-bit information. Define a′b0 and a′b1 to represent 'a' bits of all 0s and 'a' bits of all 1s, respectively. Define x... a [b] represents the b-th bit of the a-bit information x, with the least significant bit being the first bit. a [b] refers to the b-th bit of x from the least significant bit to the most significant bit. Define x. a [b:c] represents bits c to b of information in bit x, which is (b-c+1) bits of information. Therefore, for example... This indicates that (ab) bits The b-th bit of the information, i.e., the most significant bit, is related to b bits. Information is concatenated to form a bit of information; Indicates will The a-th position and The first to the (b-1)th bits are combined to form a b-bit information.

[0046] The decoding method includes the following steps:

[0047] Step 1: Initialize the iteration count k = 0, the current layer number m = 0, and perform finite-precision quantization on the soft information received from the channel. Uniform quantization is used, and the function Q(x) is the uniform quantization function. floor(x) is the floor function. Q max As a quantization threshold, Q max =2 t-1 -1, where t is the number of quantization bits. (Using the formula...) Where α is the quantization factor, thus... The bit width is limited to b bits; then, L needs to be further modified. v2c L c2v Information such as LLR is also initialized, that is...

[0048] Step 2: This decoding method calculates layer by layer according to the steps of layered decoding. Subtract the b-bit expanded to a-bit LLR information from the a-bit LLR information. Calculate in sequence all the resources needed for this layer Information, with a bit width of a bits.

[0049] Step 3: First, use the 'a' bits obtained in step S2 that this layer needs. Truncation is performed to b bits; that is, anything exceeding the b-bit representation range is truncated to the upper or lower limit of the b-bit representation range. Then according to For L v2c Perform bit-width conversion, where the function F(x) is a mapping from b bits to c bits, such that the b bits... Reduced to c bits

[0050] This decoding method, targeting 5G LDPC codes with BG1 as the base matrix, column block number N = 26–46, row block number M = 4–24, spread factor of 384, and covering code rate range [1 / 2, 11 / 12], designs three mapping schemes as shown in Table 1, completing a 4-bit (-7 to 7, 15 states) to 3-bit (-3 to 3, 7 states) mapping, and realizing L v2c Compression of soft quantity information. Different F(m) mapping schemes are selected for different situations. For example, the following five cases:

[0051] For 5G LDPC codes with 46 column blocks, 24 row blocks, and a code rate of 1 / 2, this decoding method uses F1(m) as the mapping scheme.

[0052] For 5G LDPC codes with 35 column blocks, 13 row blocks, and a code rate of 2 / 3, this decoding method uses F1(m) as the mapping scheme.

[0053] For 5G LDPC codes with 32 column blocks, 10 row blocks, and a code rate of 11 / 15, this decoding method uses F2(m) as the mapping scheme.

[0054] For 5G LDPC codes with 29 column blocks, 7 row blocks, and a code rate of 22 / 27, this decoding method uses F2(m) as the mapping scheme.

[0055] For 5G LDPC codes with 26 column blocks, 4 row blocks, and a code rate of 11 / 12, this decoding method uses F3(m) as the mapping scheme.

[0056] m 0 1 2 3 4 5 6 7 <![CDATA[F1(m)]]> 0 0 1 2 2 2 3 3 <![CDATA[F2(m)]]> 0 1 1 2 2 2 3 3 <![CDATA[F3(m)]]> 0 1 1 2 2 3 3 3

[0057] Table 1 shows the 4-bit to 3-bit mapping for 5G LDPC design.

[0058] Then, the L-bits that have been reduced to a width of c bits will be... v2c The information is sent to the verification node and calculated using the same formula as the minimum sum algorithm, i.e. Get c bits of L c2v Soft quantity information.

[0059] Finally, according to the formula For L c2v Perform bit-width conversion, where function F -1 Function (x) is the inverse mapping of c bits to b bits, transforming c bits... Reconstruct the data to restore it to b bits.

[0060] This decoding method, targeting 5G LDPC codes with BG1 as the base matrix, column block number N = 26–46, row block number M = 4–24, spread factor 384, and covering code rate range [1 / 2, 11 / 12], designs reconstruction schemes corresponding to the three mapping schemes in Table 1 (Table 2). This results in lower performance loss during the decoding process, reconstructing 3 bits (-3 to 3, 7 states) of information into 4 bits (-7 to 7, 15 states), providing higher bit width information for LLR and variable node updates in the next iteration. Different F values ​​are selected for different situations. -1 (m) is used as a reconstruction scheme. For example, the following five cases:

[0061] For 5G LDPC codes with 46 column blocks, 24 row blocks, and a code rate of 1 / 2, this decoding method adopts... As a restructuring solution.

[0062] For 5G LDPC codes with 35 column blocks, 13 row blocks, and a code rate of 2 / 3, this decoding method adopts... As a restructuring solution.

