Meteoric trail channel-oriented PAC code construction and interleaving method

Abstract

The invention discloses a meteoric trail channel-oriented PAC code construction and interleaving method, which comprises the following steps of: obtaining an interleaving pattern by adopting an enumeration mode, interleaving an under-secret meteoric trail physical channel W through the interleaving pattern to obtain a new LLR sequence under the physical channel W, obtaining an above LLR mean value through iterative calculation, calculating an error probability according to a Q function and the above LLR mean value, and constructing a PAC code according to the error probability. And obtaining an information bit set through the error probability, obtaining a block error rate after interleaving according to the error probability and the information bit set, and selecting an interleaving pattern causing the lowest block error rate as a final interleaving pattern by comparing the block error rates of N interleaving patterns. According to the method, the error code performance of the PAC code is improved, and the reliability of a stream residue system can be greatly improved.

Description

A PAC code construction and interleaving method for meteor trail channels Technical Field

[0001] This invention belongs to the field of error correction coding in wireless communication, and particularly relates to a method for constructing and interleaving PAC codes for meteor trail channels. Background Technology

[0002] When a meteoroid enters the upper atmosphere and burns up due to friction, it can form a long, thin column of ionized gas with a high electron density, about 20-30 km long and lasting from tens of milliseconds to several seconds; this is called a meteor trail. Meteor Burst Communication (MBC) is a long-distance, intermittent burst communication method that utilizes the reflection and scattering of Very High Frequency (VHF) radio waves by the meteor trail. Compared to common channels, meteor trail channels are characterized by short communication durations, mostly lasting only tens to hundreds of milliseconds, and low channel capacity.

[0003] Due to the limitations of its development era, the error correction coding modules used in the Liuyu system are still BCH, RS, and TPC codes, which are technological achievements from the 1960s and 1990s. However, with the advancement of error correction coding technology, polar codes, as the latest and most important achievement in the field of error correction coding in the past 20 years, have comprehensively surpassed the former in performance.

[0004] Meteor trail channels, being burst channels, require error-correcting codes with short code lengths. In the short code domain, PAC codes (Polarization-Adjusted Convolutional Codes) offer unparalleled performance advantages over other coding schemes. However, the lack of dedicated interleaving and coding schemes for meteor trail channels, coupled with the continued use of analysis methods from Gaussian channels, severely restricts the performance of meteor trail systems. Therefore, the introduction of PAC codes makes it possible to accurately match the fading patterns of meteor trail channels for coding, and combined with their superior short code performance, it can significantly improve the reliability of meteor trail systems. Summary of the Invention

[0005] To address the above problems, this invention provides a PAC code construction and interleaving method for meteor trail channels.

[0006] The present invention provides a PAC code construction and interleaving method for meteor trail channels, comprising the following steps:

[0007] Step 1: For a noise variance of The fading coefficient is Physical channel of low-density meteoroid trails Assuming that all-zero codewords are transmitted within it and BPSK modulation is used, the duration of each BPSK symbol is... Then the first One received symbol The log-likelihood ratio LLR is expressed as: The LLR value follows a Gaussian distribution. ,in .

[0008] Step 2: Given a codeword length of... The number of information bits is The physical channel of the under-dense meteoroid trail in step 1 is known. For non-independent and identically distributed channels, indivual After channel interleaving, polar coding is performed, using express Interlaced pattern The first LLR sequence obtained after interleaving There are elements, that is, use Indicates the first step in the encoding process The first polarization transition One channel, used Indicates channel The generated LLR value, used express The mean of the channel is then calculated iteratively using the following formula. The average LLR generated above :

[0009]

[0010] Among them, subscript Indicates the first Step polarization transition, its range is superscript Represents the channel index, in the formula The range of values ​​is The function in this formula for:

[0011]

[0012] Step 3: Use Indicates completion The second polarization transition Each channel, based on the LLR mean value in step 2. Iterative calculation formula and initial value calculation method To obtain the channel The mean of the generated LLR values The channel can be obtained using the following formula. Transmission error probability of the information bits carried on :

[0013]

[0014] in, The function is defined as superscript in the formula The range of values ​​is .

