A check concatenated polar code construction method and system suitable for an interference channel
By analyzing the interference level of the polar code sub-channel and constructing a parity-concatenated polar code, the problem of poor performance of polar codes under interference channels is solved, and the high-efficiency anti-interference performance is improved under interference channels.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2023-02-15
- Publication Date
- 2026-06-02
Smart Images
Figure CN116455407B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of error correction encoding and decoding technology, and more specifically, relates to a method and system for constructing parity-check concatenated polar codes suitable for interference channels. Background Technology
[0002] Parity-check concatenated polar codes are a type of concatenated encoding of polar codes and parity-check codes. The transmitter encoder uses a concatenated encoding structure with parity-check codes as the outer code and polar codes as the inner code. The receiver decoder employs a parity-check-assisted continuous elimination list decoding algorithm.
[0003] Traditional polar codes perform poorly in interference channels. Currently, there is no method for constructing parity-check concatenated polar codes for interference channels, and there is also a lack of methods for analyzing the interference level of polar code sub-channels under interference channels. Therefore, a parity-check concatenated polar code based on repeating codes for interference channels is proposed. Summary of the Invention
[0004] In response to the need for improvement in existing technologies, this invention provides a method and system for constructing parity-concatenated polar codes suitable for interference channels, with the aim of improving the anti-interference performance of polar codes with lower encoding and decoding complexity.
[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for constructing parity-check concatenated polar codes suitable for interference channels, comprising the following steps:
[0006] S1, randomly generate M-frame interference signals and add them to the polar code-coded and modulated signal to obtain the interference M-frame receiving sequence; according to the M-frame receiving sequence, calculate the LLR of each transmission sub-channel, and denote the sub-channel with |LLR|<δ as class 1 sub-channel, and the remaining sub-channels as class 3 sub-channel, where δ is the threshold value.
[0007] S2, in the multi-layer iterative decoding structure of polar codes, the layer containing the transmission sub-channel is layer 1; according to Determine whether each subchannel in layer m is a class 1 subchannel; based on Determine whether each subchannel in the m-th layer is a class 3 subchannel; after determining the class 1 and class 3 subchannels in the polar code subchannel layer, the remaining polar code subchannels are denoted as class 2 subchannels.
[0008] in, This indicates that the k-th subchannel in layer m is a class 1 subchannel. This means that the k-th subchannel of layer m is not a class 1 subchannel; This indicates that the k-th subchannel in layer m is a class 3 subchannel. This means that the k-th subchannel of the m-th layer is not a class 3 subchannel; m∈{2,3,…,log2N+1) and N is the polar code length, & represents bitwise AND operation, and | represents bitwise OR operation;
[0009] S3, Construct the information bit set A and the frozen bit set A of the polar code. c Check bit set A p For A p For each check bit in the M-frame, select one information bit from all the preceding information bits for verification. The selection principle is as follows: when the current check bit verifies each of the preceding information bits, calculate the number of newly added valid check frames in the M-frame, and select the check relationship with the most newly added valid check frames as the check relationship actually constructed by the current check bit.
[0010] Among them, a valid check is: in a frame, the check bit is a Class 3 sub-channel, and the information bit being checked is a Class 1 sub-channel or a Class 2 sub-channel with an information bit preceding it that is a Class 1 sub-channel.
[0011] S4. Obtain the polar code input sequence according to the aforementioned check relationships, and then encode the polar code input sequence to obtain the check concatenated polar code.
[0012] Furthermore, in step S3, the information bit set A and the frozen bit set A' of the polar code are constructed. c Check bit set A p Specifically:
[0013] Select the K bits with the lowest error probability as the information bit set A, and then select all non-information bits after the first information bit as the check bit set A. p The remaining bits are used as the frozen bit set A. c .