[0063] For 5G LDPC codes with 32 column blocks, 10 row blocks, and a code rate of 11 / 15, this decoding method uses... As a restructuring solution.

[0064] For 5G LDPC codes with 29 column blocks, 7 row blocks, and a code rate of 22 / 27, this decoding method adopts... As a restructuring solution.

[0065] For 5G LDPC codes with 26 column blocks, 4 row blocks, and a code rate of 11 / 12, this decoding method uses... As a restructuring solution.

[0066]

[0067] Table 2 shows the 3-bit to 4-bit inverse mapping for 5G LDPC design.

[0068] Step 4: Based on the b-bit L obtained from the check node update in step S3 c2v Information and step S2, the variable node update obtains the L bit of a. v2c Information, and formulas The LLR can be updated with a bit width of a bits. Next, it is determined whether this layer is the last layer. If m = M, it means that it is the last layer, the update of this iteration ends, and step S5 is entered; if m < M, it returns to step S2 and continues to update the information of the next layer.

[0069] Step 5: First, based on the LLR updated in step S4, perform a hard decision to obtain a set of codeword sequences for decoding attempts. Then, multiply the codeword sequence by the parity check matrix. If the codeword sequence satisfies the parity check matrix (i.e., the product is 0), the decoding is successful, and the codeword sequence is output. If it does not satisfy the parity check matrix (i.e., the product is not 0), compare the current iteration count with the maximum iteration count. If k < K... max In step S2, the iteration count k = k + 1, the current layer number m = 0, and the next round of decoding continues; otherwise, decoding fails within the maximum number of iterations.

[0070] See Figure 1 This invention provides a finite-precision quantization layered non-surjective finite character set (NS-FAID) decoding method suitable for 5G LDPC codes, and a specific implementation scheme is given here for illustration. In this implementation scheme, the parity-check matrix H is the BG1 matrix in 5G, with 4 rows, 26 columns, a spread factor of 384, a code rate of 11 / 12, and quantization bit widths a=6, b=4, c=3, respectively: Information received L ch The information L, which is 4 bits, is transmitted from the variable node to the check node. v2cAfter LUT mapping and compression, the bit widths are 6 bits and 3 bits respectively. The information passed from the check node to the variable node is L. c2v After inverse mapping, the bit widths are 3 bits and 4 bits respectively. The attempted decoding output information LLR is 6 bits, and the maximum number of iterations is 30. In this implementation, the LUT shown in Table 3 is used for mapping, transforming a 4-bit (-7 to 7, 15 states) to a 3-bit (-3 to 3, 7 states) mapping, thus realizing L... v2c Compression of soft data.

[0071] m 0 1 2 3 4 5 6 7 F(m) 0 1 1 2 2 3 3 3

[0072] Table 3 shows the 4-bit to 3-bit mapping under this implementation scheme.

[0073] This implementation scheme uses the LUT in Table 4 as the reconstruction scheme to reconstruct 3 bits (-3 to 3, 7 states) of information into 4 bits (-7 to 7, 15 states in total) of information, providing higher bit width information for LLR and the updating of variable nodes in the next iteration.

[0074] m 0 1 2 3 <![CDATA[F -1 (m)]]> 0 1 3 6

[0075] Table 4 shows the 3-bit to 4-bit mapping under this implementation scheme.

[0076] This invention proposes a finite-precision quantization hierarchical non-surjective finite character set (NS-FAID) decoding method suitable for 5G LDPC codes. The entire decoding process is divided into multiple stages. Compared to traditional LDPC decoding algorithms, such as the BP algorithm or the minimum sum algorithm, this decoding method implements a limit on the bit width of soft information throughout the process. Furthermore, in the relatively complex check node update unit, i.e., step 3, the bit width can be further reduced from 4 bits to 3 bits (or even 2 bits), thereby reducing the hardware resources required for decoding. With minimal performance loss, it effectively reduces decoding latency, making it more suitable for decoding scenarios under finite-precision quantization. Therefore, the entire decoding process possesses both low quantization precision and hardware complexity, high decoding convergence speed, and low decoding latency, resulting in a decoding method that combines low power consumption, low complexity, and high performance.

[0077] Figures 2 to 6The decoding performance of the Layered Minimum Sum (LNMS) algorithm under floating-point precision and the above-described implementation scheme for five 5G matrices is compared, both with 30 iterations. In the legend, FER-float-LNMS / BER-float-LNMS represent the frame error rate and bit error rate of the Layered Minimum Sum algorithm under floating-point precision, respectively, and FER-Layered-FAID(3bit) / BER-Layered-FAID(3bit) represent the frame error rate and bit error rate of the non-surjective finite character set decoding algorithm, respectively. This scheme uses a 4-bit to 3-bit F(x) mapping function and a 3-bit to 4-bit F... -1 The reconstruction function of (x).