[0015] Step 4: Based on the error probability in Step 3 The calculation method will The probability of an error Sort the values ​​in ascending order, and select the top-ranked values ​​from the sorted sequence. The polarization subchannel corresponding to each error probability The index bit is used as the information bit. This represents the set of information bits, thus completing the construction of the polar code.

[0016] Step 5: Set the channel Channel capacity This indicates that when the channel capacity For set The Middle When the element is large, the channel capacity can also be expressed as ,in That is, its capacity sequence number, number 1 A pair of channels in step polarization transition and Can be derived from the first A pair of channels generated by step polarization transition and By constructing the above, without loss of generality, we assume that the capacity index in the channel polarization transition satisfies the following conditions: , Then there is .

[0017] Step 6: In independent and identically distributed channels, the polarization effect is entirely determined by the coding tree structure of the polar codes. The physical channel is altered through interleaving. Sorting, Channel Capacity serial number The physical channel of the under-dense meteoroid trail described in step 1 will not change. The polarization effect is influenced not only by the coding tree structure of the polar codes, but also by the physical channel of the under-dense meteoroid trail. The ordering of the meteor trails is affected, therefore the physical channel of the sparse meteoroid trails is altered by interleaving. Sorting, and thus changing the channel Capacity serial number .

[0018] Step 7: Change a channel by interleaving Capacity serial number Specifically, the following steps are used to obtain the interleaving pattern that can achieve the lowest error rate. :

[0019] S1: For the channel parameter Perform enumeration, where .

[0020] S2: For each fixed Value, generating to maximize channel improvement Interlacing pattern of channel capacity .

[0021] S3: The results obtained during the enumeration process of steps S1 and S2 Interwoven pattern The block error rates are compared, and the interleaving pattern that results in the lowest block error rate is selected. As the final interwoven pattern And output it.

[0022] Step 8: Define the physical channel of the under-dense class stream-residual channel The capacity sort vector is , This refers to step 7, S2, in order to maximize... Interlacing pattern designed for channel capacity ,use Indicates the first Capacity sorting vector after polarization transformation The number of elements in is ,use Indicates completion Capacity sorting vector after secondary polarization transformation The number of elements in the fixed value is 1. After the value, superscript Do after subtracting one Expanding the binary representation, we get the binary expansion formula. ,in For the most significant bit, use express The number of 0s in the middle, then .

[0023] Step 9: Based on the results obtained in Step 8 and Recursively generate underdense class flow co-channel physical channel Capacity sorted vector ,use express The subsequence, according to and generate Specifically There are four possible ways to generate it:

[0024] A: When At that time, The generation method is as follows:

[0025]

[0026]

[0027] in, , , and The expressions are respectively , .

[0028] B: When At that time, first The elements in the vector are arranged in descending order to obtain the vector. sum vector ,satisfy ,but The generation method is as follows:

[0029]

[0030]

[0031]

[0032] in, , and The expressions are respectively , .

[0033] C: When At that time, first The elements in the vector are arranged in descending order to obtain the vector. sum vector ,satisfy ,but The generation method is as follows:

[0034]

[0035]

[0036]

[0037] in, , and The expressions are respectively , .

[0038] D: When And at times When bits 0 and 1 are randomly distributed, then The generation method is as follows:

[0039]

[0040]

[0041] in, , and The expressions are respectively , .

[0042] Step 10: Recursively obtain the capacity sort vector according to the recursive process described in Step 9. This refers to the interwoven pattern described in step 7, S2. , this As in step 2 If used, the channel is obtained according to steps 2 and 3. Transmission error probability of the information bits carried on The information bit set is obtained according to step 4. The following formula is used to calculate the interlaced pattern. Theoretical error rate resulting from this :

[0043]

[0044] Step 11: Given that S3 in step 7 requires S1 and S2 to be enumerated during the process... Compare the theoretical block error rates corresponding to the interlacing patterns, and repeat steps 8 to 10 to obtain... Choose the theoretical block error rate that results in the lowest theoretical block error rate. As the final interwoven pattern and will use The set of information bits corresponding to interleaving As the final set of information bits .