[0014] Furthermore, in S3, the calculation of the newly added number of valid verification frames is specifically as follows:
[0015] Let the set of frame indices in which the current x-th bit verifies the y-th bit within M frames be denoted as . in x∈A p And y∈A, based on the previously generated check relationships of other check bits, the set of sequence numbers of frames whose valid check bits verify this information bit is obtained as follows: Where P is the set of check bits used to check this information bit in the previously generated check relation, |P|=t and P1 <P2<…<P t <x;
[0016] The set of sequence numbers of the newly added valid check frames for the current x-th bit and y-th bit is: |I| represents the number of newly added valid verification frames, where \ represents the difference set and ∪ represents the union set.
[0017] Furthermore, S4 specifically includes:
[0018] Let the original sequence before polar code encoding be . N is the polar code length;
[0019] Checksum encoding process: u A The value is assigned to the information sequence value, for Each bit in the array is checked against the preceding bits according to the constructed check relation, resulting in... The value; for Each bit in the value is set to a fixed value known to the receiver.
[0020] Polar code encoding process: The constructed encoding map is input into the sequence. According to the encoding mapping G N Get the code
[0021] Modulation process: codeword Then, through modulation, the final transmitted signal is obtained;
[0022] Among them, u A , These represent the information bits, check bits, and freeze bits in the u-sequence during check code encoding, respectively.
[0023] Furthermore, in S4, the modulation method is any one of the following: phase modulation, frequency shift keying modulation, or pulse amplitude modulation.
[0024] To achieve the above objectives, in a second aspect, the present invention provides a system for constructing parity-check concatenated polar codes suitable for interference channels, comprising:
[0025] The transmission sub-channel interference analysis module is used to randomly generate M-frame interference signals, add them to the polar code-coded and modulated signal, and obtain the interference M-frame received sequence; based on the M-frame received sequence, the LLR of each transmission sub-channel is calculated, and the sub-channels with |LLR|<δ are denoted as Class 1 sub-channels, and the remaining sub-channels are denoted as Class 3 sub-channels, where δ is the threshold value.
[0026] The polar code sub-channel interference analysis module is used to denote the layer containing the transmission sub-channel in the multi-layer iterative decoding structure of the polar code as layer 1; according to Determine whether each subchannel in layer m is a class 1 subchannel; based on Determine whether each subchannel in the m-th layer is a class 3 subchannel; after determining the class 1 and class 3 subchannels in the polar code subchannel layer, the remaining polar code subchannels are denoted as class 2 subchannels.
[0027] in, This indicates that the k-th subchannel in layer m is a class 1 subchannel. This means that the k-th subchannel of layer m is not a class 1 subchannel; This indicates that the k-th subchannel in layer m is a class 3 subchannel. This means that the k-th subchannel of the m-th layer is not a class 3 subchannel; m∈{2,3,…,log2N+1) and N is the polar code length, & represents bitwise AND operation, and | represents bitwise OR operation;
[0028] The verification relation construction module is used to construct the information bit set A and the frozen bit set A' of the polar code. c Check bit set A p For A p For each check bit in the M-frame, select one information bit from all the preceding information bits for verification. The selection principle is as follows: when the current check bit verifies each of the preceding information bits, calculate the number of newly added valid check frames in the M-frame, and select the check relationship with the most newly added valid check frames as the check relationship actually constructed by the current check bit.
[0029] Among them, a valid check is: in a frame, the check bit is a Class 3 sub-channel, and the information bit being checked is a Class 1 sub-channel or a Class 2 sub-channel with an information bit preceding it that is a Class 1 sub-channel.
[0030] The parity-concatenated polar code encoding and modulation module is used to obtain the polar code input sequence according to the parity relationships, and then to encode the polar code input sequence to obtain the parity-concatenated polar code.
[0031] Furthermore, the verification relationship construction module is specifically used for:
[0032] Select the K bits with the lowest error probability as the information bit set A, and then select all non-information bits after the first information bit as the check bit set A. p The remaining bits are used as the frozen bit set A. c ;
[0033] And let the set of frame indices in which the current x-th bit verifies the y-th bit within M frames be denoted as . in x∈A p And y∈A, based on the previously generated check relationships of other check bits, the set of sequence numbers of frames whose valid check bits verify this information bit is obtained as follows: Where P is the set of check bits used to check this information bit in the previously generated check relation, |P|=t and P1 <P2<…<P t <x;
[0034] The set of sequence numbers of the newly added valid check frames for the current x-th bit and y-th bit is: |I| represents the number of newly added valid verification frames, where \ represents the difference set and ∪ represents the union set;
[0035] The check relationship with the most newly added valid check frames is selected as the check relationship actually constructed for the current check bit.
