A BICM-ID iterative receiving method based on LDPC code

Abstract

The application discloses a BICM-ID iterative receiving method based on LDPC code, which improves the spectrum utilization ratio under the condition of ensuring a lower error rate by joint coding and modulation, introduces an outer iteration process, fully utilizes channel symbol information, and has a system gain obviously higher than that of a BICM system; a check node satisfying probability detection node is introduced on the basis of a factor graph, information is unidirectionally transmitted, does not affect a normal demodulation-decoding iteration process, can judge the iteration state in real time according to convergence, and is convenient for the realization of a receiver system; the probability information of the check node satisfying probability detection node is used as a confidence parameter in the iteration process and is used for iteration stop criterion judgment, can reduce the implementation complexity of a traditional decoding stop criterion on the basis of ensuring the error rate performance, reduces the iteration number and system processing time delay at a low signal-to-noise ratio, and improves the system throughput. The application is suitable for the communication field, improves the reliability of decoding and the system throughput, and thus improves the communication quality.

Description

Technical Field

[0001] This invention relates to an iterative BICM-ID receiving method based on LDPC codes, belonging to the field of communication signal processing. Background Technology

[0002] Channel coding and digital modulation are two commonly used digital signal processing techniques in wireless communication systems. Currently, channel coding techniques mainly include Hamming codes, convolutional codes, concatenated codes, Turbo codes, and Low-Density Parity-Check (LDPC) codes. Among them, LDPC codes have received widespread research and attention due to their near-Shannon limit performance and ease of parallel processing. To fully improve the coding gain of the channel and facilitate low-complexity implementation, various decoding methods exist for LDPC codes, including the Belief Propagation (BP) algorithm, the Log Likelihood Ratio (LLR-BP) algorithm, the Min-Sum (MS) decoding algorithm, the Normalized Min-Sum (NMS) algorithm, the Offset Min-Sum (OMS) algorithm, and the Improved Normalized Min-Sum (INMS) algorithm. However, LDPC coding technology sacrifices spectral efficiency for signal transmission reliability, and introducing channel coding leads to a decrease in spectral efficiency. To address this shortcoming, digital modulation techniques can be introduced after coding. Bit-Interleaved Coded Modulation (BICM) based on LDPC coding can significantly improve the system's bandwidth utilization, especially in high-order modulation scenarios such as 8PSK, 16QAM, and 64QAM. This system can flexibly select the coding rate, modulation scheme, and number of iterations according to channel conditions and application requirements to achieve an optimal balance between different performance and complexity. However, existing joint LDPC-BICM algorithms cannot fully utilize channel information or maximize the coding gain effect of LDPC codes, and they suffer from excessive iterations and high processing delays in low signal-to-noise ratio regions. Summary of the Invention

[0003] To address the issue that traditional BICM systems cannot fully utilize the LDPC coding gain, and that sacrificing some Euclidean distance to maximize Hamming distance results in suboptimal performance under Additive White Gaussian Noise (AWGN) channels, the main objective of this invention is to disclose an LDPC-based BICM-ID iterative reception method. This method introduces a feedback loop, interleaving the posterior probability of the LDPC decoder and feeding it back to the demapper as prior information. The demapper then updates the probability information for each bit, completing one iteration and improving decoding reliability. Furthermore, an iterative decoding stopping criterion optimization method is used to determine the decoding state in real time, reducing invalid iterations, lowering processing latency, and increasing system throughput, thereby improving communication quality.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] This invention discloses a BICM-ID iterative reception method based on LDPC codes, comprising the following steps:

[0006] Step 1: Encode, interleave, map, and modulate the original information sequence, and then transmit it through the AWGN channel.

[0007] The original information sequence M of length k bits is multiplied by the generator matrix G of LDPC encoding to obtain the encoded result C = M·G, with a length of n for the encoded sequence C. Then, the encoded information bits are interleaved using an interleaver to obtain the symbol sequence X = π(C), where the function π represents the specific interleaving and deinterleaving method. The interleaver only changes the order of the symbols, not the total length of the symbol sequence; therefore, sequences C and X have the same length. The encoded information bits are then mapped through a constellation mapping function. The mapping is performed using m encoded and interleaved information bits x0, x1, ..., x2. m-1 The symbol is mapped to a constellation point in a space. Here, Ω represents the complete constellation space after mapping, containing M constellation points, where M = 2. m , This represents rounding down. The interleaved sequence X is then modulated and mapped to obtain the symbol sequence. It can be extended to higher-order modulation schemes by changing the specific form of the function mapping. Finally, the symbol sequence Y is transmitted through the AWGN channel.

[0008] Step 2: The demodulator receives the output symbols from the AWGN channel and performs demapping, using channel information and prior probability information to calculate the probability information of the transmitted symbols and their corresponding bits.