[0045] The beneficial technical effects of this invention are as follows:

[0046] This invention analyzes the received signal LLR sequence based on the characteristics of the under-dense meteor trail channel. The elements within the same element do not satisfy the independent and identically distributed condition. Interwoven patterns After interlacing, the result is Obtained through iterative calculation LLR mean According to the Q function and Calculate the error probability ,Will The probability of an error Sort the values ​​in ascending order, and select the top-ranked values ​​from the sorted sequence. The error probability corresponds to The index bits are used as information bits to obtain the information bit set. The result is obtained by calculating using the formula in step 10. Theoretical error rate caused by interleaving ,Compare Interwoven pattern Caused Given a theoretical block error rate, the interleaving pattern with the lowest block error rate is selected as the final interleaving pattern. , will pass The set of interleaved information bits as Experiments have proven that... and It can significantly improve the bit error rate performance of PAC codes in underdense meteor trail channels. Attached Figure Description

[0047] Figure 1 shows the system model of the present invention.

[0048] Figure 2 illustrates the interlacing pattern algorithm of this invention.

[0049] Figure 3 shows the BLER comparison between the interleaving scheme proposed in this invention and the random interleaving scheme and the sequential interleaving scheme under different code rates under the simulation conditions of this invention.

[0050] Figure 4 shows the comparison of the PAC code construction algorithm and related interleaving design proposed in this invention with BLER of LDPC and TPC under different code lengths and code rates under the simulation conditions of this invention. Detailed Implementation

[0051] The present invention will now be described in further detail with reference to the accompanying drawings and specific simulation examples.

[0052] Figure 1 is a schematic diagram of the system model of the present invention. In the transmitter section, the source bit sequence... , its origin A length of The sequence is composed of [a sequence name], which is then encoded by a PAC encoder to obtain a codeword sequence. , its origin A length of The bit sequence is constructed, and then the codeword sequence is... Sequential input depth is The external interleaver obtains the interleaved bit sequence. The external interweaving is the result obtained by the steps proposed according to the present invention. To reduce the impact of deep fading in the residual channel on the decoding performance of polar codes, the bit sequence is... The input is an inner interleaver, which writes the bit sequence row by row and reads it column by column, resulting in an interleaved sequence. After being modulated by BPSK, the signal is transmitted, and the receiver performs two deinterleaving operations before decoding.

[0053] The present invention provides a PAC code construction and interleaving method for meteor trail channels, comprising the following steps:

[0054] Step 1: For a noise variance of The fading coefficient is Physical channel of low-density meteoroid trails Assuming that all-zero codewords are transmitted within it and BPSK modulation is used, the duration of each BPSK symbol is... Then the first One received symbol The log-likelihood ratio LLR is expressed as: The LLR value follows a Gaussian distribution. ,in .

[0055] Step 2: Given a codeword length of... The number of information bits is The physical channel of the under-dense meteoroid trail in step 1 is known. For non-independent and identically distributed channels, indivual After channel interleaving, polar coding is performed, using express Interlaced pattern The first LLR sequence obtained after interleaving There are elements, that is, use Indicates the first step in the encoding process The first polarization transition One channel, used Indicates channel The generated LLR value, used express The mean of the channel is then calculated iteratively using the following formula. The average LLR generated above :

[0056]

[0057] Among them, subscript Indicates the first Step polarization transition, its range is superscript Represents the channel index, in the formula The range of values ​​is The function in this formula for:

[0058]

[0059] Step 3: Use Indicates completion The second polarization transition Each channel, based on the LLR mean value in step 2. Iterative calculation formula and initial value calculation method To obtain the channel The mean of the generated LLR values The channel can be obtained using the following formula. Transmission error probability of the information bits carried on :

[0060]

[0061] in, The function is defined as superscript in the formula The range of values ​​is .