[0036] To achieve the above objectives, in a third aspect, the present invention provides an electronic device, comprising: a processor; and a memory storing a computer-executable program, wherein when executed by the processor, the program causes the processor to perform the parity-check concatenated polar code construction method applicable to interference channels as described in the first aspect.
[0037] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:
[0038] This invention analyzes the interference levels of polar code sub-channels under interference conditions, classifying them into three levels. It also identifies a recursive rule for deriving the interference level of the polar code sub-channel from the interference level of the transmission sub-channel. Furthermore, it constructs a verification relationship based on the interference levels of the polar code sub-channels, significantly improving the anti-interference performance of polar codes using only a relatively simple duplicate code verification method. Attached Figure Description
[0039] Figure 1 This is a diagram illustrating the recursive derivation of the interference level of the transmission sub-channel to the interference level of the polar code sub-channel for a polar code with a code length of 8.
[0040] Figure 2(a) and Figure 2(b) are schematic diagrams of two effective verification methods;
[0041] Figure 3 This is a subchannel error probability diagram obtained from Monte Carlo simulation under conditions of both noise and interference.
[0042] Figure 4 Taking the 105th check bit as an example, here is a diagram showing the number of newly added valid check frames when checking all the preceding information bits.
[0043] Figure 5 This is a performance comparison chart between the proposed parity-check concatenated polar code encoding scheme for interference and traditional polar codes. Detailed Implementation
[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0045] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.
[0046] The specific encoding method of traditional polar codes is as follows: select the K bits with the lowest error probability as the information bit set A, and use all remaining bits as the freeze bit set A. c Let the original sequence before encoding be . will u A The value is assigned to the information sequence value, for Each bit in the sequence is set to a fixed value known to the receiver; the constructed encoded map is then input into the sequence. According to the encoding mapping G N Get the code
[0047] Example 1
[0048] This invention provides a method for constructing parity-check concatenated polar codes suitable for interference channels, the method comprising the following steps:
[0049] (1) Sub-channel interference analysis steps: Randomly generate M-frame interference signals and add them to the polar code-coded and modulated signal to obtain the interference M-frame received sequence. Using these received sequences, calculate the degree of interference of each sub-channel of the polar code in the M-frame.
[0050] (2) Steps for constructing the check code: Construct the information bit set A of the polar code and the frozen bit set A'. c Check bit set A p Based on the aforementioned analysis of the interference levels in the sub-channels, a verification relationship is constructed, namely A. p Each subchannel in A verifies which subchannels in A;
[0051] (3) Check-concatenated polar code encoding and modulation steps: Obtain the polar code input sequence according to each check relationship, and then encode the polar code input sequence to obtain the check-concatenated polar code.
[0052] Specifically, in step (1), the interference level of the polar code sub-channels is divided into three categories: category 1, category 2, and category 3. The specific definitions of the three categories of sub-channels are as follows: due to interference with the received sequence, during the polar code decoding process, the logarithm likelihood ratio (LLR) of some polar code sub-channels satisfies |LLR|<δ, and these sub-channels are category 1; during the decoding process, the |LLR| of some polar code sub-channels is ≥δ and the sign of LLR is determined by the value of the decoding decision of the category 1 sub-channels on the previous decoding path, and these sub-channels are category 2; the |LLR| of some polar code sub-channels is ≥δ and the sign of LLR does not depend on the value of the decoding decision of the category 1 sub-channels on the previous decoding path, but is determined only by itself, and these sub-channels are category 3.