[0009] The channel output symbol sequence is denoted by Z = {z1, z2, ..., z}. t This means that when deriving soft bit information using the initial symbol information of the received channel, the source can be considered as having an equal probability distribution. Therefore, the probability of each bit node being initially 0 or 1 is equal, i.e.:

[0010]

[0011] Where, x i This represents the value of the i-th bit in the transmission sequence. Each mapping symbol in the constellation mapping space. The probabilities are also the same, that is:

[0012]

[0013] The probability information for each transmitted symbol is as follows:

[0014]

[0015] Among them, y t z represents the t-th symbol in the transmitted symbol sequence. t This represents the t-th symbol in the received symbol sequence. The "^" in the middle represents its estimated value.

[0016] Based on the additive white Gaussian noise channel, the probability density function is:

[0017]

[0018] For a complex Gaussian channel, the probability density function is:

[0019]

[0020] Where, σ 2 y represents the variance of the Gaussian channel. I and y Q Let z represent the real and imaginary parts of the channel transmitted symbol y, respectively. I and z Q Let z represent the real and imaginary parts of the channel received symbol z, respectively.

[0021] Substituting into the above equation and simplifying, we obtain the initial probability information for each transmitted symbol as follows:

[0022]

[0023] in, and Let z represent the real and imaginary parts of the k-th constellation mapping point in the constellation mapping space, respectively. re and z im Let z represent the real and imaginary parts of the channel received symbol z, respectively.

[0024] The probability information of each bit is derived from the symbol probability information:

[0025]

[0026] in This represents the constellation point with bit b at position i in the constellation mapping graph χ. A set of.

[0027] The above expression can be expressed over the logarithmic field as:

[0028]

[0029] Step 3: Pass the demapped bit probability information through the deinterleaver π. -1 A global detailed factor graph model was established for the receiver of the LDPC-BICM-ID system.

[0030] Deinterleaving only changes the bit order and has no effect on probabilistic information, therefore... and No distinction is made.

[0031] Construct a factor graph model G = (VNs∪CNs,Ξ) with check constraint relationship based on the check matrix of LDPC code, where VNs represents the set of variable nodes, CNs represents the set of check nodes, and Ξ represents the set of edges between variable nodes and check nodes, corresponding to the position of 1 in the check matrix H.

[0032] The channel received symbol sequence Z = {Z1, Z2, ..., Z} t After passing through the mapping module φ, the bitstream sequence X = {X1, X2, ..., X} is obtained. n After deinterleaving module π, the sequence C = {C1, C2, ..., C} is obtained. n}, corresponding to the set of variable nodes VNs in the model G=(VNs∪CNs,Ξ), the first k variable nodes correspond to the final decoding result sequence M={M1,M2,…,M k}

[0033] Based on this, add a verification node that satisfies the probability detection node G={g1,g2,…,g n-k} and the verification node normalization satisfies the probability statistics node G sum Verification nodes CNs = {h1, h2, ..., h n-k} The verification nodes connected to it satisfy the probability check node G={g1,g2,…,g n-k} One-way information transmission, where h i G represents the i-th verification node. i This represents the i-th detection node, and there is a one-to-one correspondence between the two.

[0034] Step 4: Complete the iterative decoding of the confidence propagation algorithm within the LDPC decoder.

[0035] Use r ji (x i ) represents the j-th verification node C j The probability density function passed to the i-th variable node, where the corresponding bit is either "0" or "1". (Using q) ij (x i ) represents the i-th variable node V i The probability density function of the corresponding bit being "0" or "1" transmitted to the j-th check node. The check node update process is represented as:

[0036]

[0037]

[0038] The variable node update process is represented as follows:

[0039]

[0040]

[0041] Among them, set R j\i Let set C represent the set of positions in the j-th row of the parity check matrix H, excluding the i-th 1. i\j Let H represent the set of positions in the i-th row of the parity check matrix H, excluding the j-th 1.

[0042] The node update process can be represented over the logarithmic field as follows:

[0043]

[0044]

[0045] Each node update process is considered a single internal iteration. This node update process is repeated until the stopping criterion is met. (Using Q...) i (x i ) represents the posterior likelihood probability of the i-th variable node, which is the probability value that needs to be calculated in the final step of the iterative decoding process.

[0046]

[0047]

[0048] The above expression can be expressed over the logarithmic field as:

[0049]

[0050] Step 5: The decoded soft bit information is fed back to the demodulator via the interleaver as prior information for the next demodulation.

[0051] The interleaver only changes the order and does not affect the probability information; it does not distinguish between x and c, and uses p. a (x i This represents prior information for the next demodulation process:

[0052] p a (x i =0)=Q i (x i =0)

[0053] p a (x i =1)=Q i (x i =1)

[0054] The above expression can be expressed over the logarithmic field as:

[0055]

[0056] Step 6: The demodulator updates each bit using the channel symbol information and the received prior soft bit information.