[0062] Step 4: Based on the error probability in Step 3 The calculation method will The probability of an error Sort the values ​​in ascending order, and select the top-ranked values ​​from the sorted sequence. The polarization subchannel corresponding to each error probability The index bit is used as the information bit. This represents the set of information bits, thus completing the construction of the polar code.

[0063] Step 5: Set the channel Channel capacity This indicates that when the channel capacity For set The Middle When the element is large, the channel capacity can also be expressed as ,in That is, its capacity sequence number, number 1 A pair of channels in step polarization transition and Can be derived from the first A pair of channels generated by step polarization transition and By constructing the above, without loss of generality, we assume that the capacity index in the channel polarization transition satisfies the following conditions: , Then there is .

[0064] Step 6: In independent and identically distributed channels, the polarization effect is entirely determined by the coding tree structure of the polar codes. The physical channel is altered through interleaving. Sorting, Channel Capacity serial number The physical channel of the under-dense meteoroid trail described in step 1 will not change. The polarization effect is influenced not only by the coding tree structure of the polar codes, but also by the physical channel of the under-dense meteoroid trail. The ordering of the meteor trails is affected, therefore the physical channel of the sparse meteoroid trails is altered by interleaving. Sorting, and thus changing the channel Capacity serial number .

[0065] Step 7: Change a channel by interleaving Capacity serial number Specifically, the following steps are used to obtain the interleaving pattern that can achieve the lowest error rate. :

[0066] S1: For the channel parameter Perform enumeration, where .

[0067] S2: For each fixed Value, generating to maximize channel improvement Interlacing pattern of channel capacity .

[0068] S3: The results obtained during the enumeration process of steps S1 and S2 Interwoven pattern The block error rates are compared, and the interleaving pattern that results in the lowest block error rate is selected. As the final interwoven pattern And output it.

[0069] Step 8: Define the physical channel of the under-dense class stream-residual channel The capacity sort vector is , This refers to step 7, S2, in order to maximize... Interlacing pattern designed for channel capacity ,use Indicates the first Capacity sorting vector after polarization transformation The number of elements in is ,use Indicates completion Capacity sorting vector after secondary polarization transformation The number of elements in the fixed value is 1. After the value, superscript Do after subtracting one Expanding the binary representation, we get the binary expansion formula. ,in For the most significant bit, use express The number of 0s in the middle, then .

[0070] Step 9: Based on the results obtained in Step 8 and Recursively generate underdense class flow co-channel physical channel Capacity sorted vector ,use express The subsequence, according to and generate Specifically There are four possible ways to generate it:

[0071] A: When At that time, The generation method is as follows:

[0072]

[0073]

[0074] in, , , and The expressions are respectively , .

[0075] B: When At that time, first The elements in the vector are arranged in descending order to obtain the vector. sum vector ,satisfy ,but The generation method is as follows:

[0076]

[0077]

[0078]

[0079] in, , and The expressions are respectively , .

[0080] C: When At that time, first The elements in the vector are arranged in descending order to obtain the vector. sum vector ,satisfy ,but The generation method is as follows:

[0081]

[0082]

[0083]

[0084] in, , and The expressions are respectively , .

[0085] D: When And at times When bits 0 and 1 are randomly distributed, then The generation method is as follows:

[0086]

[0087]

[0088] in, , and The expressions are respectively , .

[0089] Step 10: Recursively obtain the capacity sort vector according to the recursive process described in Step 9. This refers to the interwoven pattern described in step 7, S2. , this As in step 2 If used, the channel is obtained according to steps 2 and 3. Transmission error probability of the information bits carried on The information bit set is obtained according to step 4. The following formula is used to calculate the interlaced pattern. Theoretical error rate resulting from this :

[0090]

[0091] Step 11: Given that S3 in step 7 requires S1 and S2 to be enumerated during the process... Compare the theoretical block error rates corresponding to the interlacing patterns, and repeat steps 8 to 10 to obtain... Choose the theoretical block error rate that results in the lowest theoretical block error rate. As the final interwoven pattern and will use The set of information bits corresponding to interleaving As the final set of information bits .