[0053] Further, in step (1), the interference level of each sub-channel of the polar code is obtained from the interfered received sequence. Specifically, firstly, the LLR of each transmission sub-channel is obtained based on the received sequence. Combining the definitions of the three types of interference levels, the interference level of the transmission sub-channel is obtained. Let α be the set of sub-channels of type 1 and β be the set of sub-channels of type 3 in the transmission sub-channel. By definition, α∪β={1,2,…,N}. Then, by using the recursive rule from the interference level of the transmission sub-channel to the interference level of the polar code sub-channel, the interference level of the polar code sub-channel is obtained. The recursive rule is specifically: let the variable for whether each sub-channel in the multi-layer polarization structure of the polar code is of type 1 be α. like This indicates that the k-th subchannel of the m-th layer is not a class 1 subchannel. Specifically, in the multi-layer iterative decoding structure of the polar code, the transmission subchannel is denoted as layer 1, and the number of layers increases sequentially from the transmission subchannel layer to the polar code subchannel layer, with the polar code subchannel being layer (log₂N+1). Conversely, if... This means that the k-th subchannel in the m-th layer is a class 1 subchannel. For a pair of sub-channels before and after polarization between two layers, the recursive rule for class 1 sub-channels is as follows:
[0054]
[0055]
[0056] (m∈{2,3,…,log2 N+1) and )
[0057] Let the variable representing whether each subchannel in the multi-level polarization structure of the polarization code is of class 3 be denoted as . like This means that the k-th subchannel of layer m is not a class 3 subchannel; otherwise, if This means that the k-th subchannel in the m-th layer is a class 3 subchannel. For a pair of sub-channels before and after polarization between two layers, the recursive rule for sub-channel type 3 is as follows:
[0058]
[0059]
[0060] (m∈{2,3,…,log2 N+1) and )
[0061] The & represents bitwise AND operation, and the | represents bitwise OR operation.
[0062] After obtaining the Class 1 and Class 3 sub-channels in the polar code sub-channels, the remaining polar code sub-channels are Class 2 sub-channels, thus completing the interference level analysis of the polar code sub-channels.
[0063] The following explanation uses an 8-bit polar code as an example to illustrate the sub-channel interference analysis in the above steps.
[0064] Suppose that in a certain frame, based on the interfered received sequence, the LLR of the 3rd and 6th sub-channels in the transmission sub-channels satisfies |LLR|<δ (δ is taken as 0.05 in this example), while the LLR of the remaining transmission sub-channels does not satisfy this condition. Then, according to the definition of sub-channel interference level, the set of class 1 sub-channels in the transmission sub-channels is α={3,6}, and the set of class 3 sub-channels is β={1,2,4,5,7,8}. Let T1 be the variable representing whether each sub-channel in the multi-layer polarization structure of the polar code is class 1. We can obtain... The recursive law of class 1 subchannels in a pair of subchannels before and after polarization between two layers can be used to obtain the law of class 4 in the fourth layer. The value is 1, meaning the set of class 1 subchannels in the polar code subchannels is {1,2}; for the variable T3 representing whether each subchannel in the multi-layer polarization structure of the polar code is class 3, we can obtain The recursive law of class 3 subchannels in a pair of subchannels before and after polarization between two layers can be used to obtain the law of class 4 subchannels. The value is 1, meaning the set of class 3 subchannels in the polar codec channel is {4,7,8}; the remaining polar codec channels {3,5,6} are class 2 subchannels. This completes the polar codec channel interference level analysis under one frame of random interference, as illustrated in the diagram below. Figure 1 As shown.
[0065] Specifically, in step (2), the first step involves performing a Monte Carlo simulation under conditions of both noise and interference, selecting the K bits with the lowest error probability as the information bit set A, and then... As the set of check bits A p The remaining bits are used as the frozen bit set A. c .