[0057] Using the symbol information from the channel calculated in step two and the prior information p obtained in step five a (x i =b) Jointly update each bit information, complete one outer iteration process, and obtain the updated probability information of each bit as follows:

[0058]

[0059] The above expression can be expressed over the logarithmic field as:

[0060]

[0061] in, Let y represent the i-th bit of the t-th symbol, b∈{0,1}. t This represents the t-th symbol transmitted through the channel. This represents the constellation point with bit b at position i in the constellation mapping graph χ. The set, This represents the j-th bit value corresponding to the k-th constellation mapping point.

[0062] Step 7: Use the probability information of the verification node satisfying the probability detection node as the confidence parameter in the iteration process, and use it to determine the iteration stopping criterion.

[0063] node g iThis represents whether the i-th check equation is satisfied, therefore we can use the probability p(g) i =0) represents the probability mass function of whether the i-th equation in the verification equation is true. Verification node h i Transmitted to detection node g i The information needs to be calculated using the information of all variable nodes connected to the i-th check node, and is expressed as:

[0064]

[0065] in, Indicates that except for g i Summation of functions for all variable nodes except V m′ ∈N(C i )\g i V represents m′ Belongs to the verification node C i Connected, but excluding node g i The set of all variable nodes, f i (x) is the indicator function I C (C i )=δ(·), which means that when the sum of all variable nodes connected to the check node modulo 2 is 0, the value of this function is 1.

[0066] The output of the detection node G is the probability p(g) that the verification node satisfies the condition. i =0|H,Y), representing the parity check relation g output by the detection node under the condition that the received channel sequence Y and the parity check matrix H are known. i The probability that the value is 0 is expressed as:

[0067]

[0068] The normalization of the verification node satisfies the probability node G. sum The output p(G) sum To normalize the output values ​​of all detection nodes G:

[0069]

[0070] p(G) sum As a confidence parameter, its trend during the internal and external iterations indicates that if the confidence parameter gradually approaches 1 from 0.5 and converges, the codeword is correctly decoded. If the confidence parameter converges to around 0.5 during decoding, it indicates that the codeword converged to an incorrect codeword in this decoding process, and the next external iteration can be performed, introducing channel information again to re-decode the frame. If the confidence parameter oscillates continuously between 0.5 and 1, the codeword is a non-convergent codeword.

[0071] Based on the above introduction, the stopping criterion is expressed as: (i) when the normalization of the verification node satisfies the probability p(G) sum (i) When the decoding success threshold is reached, the current frame iteration stops, which is considered a successful decoding; (ii) When the normalization of the verification node satisfies the probability p(G) sum (iii) Stop the current decoding iteration when the symbol convergence threshold is reached, and enter the external iteration process; (iv) Stop the iteration when the internal and external iterations reach the maximum number of internal and external iterations.

[0072] The stopping criterion provides three threshold parameters T, γ, and η for judgment. Here, T represents the successful decoding threshold, γ represents the continuous periodicity threshold for convergence, and η represents the range of variation threshold.

[0073] The specific implementation process of the stopping criterion is as follows: First, determine the confidence parameter p(G) sum Does the value of p(G) exceed the decoding success threshold T? sum If the value of the decoder is greater than or equal to T, then the correct codeword has been found in the frame being processed by the current decoder, and the decoding process of the system immediately stops. The posterior probability of the bits output by the decoder is then used for decision-making. Next, the current iteration period p(G) is compared. sum If the difference between the value of the current decoding process and the value of the previous cycle is less than the set threshold η, the counter is incremented by 1; otherwise, the counter is set to 0. When the counter reaches the set threshold γ for convergence of consecutive cycles, the current decoding process is considered to have converged, and subsequent decoding iterations are invalid. At this point, the internal decoding iteration process also terminates immediately, and the external iteration update process begins. Besides the above two cases, if the iterative decoding process exceeds the preset number of iterations and cannot find the correct codeword, the decoder stops the current iteration process and proceeds to the next frame's iteration process.

[0074] Step 8: Bit decision output, obtain the codeword sequence after receiver decoding, and complete the digital communication process.

[0075] Based on the posterior probability information of the decoded output, a decision is made on the first k bits. If Q... i (x i =0)>Q i (x i =1), then m i The decision is 0, otherwise it is 1, thus obtaining the received codeword sequence and completing the demodulation-decoding process.

[0076] This invention uses the above eight steps to obtain the approximate posterior probability of the codeword using prior channel information and parity check matrix information, completes the joint demodulation-decoding iterative process, and guides the stopping criteria of the inner and outer iterations based on the convergence analysis of the normalization probability of the parity check nodes.

[0077] Beneficial effects:

[0078] 1. The present invention discloses a BICM-ID iterative reception method based on LDPC code, which combines coding and modulation to improve spectrum utilization while ensuring a low bit error rate. It introduces an external iterative process to make full use of channel symbol information, and the system gain is significantly higher than that of the BICM system.

[0079] 2. The present invention discloses a BICM-ID iterative reception method based on LDPC code, which introduces a check node to satisfy the probability detection node on the basis of the factor graph. The information is transmitted in one direction and does not affect the normal demodulation-decoding iterative process. It can judge the iteration status in real time based on convergence, which facilitates the implementation of the receiver system.