[0078] Figure 2 The 5G matrix tested was a BG1 matrix, with 46 columns and 24 rows, a spread factor of 384, and a code rate of 1 / 2. Figure 2 It can be seen that under this 5G matrix, the frame error rate (FER) is 1×10⁻⁶. -3 At that time, the signal-to-noise ratio required by the layered minimum sum algorithm under floating-point precision is about 1.41dB, while the signal-to-noise ratio required by the decoding algorithm proposed in this invention is about 1.72dB, with only about 0.3dB of performance loss under finite precision quantization.

[0079] Figure 3 The 5G matrix tested was a BG1 matrix, with 35 columns and 13 rows, a spread factor of 384, and a code rate of 2 / 3. Figure 3 It can be seen that under this 5G matrix, the frame error rate (FER) is 1×10⁻⁶. -3 At that time, the signal-to-noise ratio required by the layered minimum sum algorithm under floating-point precision is about 1.92dB, while the signal-to-noise ratio required by the decoding algorithm proposed in this invention is about 2.32dB, with only about 0.4dB of performance loss under finite precision quantization.

[0080] Figure 4 The 5G matrix tested was a BG1 matrix, with 32 columns, 10 rows, a spread factor of 384, and a code rate of 11 / 15. Figure 4 It can be seen that under this 5G matrix, the frame error rate (FER) is 1×10⁻⁶. -3 At that time, the signal-to-noise ratio required by the layered minimum sum algorithm under floating-point precision is about 2.31dB, while the signal-to-noise ratio required by the decoding algorithm proposed in this invention is about 2.62dB, with only about 0.3dB of performance loss under finite precision quantization.

[0081] Figure 5 The 5G matrix tested was a BG1 matrix, with 29 columns and 7 rows, a spread factor of 384, and a code rate of 22 / 27. Figure 5It can be seen that under this 5G matrix, the frame error rate (FER) is 1×10⁻⁶. -3 At that time, the signal-to-noise ratio required by the layered minimum sum algorithm under floating-point precision is about 2.91dB, while the signal-to-noise ratio required by the decoding algorithm proposed in this invention is about 3.2dB, with only about 0.3dB of performance loss under finite precision quantization.

[0082] Figure 6 The 5G matrix tested was a BG1 matrix, with 26 columns and 4 rows, a spread factor of 384, and a code rate of 11 / 12. Figure 6 It can be seen that under this 5G matrix, the frame error rate (FER) is 1×10⁻⁶. -3 At that time, the signal-to-noise ratio required by the layered minimum sum algorithm under floating-point precision is about 4.26dB, while the signal-to-noise ratio required by the decoding algorithm proposed in this invention is about 4.48dB, with only about 0.2dB of performance loss under finite precision quantization.

[0083] In summary, the finite-precision quantization hierarchical non-surjective finite character set (NS-FAID) decoding method for 5G LDPC codes proposed in this invention can further reduce the bit width in the most complex check node update process during decoding, while maintaining finite-precision quantization, and exhibits less performance loss compared to the hierarchical minimum sum algorithm under floating-point precision. Compared to existing decoding methods, the hierarchical NS-FAID decoding method for 5G LDPC codes proposed in this invention not only saves hardware resources, reduces power consumption, and decreases decoding latency, but also suffers from minimal performance loss, making it suitable for use in hardware systems with high requirements for power consumption and complexity.