[0066] Specifically, for the second step, for each parity bit in A p all the information bits in A before it are candidate bits to be verified, and the verification relationship is constructed starting from the first parity bit. Each parity bit only selects one candidate bit to be verified. The specific selection method is as follows: for each candidate bit to be verified in front of the current parity bit, calculate the number of frames with newly added valid verification in the M frames, and select the verification relationship with the most newly added valid verification frames as the verification relationship actually constructed by this parity bit. The calculation of the number of newly added valid verification frames is specifically as follows: Denote the set of frame numbers in the M frames that can be effectively verified by the x-th bit checking the y-th bit as where x ∈ A p and y ∈ A. According to the verification relationships of other parity bits generated before, obtain the set of frame numbers of the valid verification of other parity bits checking this candidate bit to be verified as where P is the set of parity bits that check this information bit in the previously generated verification relationships, |P| = t and P1 < P2 <... < P t < x. Then the set of frame numbers of the newly added valid verification frames when the x-th bit checks the y-th bit is |I| is the number of newly added valid verification frames, where \ represents the difference set and ∪ represents the union set. The valid verification is specifically as follows: in one frame, when the parity bit is of class 3 and the information bit to be verified is in the following two cases, such a set of verification relationships is considered a valid verification in this frame: 1) Class 1 sub-channel; 2) Class 2 sub-channel and there is a class 1 information bit in front of it.
[0067] Taking Figure 1 the related frame interference as an example, the above-mentioned valid verification is illustrated. Suppose the constructed set of information bits is {2, 5, 8}, the set of parity bits is {3, 4, 6, 7}, and the set of frozen bits is {1}. For the 7th bit, verifying the information bit 2 in front of it is a valid verification, which conforms to case 1 in the valid verification, that is, the parity bit is of class 3 and the information bit to be verified is of class 1; verifying the information bit 5 in front of it is also a valid verification, which conforms to case 2 in the valid verification, that is, the parity bit is of class 3, the information bit to be verified is of class 2, and there is a class 1 information bit in front of the bit to be verified (the information bit 2 in front of the bit to be verified 5 is of class 1). Schematic diagrams of the two cases of valid verification are shown in Figures 2(a) and 2(b).
[0068] For the construction of the verification relationship, starting from the first parity bit to the last parity bit, each parity bit selects the information bit that can make the number of newly added valid verification frames the most for verification.
[0069] Specifically, in step (3), after completing the construction of the check code, uA The value is assigned to the information sequence value, for Each bit in the array is checked against the preceding bits according to the constructed check relation (if there are no preceding bits, no check is performed), resulting in... The value of, for Each bit in the sequence is set to a fixed value known to the receiver; the constructed encoded map is then input into the sequence. According to the encoding mapping G N Get the code Typing The final transmitted signal is obtained after modulation. The modulation can employ memoryless modulation methods, such as phase modulation (BPSK). Etc.; Frequency Shift Keying (FSK); Pulse Amplitude Modulation (PAM). The subsequent examples use BPSK modulation.
[0070] The following specific example illustrates the proposed method for constructing parity-check concatenated polar codes suitable for interference channels:
[0071] The code length is 512, the code rate is 1 / 4, and it contains a 19-bit CRC polar code, meaning the number of information bits is [missing information]. BPSK modulation. Let the codeword after polar code encoding be x, then the symbol after BPSK modulation is s(x) = 1 - 2x. After passing through a power of 2σ... 2 The channel contains additive white Gaussian noise (AWGN), and random Markov chain interference is added to the channel. The interference sequence can be represented as B. i =H i b, where H = {0, 1}, b is a constant complex number, and the amplitude of the interference |b| is much greater than 1. In this example, b = 1000 + 1000j, where j is the imaginary unit.
[0072] Set the transition probability of the Markov state chain. And it ensures that the number of interfering symbols in a single frame does not exceed 100. The received sequence can be represented as Y. i =H i b+(1-H i )(s(x i )+Z i ), where Z is a noise sequence.
[0073] Therefore, the transmission subchannel LLR is calculated from the received sequence as follows:
[0074]
[0075] real() is a function that takes the real part of a function.
[0076] Following the above, the interference level of the polar code sub-channels is first analyzed. Based on the recursive rule described above, from the interference level of the transmission sub-channels to the interference level of the polar code sub-channels, the interference level of the polar code sub-channels is obtained. Under random interference of 25,000 frames, the interference level of the polar code sub-channels in each frame is obtained. Taking one frame as an example, the interfered symbols in this frame are the 119th, 360th, and 361st symbols. After analyzing the interference level of the polar code sub-channels, it is found that the 1st, 129th, and 257th sub-channels are of class 1, 85 sub-channels are of class 2, and 424 sub-channels are of class 3.