[0080] 3. The present invention discloses a BICM-ID iterative reception method based on LDPC code, which uses the probability information of the verification node satisfying the probability detection node as a confidence parameter in the iteration process for determining the iteration stopping criterion. It can reduce the implementation complexity of the traditional decoding stopping criterion while ensuring bit error rate performance, reduce the number of iterations and system processing latency at low signal-to-noise ratio, and improve system throughput. Attached Figure Description

[0081] Figure 1 This is a schematic diagram of the overall process of a BICM-ID iterative receiving method based on LDPC codes disclosed in this invention;

[0082] Figure 2 This is the detailed global factor graph model of the joint 8PSK demodulation-LDPC decoding described in the embodiments of the present invention;

[0083] Figure 3 This is a schematic diagram of the stopping criterion process for a BICM-ID iterative reception method based on LDPC codes disclosed in this invention.

[0084] Figure 4 This is the bit error rate simulation curve of the reference code pattern combined with 8PSK modulation as described in the embodiments of the present invention;

[0085] Figure 5 The figure shows the simulation curve of the average number of decoding iterations for the reference code combined with 8PSK modulation receiver described in this embodiment of the invention, using the design stopping criterion for decoding. Detailed Implementation

[0086] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The technical problems solved by the present invention and its beneficial effects are also described. It should be noted that the described embodiments are only intended to facilitate understanding of the present invention and do not constitute any limitation thereof.

[0087] This embodiment discloses an iterative reception method for BICM-ID based on LDPC codes, as per the US Deep Space Communications CCSDS131.1-0-1 standard. The system parameters are shown in the table below:

[0088] Bits per frame 120 Bitrate 1 / 2 Drilling method Last 60 bits of the check digit Modulation method 8PSK Channel Model Gaussian white noise Maximum number of decoding iterations 30 Maximum demodulation-decoding iterations 3

[0089] like Figure 1 As shown, the specific implementation steps of this embodiment are as follows:

[0090] Step 1: Encode, interleave, map, and modulate the original information sequence, and then transmit it through the AWGN channel.

[0091] The original information sequence M of length k bits is multiplied by the generator matrix G of LDPC encoding to obtain the encoded result C = M·G, with a length of n for the encoded sequence C. Then, the encoded information bits are interleaved using an interleaver to obtain the symbol sequence X = π(C), where the function π represents the specific interleaving and deinterleaving method. The interleaver only changes the order of the symbols, not the total length of the symbol sequence; therefore, sequences C and X have the same length. The encoded information bits are then mapped through a constellation mapping function. The mapping is performed using m encoded and interleaved information bits x0, x1, ..., x2. m-1 The symbol is mapped to a constellation point in a space. Here, Ω represents the complete constellation space after mapping, containing M constellation points, where M = 2. m , This represents rounding down. The interleaved sequence X is then modulated and mapped to obtain the symbol sequence. It can be extended to higher-order modulation schemes by changing the specific form of the function mapping. Finally, the symbol sequence Y is transmitted through the AWGN channel.

[0092] Step 2: The demodulator receives the output symbols from the AWGN channel and performs demapping, using channel information and prior probability information to calculate the probability information of the transmitted symbols and their corresponding bits.

[0093] The channel output symbol sequence is denoted by Z = {z1, z2, ..., z}. t This means that when deriving soft bit information using the initial symbol information of the received channel, the source can be considered as having an equal probability distribution. Therefore, the probability of each bit node being initially 0 or 1 is equal, i.e.:

[0094]

[0095] Where, x i This represents the value of the i-th bit in the transmission sequence. Therefore, each mapping symbol in the constellation mapping space... The probabilities are also the same, that is:

[0096]

[0097] The probability information for each transmitted symbol is as follows:

[0098]

[0099] Among them, y t z represents the t-th symbol in the transmitted symbol sequence. t This represents the t-th symbol in the received symbol sequence. The "^" in the middle represents its estimated value.

[0100] Based on the additive white Gaussian noise channel, the probability density function is:

[0101]

[0102] For a complex Gaussian channel, the probability density function is:

[0103]

[0104] Where, σ 2 y represents the variance of the Gaussian channel. I and y Q Let z represent the real and imaginary parts of the channel transmitted symbol y, respectively. I and z Q Let z represent the real and imaginary parts of the channel received symbol z, respectively.

[0105] Substituting into the above equation and simplifying, we obtain the initial probability information for each transmitted symbol as follows:

[0106]

[0107] in, and Let z represent the real and imaginary parts of the k-th constellation mapping point in the constellation mapping space, respectively. re and z im Let z represent the real and imaginary parts of the channel received symbol z, respectively.

[0108] The probability information of each bit is derived from the symbol probability information:

[0109]

[0110] in This represents the constellation point with bit b at position i in the constellation mapping graph χ. A set of.

[0111] The above expression can be expressed over the logarithmic field as:

[0112]

[0113] Step 3: Pass the demapped bit probability information through the deinterleaver π. -1 A global detailed factor graph model was established for the receiver of the LDPC-BICM-ID system.