[0084] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A finite precision quantized layered non-surjective finite character set decoding method suitable for 5G LDPC codes, characterized in that, Let H be the parity-check matrix corresponding to the 5G LDPC code base matrix BG1. The number of row blocks in the 5G LDPC code base matrix BG1 form is M = 4, ..., 24, the number of column blocks is N = 26, ..., 46, and the spread factor is Z = 384. The decoder uses soft information bit widths a > b > c, and the bit width of each piece of information is reflected in its superscripts a, b, and c. The soft information y received from the channel is quantized as... The bit width is b bits, and the soft information passed from the variable node to the check node in the iterative decoding is L. v2c The bit widths before and after compression via lookup table (LUT) are a bits respectively. and c-bit information In iterative decoding, the soft information passed from the check node to the variable node is L. c2v The bit widths before and after the inverse mapping are c bits of information. and b-bit information In iterative decoding, the soft information used for each probe output is LLR, with a bit width of a bits, i.e., LLR a All the above information is represented in two's complement; let the trial decoding output sequence be D, the number of iterations be k, the current layer number be m, and the maximum number of iterations be K. max ; Definition x a , y b} represents a bit x information spliced in the high bit of b bit y information, to form an (a+b) bit information; define a' b0 represents a bit of all 0 information, a' b1 represents a bit of all 1 information, (a-b) bit information of the bth bit, that is, if the bth bit is 1, it is (a-b) bit all 1 information, otherwise it is (a-b) bit all 0 information; define x a [b] represents the bth bit of a bit x information; define x a [b:c] represents the cth bit to the bth bit of a bit x information, which is (b-c+1) bit information; The decoding method comprises the following steps: Step S1: initialize iteration number k=0, current calculated layer number m=0, quantize the soft information received from the channel by using uniform quantization, set function Q(x) as the uniform quantization function, floor(x) is the down-rounding function, Q max is the quantization threshold, Q max =2 t-1 -1, t is the quantization bit number; through the formula wherein α is the quantization factor, thereby limiting the bit width of L to b bits; then initialize the L v2c , L c2v and LLR information, i.e. Step S2: The decoding method calculates layer by layer according to the steps of layered decoding. Subtract the b-bit expanded to a-bit LLR information from the a-bit LLR information. Calculate in sequence all the resources needed for this layer Information, with a bit width of a bits; Step S3: First, use the 'a' bits obtained in step S2 that this layer needs. Truncate to b bits; any value exceeding the b-bit representation range is truncated to either the upper or lower bound of the b-bit representation range. Then according to For L v2c A bit-width conversion is performed, where the function F(x) maps b-bit information to c-bit information, making the b-bit... Reduced to c bits The F(x) mapping function of the decoding method adopts a lookup table mode to map 0-7, eight kinds of information, into one of 0-3, four kinds of information, thereby completing a 4-bit to 3-bit mapping, realizing L v2c Compression of soft information; wherein 4 bits are -7-7, a total of 15 states; 3 bits are -3-3, a total of 7 states; different F(x) is selected as a mapping scheme for different configurations of the 5G LDPC code BG1 matrix; Finally, according to the formula For L c2v bit width conversion is performed, where the function F -1 (x) is the inverse mapping of the c-bit information to b-bit information, and F(x) is the inverse transform of each other, and the c-bit is reconstructed to recover the b-bit Step S4: updating the L of b bits according to the check node update in step S3 c2v information and the L of a bits updated by the variable node in step S2 v2c information, and the formula updating the LLR with a bits as the bit width; then judging whether the layer is the last layer or not, if m=M, it means the last layer, the updating of this iteration is finished, and step S5 is entered; if m Step S5: first, according to the LLR updated in step S4, a hard decision is made, and 0 or 1 is decided according to whether the LLR is greater than 0, to obtain a set of code word sequences for trial decoding, then the code word is multiplied by the check matrix, if the code word sequence satisfies the check matrix, the decoding is successful, and the code word sequence is output; if it does not satisfy the check matrix, the current iteration number is compared with the maximum iteration number, if k max to step S2, iteration number k=k+1, the current calculated layer number m=0, continue the next round of iteration decoding, otherwise, within the maximum iteration number, the decoding fails.

2. The method of Claim 1, wherein the method is applicable to 5G LDPC codes with finite precision quantized layered non-surjective finite character set decoding. For different configurations of the 5G LDPC code BG1 matrix, different mapping schemes are selected, including the following five cases: For the 5G LDPC code with 46 column blocks, 24 row blocks and a code rate of 1 / 2, the decoding method adopts F1(m) as the mapping scheme; For the 5G LDPC code with 35 column blocks, 13 row blocks and a code rate of 2 / 3, the decoding method adopts F1(m) as the mapping scheme; For the 5G LDPC code with 32 column blocks, 10 row blocks and a code rate of 11 / 15, the decoding method adopts F2(m) as the mapping scheme; For the 5G LDPC code with 29 column blocks, 7 row blocks and a code rate of 22 / 27, the decoding method adopts F2(m) as the mapping scheme; For the 5G LDPC code with 26 column blocks, 4 row blocks and a code rate of 11 / 12, the decoding method adopts F3(m) as the mapping scheme; Then, the L v2c The information is fed into the check node and calculated by the same formula as in the min-sum algorithm, i.e. The L v2v Soft information.

3. The method of Claim 2, wherein the method is applicable to 5G LDPC codes with finite precision quantized layered non-surjective finite character set decoding. For the 5 mapping schemes, the following 5 F -1 (m) as a reconstruction scheme: For the 5G LDPC code with column block number 46, row block number 24 and code rate 1 / 2, the decoding method adopts as a reconstruction scheme; For the 5G LDPC code with column block number 35, row block number 13 and code rate 2 / 3, the decoding method adopts as a reconstruction scheme; For the 5G LDPC code with column block number 32, row block number 10 and code rate 11 / 15, the decoding method adopts as a reconstruction scheme; For the 5G LDPC code with column block number 29, row block number 7 and code rate 22 / 27, the decoding method adopts as a reconstruction scheme; For the 5G LDPC code with column block number 26, row block number 4 and code rate 11 / 12, the decoding method adopts as a reconstruction scheme.

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