[0077] At a signal-to-noise ratio of -3dB, random Markov chain interference was added to the channel, and a Monte Carlo simulation was performed for 1000 frames. The 147 bits with the lowest channel error probability were selected as information bits. The 238 bits after the first information bit (not information bits) were used as check bits, and the remaining 127 bits were used as freeze bits. The sub-channel error probabilities are as follows: Figure 3 As shown.
[0078] Starting with the first parity bit, each parity bit uses all its preceding information bits as candidate parity bits. The number of new valid parity frames required to verify each candidate parity bit is calculated, and the candidate parity bit with the highest number of new valid parity frames is selected as the actual parity bit for that parity bit. This process continues until the last parity bit selects its parity bit, completing the construction of the parity relationship. Taking the 105th parity bit (bit 260) as an example, the calculation of the number of new valid parity frames will be illustrated below using the parity bit verifying bit 249 as an example. In the parity relationship constructed before the current parity bit, only bit 258 verified bit 249, and this verification was valid for 11 frames. This set of 11 frames is denoted as [the set of 11 frames is missing from the original text]. The set of frames for valid check of the 249th bit is denoted as . There are a total of 62 frames. Therefore, the set of frames for the newly added valid check bit (currently checking the 249th bit) is: A total of 51 frames are involved, therefore the number of newly added valid check frames is 51. When this check bit checks the previous 28 candidate check bits respectively, the number of newly added valid check frames is as follows: Figure 4 As shown, therefore, for this check bit, the 21st candidate check bit is selected as the check bit.
[0079] After encoding according to the coding structure, the resulting codeword is modulated by a BPSK modulator, and the modulated signal is sent out, thus completing the work of the transmitter using a check-concatenated polar code to counter interference.
[0080] The frame error rate of the proposed scheme is compared with that of traditional polar codes. Figure 5 As shown. By Figure 5 It can be seen that the performance of the proposed scheme is improved by 0.5dB to 0.75dB compared with the traditional polar code, and the performance improvement tends to increase gradually with the increase of signal-to-noise ratio.
[0081] Example 2
[0082] A system for constructing parity-check concatenated polar codes suitable for interference channels, characterized in that it comprises:
[0083] The transmission sub-channel interference analysis module is used to randomly generate M-frame interference signals, add them to the polar code-coded and modulated signal, and obtain the interference M-frame received sequence; based on the M-frame received sequence, the LLR of each transmission sub-channel is calculated, and the sub-channels with |LLR|<δ are denoted as Class 1 sub-channels, and the remaining sub-channels are denoted as Class 3 sub-channels, where δ is the threshold value.
[0084] The polar code sub-channel interference analysis module is used to denote the layer containing the transmission sub-channel in the multi-layer iterative decoding structure of the polar code as layer 1; according to Determine whether each subchannel in layer m is a class 1 subchannel; based on Determine whether each subchannel in the m-th layer is a class 3 subchannel; after determining the class 1 and class 3 subchannels in the polar code subchannel layer, the remaining polar code subchannels are denoted as class 2 subchannels.
[0085] in, This indicates that the k-th subchannel in layer m is a class 1 subchannel. This means that the k-th subchannel of layer m is not a class 1 subchannel; This indicates that the k-th subchannel in layer m is a class 3 subchannel. This means that the k-th subchannel of the m-th layer is not a class 3 subchannel; m∈{2,3,…,log2N+1) and N is the polar code length, & represents bitwise AND operation, and | represents bitwise OR operation;
[0086] The verification relation construction module is used to construct the information bit set A and the frozen bit set A' of the polar code. c Check bit set A p For A p For each check bit in the M-frame, select one information bit from all the preceding information bits for verification. The selection principle is as follows: when the current check bit verifies each of the preceding information bits, calculate the number of newly added valid check frames in the M-frame, and select the check relationship with the most newly added valid check frames as the check relationship actually constructed by the current check bit.