[0114] Deinterleaving only changes the bit order and has no effect on probabilistic information, therefore... and No distinction is made.

[0115] Construct a factor graph model G = (VNs∪CNs,Ξ) with check constraint relationship based on the check matrix of LDPC code, where VNs represents the set of variable nodes, CNs represents the set of check nodes, and Ξ represents the set of edges between variable nodes and check nodes, corresponding to the position of 1 in the check matrix H.

[0116] In the CCSDS standard, the parity check matrix is ​​a quasi-cyclic matrix composed of cyclic submatrices. This embodiment uses an LDPC code with information bits k = 120 and a code rate R = 1 / 2. Its parity check matrix is ​​a 180×300 parity check matrix H constructed by concatenating 3×5 subcyclic matrices M of size 60. To ensure the code pattern conforms to the given code rate, the codewords need to be punctured. This means that at the transmitting end, a portion of the parity bits are not transmitted, and at the receiving end, zeros are padded at the corresponding codeword positions for decoding. This embodiment selects the last 60 bits of the parity bits for puncturing to ensure the transmission code rate meets the 1 / 2 requirement.

[0117] The channel received symbol sequence Z = {Z1, Z2, ..., Z} t After passing through the mapping module φ, the bitstream sequence X = {X1, X2, ..., X} is obtained. n After deinterleaving module π, the sequence C = {C1, C2, ..., C} is obtained. n}, corresponding to the set of variable nodes VNs in the model G=(VNs∪CNs,Ξ), the first k variable nodes correspond to the final decoding result sequence M={M1,M2,…,M k}

[0118] Based on this, add a verification node that satisfies the probability detection node G={g1,g2,…,g n-k} and the verification node normalization satisfies the probability statistics node G sum Verification nodes CNs = {h1, h2, ..., h n-k} The verification nodes connected to it satisfy the probability check node G={g1,g2,…,g n-k} One-way information transmission, where h i G represents the i-th verification node. i This represents the i-th detection node, and there is a one-to-one correspondence between the two. The detailed factor graph model is as follows: Figure 2 As shown.

[0119] Step 4: The LDPC decoder completes the iterative decoding process of the confidence propagation algorithm.

[0120] Use r ji (x i ) represents the j-th verification node C j The probability density function passed to the i-th variable node, where the corresponding bit is either "0" or "1". (Using q) ij (x i ) represents the i-th variable node V i The probability density function of the corresponding bit being "0" or "1" transmitted to the j-th check node. The check node update process is represented as:

[0121]

[0122]

[0123] The variable node update process is represented as follows:

[0124]

[0125]

[0126] Among them, set R j\i Let set C represent the set of positions in the j-th row of the parity check matrix H, excluding the i-th 1. i\j Let H represent the set of positions in the i-th row of the parity check matrix H, excluding the j-th 1.

[0127] The node update process can be represented over the logarithmic field as follows:

[0128]

[0129]

[0130] Each node update process is considered a single internal iteration. This node update process is repeated until the stopping criterion is met. (Using Q...) i (x i ) represents the posterior likelihood probability of the i-th variable node, which is the probability value that needs to be calculated in the final step of the iterative decoding process.

[0131]

[0132]

[0133] The above expression can be expressed over the logarithmic field as:

[0134]

[0135] Step 5: The decoded soft bit information is fed back to the demodulator via the interleaver as prior information for the next demodulation.

[0136] Similarly, the interleaver only changes the order and does not affect the probability information; it does not distinguish between x and c, and uses p. a (x i This represents prior information for the next demodulation process:

[0137] p a (x i =0)=Q i (x i =0)

[0138] p a (x i =1)=Q i (x i =1)

[0139] The above expression can be expressed over the logarithmic field as:

[0140]

[0141] Step 6: The demodulator updates each bit using the channel symbol information and the received prior soft bit information.

[0142] Using the symbol information from the channel calculated in step two and the prior information p obtained in step five a (x i =b) Jointly update each bit information, complete one outer iteration process, and obtain the updated probability information of each bit as follows:

[0143]

[0144] The above expression can be expressed over the logarithmic field as:

[0145]

[0146] in, Let y represent the i-th bit of the t-th symbol, b∈{0,1}. t This represents the t-th symbol transmitted through the channel. This represents the constellation point with bit b at position i in the constellation mapping graph χ. The set, This represents the j-th bit value corresponding to the k-th constellation mapping point.

[0147] Step 7: Use the probability information of the verification node satisfying the probability detection node as the confidence parameter in the iteration process, and use it to determine the iteration stopping criterion.

[0148] node g i This represents whether the i-th check equation is satisfied, therefore we can use the probability p(g) i =0) represents the probability mass function of whether the i-th equation in the verification equation is true. Verification node h i Transmitted to detection node g i The information needs to be calculated using the information of all variable nodes connected to the i-th check node, and is expressed as:

[0149]

[0150] in, Indicates that except for g i Summation of functions for all variable nodes except V m′ ∈N(C i )\g i V represents m′ Belongs to the verification node C i Connected, but excluding node g i The set of all variable nodes, f i (x) is the indicator function I C (C i )=δ(·), which means that when the sum of all variable nodes connected to the check node modulo 2 is 0, the value of this function is 1.

[0151] The output of the detection node G is the probability p(g) that the verification node satisfies the condition. i =0|H,Y), representing the parity check relation g output by the detection node under the condition that the received channel sequence Y and the parity check matrix H are known. i The probability that the value is 0 is expressed as:

[0152]

[0153] The normalization of the verification node satisfies the probability node G. sum The output p(G) sum To normalize the output values ​​of all detection nodes G:

[0154]

[0155] p(G) sum As a confidence parameter, its trend during the internal and external iterations indicates that if the confidence parameter gradually approaches 1 from 0.5 and converges, the codeword is correctly decoded. If the confidence parameter converges to around 0.5 during decoding, it indicates that the codeword converged to an incorrect codeword in this decoding process, and the next external iteration can be performed, introducing channel information again to re-decode the frame. If the confidence parameter oscillates continuously between 0.5 and 1, the codeword is a non-convergent codeword.

[0156] Based on the above introduction, the stopping criterion is expressed as: (i) when the normalization of the verification node satisfies the probability p(G) sum (i) When the decoding success threshold is reached, the current frame iteration stops, which is considered a successful decoding; (ii) When the normalization of the verification node satisfies the probability p(G) sum (iii) Stop the current decoding iteration when the symbol convergence threshold is reached, and enter the external iteration process; (iv) Stop the iteration when the internal and external iterations reach the maximum number of internal and external iterations.

[0157] The stopping criterion provides three threshold parameters T, γ, and η for judgment. Here, T represents the successful decoding threshold, γ represents the continuous periodicity threshold for convergence, and η represents the range of variation threshold.

[0158] like Figure 3 As shown, the specific implementation process of this stopping criterion is as follows: First, determine the confidence parameter p(G) sum Does the value of p(G) exceed the decoding success threshold T? sum If the value of the decoder exceeds T, it is considered that the correct codeword has been found in the frame being processed by the current decoder, and the decoding process of the system immediately stops. The posterior probability of the bits output by the decoder is then used for decision-making. Next, the current iteration period p(G) is compared. sum If the difference between the value of the current decoding process and the value of the previous cycle is less than the set threshold η, the counter is incremented by 1; otherwise, the counter is set to 0. When the counter reaches the set threshold γ for convergence of consecutive cycles, the current decoding process is considered to have converged, and subsequent decoding iterations are invalid. At this point, the internal decoding iteration process also terminates immediately, and the external iteration update process begins. Besides the above two cases, if the iterative decoding process exceeds the preset number of iterations and cannot find the correct codeword, the decoder stops the current iteration process and proceeds to the next frame's iteration process.

[0159] Step 8: Bit decision output, obtain the codeword sequence after receiver decoding, and complete the digital communication process.

[0160] Based on the posterior probability information of the decoded output, a decision is made on the first k bits. If Q... i (x i =0)>Q i (x i =1), then m i The decision is 0, otherwise it is 1, thus obtaining the received codeword sequence and completing the demodulation-decoding process.

[0161] This embodiment combines LDPC codes and 8PSK modulation, which improves bandwidth utilization while ensuring channel coding gain. It also uses convergence analysis of the normalization probability of the check nodes to determine the iterative stopping criterion, which reduces the implementation complexity and number of iterations of traditional stopping criteria. This can effectively reduce latency and improve system throughput.

[0162] Simulation analysis of bit error rate and average number of internal and external iterations was performed for this example. The three threshold parameters T, γ, and η of the stopping criterion were set to 0.83, 3, and 0.008, respectively. The simulation results are as follows: Figure 4 , Figure 5 As shown. Figure 4 As shown, the LDPC-BICM-ID system with joint coding-modulation improves the bit error rate performance to a certain extent compared to the BICM system, while the stopping criterion designed in this invention has virtually no impact on the bit error rate performance. Figure 5 As shown, at low signal-to-noise ratios, the stopping criterion method based on this example significantly reduces the average number of decoding iterations.

[0163] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A BICM-ID iterative reception method based on LDPC codes, characterized in that: Includes the following steps, Step 1: Encode, interleave, map, and modulate the original information sequence, and then transmit it through the AWGN channel; Step 2: The demodulator receives the output symbols from the AWGN channel and performs demapping, using channel information and prior probability information to calculate the probability information of the transmitted symbols and corresponding bits; Step 3: Pass the demapped bit probability information through the deinterleaver π. -1 A global detailed factor graph model was established for the receiver of the LDPC-BICM-ID system; Step 4: Perform iterative decoding of the confidence propagation algorithm within the LDPC decoder; Step 5: The decoded soft bit information is fed back to the demodulator via the interleaver as prior information for the next demodulation. Step 6: The demodulator updates each bit using the channel symbol information and the received prior soft bit information; Step 7: Use the probability information of the verification node satisfying the probability detection node as the confidence parameter in the iteration process, and use it to determine the iteration stopping criterion; Step 8: Bit decision output, obtain the codeword sequence after receiver decoding, and complete the digital communication process.