[0087] The valid check is defined as follows: in a frame, the check bit is a Class 3 sub-channel, and the information bit being checked is a Class 1 sub-channel or a Class 2 sub-channel with an preceding information bit of a Class 1 sub-channel.
[0088] The parity-concatenated polar code encoding and modulation module is used to obtain the polar code input sequence according to the parity relationships, and then to encode the polar code input sequence to obtain the parity-concatenated polar code.
[0089] The relevant technical solutions are the same as in Embodiment 1, and will not be repeated here.
[0090] Example 3
[0091] An electronic device includes: a processor; and a memory storing a computer-executable program, which, when executed by the processor, causes the processor to perform the parity-check concatenated polar code construction method applicable to interference channels as described in Embodiment 1.
[0092] The relevant technical solutions are the same as in Embodiment 1, and will not be repeated here.
[0093] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 method for constructing parity-check concatenated polar codes suitable for interference channels, characterized in that, Includes the following steps: S1, randomly generate M-frame interference signals and add them to the polar code-coded and modulated signal to obtain the interference M-frame receiving sequence; according to the M-frame receiving sequence, calculate the LLR of each transmission sub-channel, and denote the sub-channel with |LLR|<δ as class 1 sub-channel, and the remaining sub-channels as class 3 sub-channel, where δ is the threshold value. S2, in the multi-layer iterative decoding structure of polar codes, the layer containing the transmission sub-channel is layer 1; according to Determine whether each subchannel in layer m is a class 1 subchannel; based on Determine whether each subchannel in the m-th layer is a class 3 subchannel; after determining the class 1 and class 3 subchannels in the polar code subchannel layer, the remaining polar code subchannels are denoted as class 2 subchannels. in, This indicates that the k-th subchannel in layer m is a class 1 subchannel. This means that the k-th subchannel of layer m is not a class 1 subchannel; This indicates that the k-th subchannel in layer m is a class 3 subchannel. This means that the k-th subchannel of the m-th layer is not a class 3 subchannel; m∈{2,3,…,log2N+1) and N is the polar code length, & represents bitwise AND operation, and | represents bitwise OR operation; S3, Construct the information bit set A and the frozen bit set A of the polar code. c Check bit set A p For A p For each check bit in the M-frame, select one information bit from all the preceding information bits for verification. The selection principle is as follows: when the current check bit verifies each of the preceding information bits, calculate the number of newly added valid check frames in the M-frame, and select the check relationship with the most newly added valid check frames as the check relationship actually constructed by the current check bit. Among them, a valid check is: in a frame, the check bit is a Class 3 sub-channel, and the information bit being checked is a Class 1 sub-channel or a Class 2 sub-channel with an information bit preceding it that is a Class 1 sub-channel. S4. Obtain the polar code input sequence according to the aforementioned check relationships, and then encode the polar code input sequence to obtain the check concatenated polar code.
2. The method for constructing parity-check concatenated polar codes suitable for interference channels according to claim 1, characterized in that, In step S3, the information bit set A and the frozen bit set A' of the polar code are constructed. c Check bit set A p Specifically: Select the K bits with the lowest error probability as the information bit set A, and then select all non-information bits after the first information bit as the check bit set A. p The remaining bits are used as the frozen bit set A. c .
3. The method for constructing parity-check concatenated polar codes suitable for interference channels according to claim 1 or 2, characterized in that, In S3, the calculation of the newly added number of valid verification frames is as follows: Let the set of frame indices in which the current x-th bit verifies the y-th bit within M frames be denoted as . in x∈A p And y∈A, based on the previously generated check relationships of other check bits, the set of sequence numbers of frames whose valid check bits verify this information bit is obtained as follows: Where P is the set of check bits used to check this information bit in the previously generated check relation, |P|=t and P1 <P2<…<P t <x; The set of sequence numbers of the newly added valid check frames for the current x-th bit and y-th bit is: |I| represents the number of newly added valid verification frames, where \ represents the difference set and ∪ represents the union set.