2. The BICM-ID iterative reception method based on LDPC codes as described in claim 1, characterized in that: The implementation method for step one is as follows: The original information sequence M of length k bits is multiplied by the generator matrix G of LDPC encoding to obtain the encoded result C = M·G, and the length of the encoded sequence C is n. Then, the encoded information bits are interleaved using an interleaver to obtain the symbol sequence X = π(C), where the function π represents the specific interleaving and deinterleaving method. The interleaver only changes the order of the symbols, not the total length of the symbol sequence; therefore, sequences C and X have the same length. The encoded information bits are then mapped through a constellation mapping function. {0,1} n →Ω t The mapping is performed using m encoded and interleaved information bits x0, x1, ..., x2. m-1 The mapping is represented by constellation points in a single space; where Ω represents the complete constellation space of the mapped symbol, containing M constellation points, where M = 2. m , This represents rounding down; the interleaved sequence X is modulated and mapped to obtain the symbol sequence. It can be extended to higher-order modulation schemes by changing the specific form of the function mapping; finally, the symbol sequence Y is transmitted through the AWGN channel.

3. The BICM-ID iterative reception method based on LDPC codes as described in claim 2, characterized in that: The implementation method for step two is as follows: The channel output symbol sequence is denoted by Z = {z1, z2, ..., z}. t This means that when deriving soft bit information using the initial symbol information of the received channel, the source can be considered as having an equal probability distribution. Therefore, the probability of each bit node being initially 0 or 1 is equal, i.e.: Where, x i Represents the value of the i-th bit in the transmission sequence; each mapping symbol in the constellation mapping space The probabilities are also the same, that is: The probability information for each transmitted symbol is as follows: Among them, y t z represents the t-th symbol in the transmitted symbol sequence. t This represents the t-th symbol in the received symbol sequence; The "^" in the middle indicates its estimated value; Based on the additive white Gaussian noise channel, the probability density function is: For a complex Gaussian channel, the probability density function is: Where, σ 2 This represents the variance of the Gaussian channel; y I and y Q Let z represent the real and imaginary parts of the channel transmitted symbol y, respectively. I and z Q Let z represent the real and imaginary parts of the channel received symbol z, respectively. Substituting into the above equation and simplifying, we obtain the initial probability information for each transmitted symbol as follows: in, and Let z represent the real and imaginary parts of the k-th constellation mapping point in the constellation mapping space, respectively. re and z im Let z represent the real and imaginary parts of the channel received symbol z, respectively. The probability information of each bit is derived from the symbol probability information: in This represents the constellation point with bit b at position i in the constellation mapping graph χ. A set; The above expression can be expressed over the logarithmic field as:

4. The BICM-ID iterative reception method based on LDPC code as described in claim 3, characterized in that: The implementation method for step three is as follows: Deinterleaving only changes the bit order and has no effect on probabilistic information, therefore... and No distinction is made; Construct a factor graph model G = (VNs∪CNs,Ξ) with check constraint relationship based on the check matrix of LDPC code, where VNs represents the set of variable nodes, CNs represents the set of check nodes, and Ξ represents the set of edges between variable nodes and check nodes, corresponding to the position of 1 in check matrix H. The channel received symbol sequence Z = {Z1, Z2, ..., Z} t After passing through the mapping module φ, the bitstream sequence X = {X1, X2, ..., X} is obtained. n After deinterleaving module π, the sequence C = {C1, C2, ..., C} is obtained. n }, corresponding to the set of variable nodes VNs in the model G=(VNs∪CNs,Ξ), the first k variable nodes correspond to the final decoding result sequence M={M1,M2,…,M k }; Based on this, add a verification node that satisfies the probability detection node G={g1,g2,…,g n-k } and the verification node normalization satisfies the probability statistics node G sum ; Verify node CNs = {h1,h2,…,h n-k } The verification nodes connected to it satisfy the probability check node G={g1,g2,…,g n-k } One-way information transmission, where h i G represents the i-th verification node. i This represents the i-th detection node, and there is a one-to-one correspondence between the two.

5. The BICM-ID iterative reception method based on LDPC codes as described in claim 4, characterized in that: The implementation method for step four is as follows: Use r ji (x i ) represents the j-th verification node C j The probability density function passed to the i-th variable node, where the corresponding bit is either "0" or "1"; q ij (x i ) represents the i-th variable node V i The probability density function of the corresponding bit being "0" or "1" transmitted to the j-th check node; the check node update process is represented as: The variable node update process is represented as follows: Among them, set R j\i Let set C represent the set of positions in the j-th row of the parity check matrix H, excluding the i-th 1. i\j Let H represent the set of positions in the i-th row of the parity check matrix H, excluding the j-th 1. The node update process can be represented over the logarithmic field as follows: A single node update process is considered a single internal iteration; this node update process is repeated until the stopping criterion is met; Q is used as the unit of measurement. i (x i ) represents the posterior likelihood probability of the i-th variable node, which is the probability value that needs to be calculated in the final iterative decoding process; The above expression can be expressed over the logarithmic field as:

6. The BICM-ID iterative reception method based on LDPC codes as described in claim 5, characterized in that: The implementation method for step five is as follows: The interleaver only changes the order and does not affect the probability information; it does not distinguish between x and c, and uses p. a (x i This represents prior information for the next demodulation process: p a (x i =0)=Q i (x i =0) p a (x i =1)=Q i (x i =1) The above expression can be expressed over the logarithmic field as:

7. The BICM-ID iterative reception method based on LDPC codes as described in claim 6, characterized in that: The implementation method for step six is ​​as follows: Using the symbol information from the channel calculated in step two and the prior information p obtained in step five a (x i =b) Jointly update each bit information, complete one outer iteration process, and obtain the updated probability information of each bit as follows: The above expression can be expressed over the logarithmic field as: in, Let y represent the i-th bit of the t-th symbol, b∈{0,1}. t This represents the t-th symbol transmitted through the channel. This represents the constellation point with bit b at position i in the constellation mapping graph χ. The set, This represents the j-th bit value corresponding to the k-th constellation mapping point.

8. The BICM-ID iterative reception method based on LDPC code as described in claim 7, characterized in that: The implementation method for step seven is as follows: node g i This represents whether the i-th check equation is satisfied, therefore we can use the probability p(g) i =0) represents the probability mass function of whether the i-th equation in the verification equation is true; verification node h i Transmitted to detection node g i The information needs to be calculated using the information of all variable nodes connected to the i-th check node, and is expressed as: in, Indicates that except for g i Summation of functions for all variable nodes except V m′ ∈N(C i )\g i V represents m′ Belongs to the verification node C i Connected, but excluding node g i The set of all variable nodes, f i (x) is the indicator function I C (C i )=δ(·), which means that when the sum of all variable nodes connected to the check node modulo 2 is 0, the value of this function is 1; The output of the detection node G is the probability p(g) that the verification node satisfies the condition. i =0|H,Y), representing the parity check relation g output by the detection node under the condition that the received channel sequence Y and the parity check matrix H are known. i The probability that the value is 0 is expressed as: The normalization of the verification node satisfies the probability node G. sum The output p(G) sum To normalize the output values ​​of all detection nodes G: p(G) sum As a confidence parameter, its changing trend during the internal and external iterations reveals that if the confidence parameter gradually approaches 1 from 0.5 and converges, then the codeword is a correctly decoded codeword; if the confidence parameter converges to around 0.5 during the decoding process, it indicates that the codeword converged to an incorrect codeword in this decoding process, and the next external iteration process can be performed to re-introduce channel information to re-decode the current frame; if the confidence parameter oscillates continuously between 0.5 and 1, then the codeword is a non-convergent codeword. Based on the above introduction, the stopping criterion is expressed as: (i) when the normalization of the verification node satisfies the probability p(G) sum (i) When the decoding success threshold is reached, the current frame iteration stops, which is considered a successful decoding; (ii) When the normalization of the verification node satisfies the probability p(G) sum (iii) Stop the current decoding iteration and enter the outer iteration process when the symbol convergence threshold is reached; The stopping criterion provides three threshold parameters T, γ, and η for judgment; where T represents the decoding success threshold, γ represents the continuous periodicity threshold for convergence, and η represents the range threshold. The specific implementation process of the stopping criterion is as follows: First, determine the confidence parameter p(G) sum Does the value of p(G) exceed the decoding success threshold T? sum If the value of the decoder is greater than or equal to T, then the correct codeword has been found in the frame being processed by the current decoder, and the decoding process of the system immediately stops. The posterior probability of the bits output by the decoder is then used for a decision. Next, the current iteration period p(G) is compared. sum If the difference between the value of the current decoding process and the value of the previous cycle is less than the set threshold η of the change range, the counter is incremented by 1; otherwise, the counter is set to 0. When the counter reaches the set threshold γ of the continuous cycle for convergence, it is determined that the current decoding process has converged, and subsequent decoding iterations are invalid. At this time, the internal decoding iteration process also terminates immediately and the external iteration update process begins. In addition to the above two cases, when the iterative decoding process exceeds the preset number of iterations and cannot find the correct codeword, the decoder stops the current iteration process and proceeds to the iteration process of the next frame.

9. The BICM-ID iterative reception method based on LDPC code as described in claim 8, characterized in that: The implementation method for step eight is as follows: Based on the posterior probability information of the decoded output, a decision is made on the first k bits. If Q... i (x i =0)>Q i (x i =1), then m i The decision is 0, otherwise it is 1, thus obtaining the received codeword sequence and completing the demodulation-decoding process.

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