4. The method for constructing parity-check concatenated polar codes suitable for interference channels according to claim 1, characterized in that, Specifically, S4 is: Let the original sequence before polar code encoding be . N is the polar code length; Checksum encoding process: u A The value is assigned to the information sequence value, for Each bit in the array is checked against the preceding bits according to the constructed check relation, resulting in... The value; for Each bit in the value is set to a fixed value known to the receiver. Polar code encoding process: The constructed encoding map is input into the sequence. According to the encoding mapping G N Get the code Modulation process: codeword Then, through modulation, the final transmitted signal is obtained; Among them, u A u Ap , These represent the information bits, check bits, and freeze bits in the u-sequence during check code encoding, respectively.
5. The method for constructing parity-check concatenated polar codes suitable for interference channels according to claim 4, characterized in that, In S4, the modulation method is any one of the following: phase modulation, frequency shift keying modulation, or pulse amplitude modulation.
6. A system for constructing parity-check concatenated polar codes suitable for interference channels, characterized in that, include: The transmission sub-channel interference analysis module is used to randomly generate M-frame interference signals, add them to the polar code-coded and modulated signal, and obtain the interference M-frame received sequence; based on the M-frame received sequence, the LLR of each transmission sub-channel is calculated, and the sub-channels with |LLR|<δ are denoted as Class 1 sub-channels, and the remaining sub-channels are denoted as Class 3 sub-channels, where δ is the threshold value. The polar code sub-channel interference analysis module is used to denote the layer containing the transmission sub-channel in the multi-layer iterative decoding structure of the polar code as layer 1; according to Determine whether each subchannel in layer m is a class 1 subchannel; based on Determine whether each subchannel in the m-th layer is a class 3 subchannel; after determining the class 1 and class 3 subchannels in the polar code subchannel layer, the remaining polar code subchannels are denoted as class 2 subchannels. in, This indicates that the k-th subchannel in layer m is a class 1 subchannel. This means that the k-th subchannel of layer m is not a class 1 subchannel; This indicates that the k-th subchannel in layer m is a class 3 subchannel. This means that the k-th subchannel of the m-th layer is not a class 3 subchannel; m∈{2,3,…,log2N+1) and N is the polar code length, & represents bitwise AND operation, and | represents bitwise OR operation; The verification relation construction module is used to construct the information bit set A and the frozen bit set A' of the polar code. c Check bit set A p For A p For each check bit in the M-frame, select one information bit from all the preceding information bits for verification. The selection principle is as follows: when the current check bit verifies each of the preceding information bits, calculate the number of newly added valid check frames in the M-frame, and select the check relationship with the most newly added valid check frames as the check relationship actually constructed by the current check bit. Among them, a valid check is: in a frame, the check bit is a Class 3 sub-channel, and the information bit being checked is a Class 1 sub-channel or a Class 2 sub-channel with an information bit preceding it that is a Class 1 sub-channel. The parity-concatenated polar code encoding and modulation module is used to obtain the polar code input sequence according to the parity relationships, and then to encode the polar code input sequence to obtain the parity-concatenated polar code.
7. The parity-check concatenated polar code construction system suitable for interference channels according to claim 6, characterized in that, The verification relationship construction module is specifically used for: Select the K bits with the lowest error probability as the information bit set A, and then select all non-information bits after the first information bit as the check bit set A. p The remaining bits are used as the frozen bit set A. c ; And let the set of frame indices in which the current x-th bit verifies the y-th bit within M frames be denoted as . in x∈A p And y∈A, based on the previously generated check relationships of other check bits, the set of sequence numbers of frames whose valid check bits verify this information bit is obtained as follows: Where P is the set of check bits used to check this information bit in the previously generated check relation, |P|=t and P1 <P2<…<P t <x; The set of sequence numbers of the newly added valid check frames for the current x-th bit and y-th bit is: |I| represents the number of newly added valid verification frames, where \ represents the difference set and ∪ represents the union set; The check relationship with the most newly added valid check frames is selected as the check relationship actually constructed for the current check bit.
8. An electronic device, characterized in that, include: processor; A memory storing a computer-executable program, which, when executed by the processor, causes the processor to perform the method for constructing a parity-check concatenated polar code under interference channels as described in any one of claims 1-5.