[0092] Figure 2 shows the interleaving pattern algorithm proposed in this invention, whose input is the polar code length. Number of information bits Polarization transformation recursion depth Fixed signal-to-noise ratio fading coefficient Duration of a single symbol and interlacing depth The output is the external interleaving pattern with the lowest block error rate under this condition. and information bit set In the algorithm Indicates to After subtracting one, perform binary expansion. This indicates the physical channel of the faint meteoroid trail. go through After interleaving, iterative calculations are performed to obtain... mean and according to The function obtains Transmission error probability of the information bits carried on , Indicates based on transmission error probability Obtain the set of information bits under this channel condition. .

[0093] Simulation experiment:

[0094] The specific conditions for the simulation experiment are as follows:

[0095] Set fading coefficient The polynomial of the convolutional code in the PAC code is 0.2. Set the list number in the SCL decoding algorithm Because the transmitter section needs to send a bit sequence , its origin A length of bit sequence Therefore, when the duration of a single symbol is set to... At that time, the transmission time of the entire bit sequence is When constructing the interleaving pattern and selecting information bits, the input to the algorithm needs to use... .

[0096] Figure 3 shows the method of the present invention under the specific simulation conditions described above, with the code length set. symbol rate Fixed signal-to-noise ratio , The proposed interleaving scheme for meteor trail channels is implemented using PAC encoding. With no external interlacing pattern and random interwoven patterns Comparison, based on simulation results, shows that the interlaced pattern proposed in this invention... Performance is always better and When the code length And the number of information bits At that time, the interleaving scheme proposed in this invention can achieve dB gain.

[0097] Figure 4 shows the method of the present invention under the specific simulation conditions described above, with a fixed signal-to-noise ratio. symbol rate Number of rows in the interlaced matrix This paper compares the performance of the proposed PAC code construction algorithm and interleaving design for meteor trail channels with that of 5G LDPC and TPC codes in meteor trail channels. Both 5G LDPC and TPC codes employ internal interleaving and no external interleaving schemes, while the TPC code uses extended BCH codes as its component codes. In the receiver section, the maximum number of iterations for the LDPC belief propagation decoder is set to 50, and the maximum number of iterations for the TPC Chase decoder is set to 10. Simulation results show that the PAC code improves performance by at least approximately 0.18 dB and 0.55 dB compared to LDPC and TPC codes, respectively. The performance gain of the PAC code is more significant in short code cases, such as when the code length is short. At that time, the PAC code achieved a 1.5dB gain compared to the LDPC code.

Claims

1. A method for constructing and interleaving PAC codes for meteor trail channels, characterized in that, Includes the following steps: Step 1: For a noise variance of The fading coefficient is Physical channel of low-density meteoroid trails Assuming that all-zero codewords are transmitted within it and BPSK modulation is used, the duration of each BPSK symbol is... Then the first One received symbol The log-likelihood ratio LLR is expressed as: The LLR value follows a Gaussian distribution. ,in Step 2: Given a codeword length of... The number of information bits is The physical channel of the under-dense meteoroid trail in step 1 is known. For non-independent and identically distributed channels, indivual After channel interleaving, polar coding is performed, using express Interlaced pattern The first LLR sequence obtained after interleaving There are elements, that is, use Indicates the first step in the encoding process The first polarization transition One channel, used Indicates channel The generated LLR value, used express The mean of the channel is then calculated iteratively using the following formula. The average LLR generated above ： ; where subscript Indicates the first Step polarization transition, its range is superscript Represents the channel index, in the formula The range of values ​​is The function in this formula for: Step 3: Use Indicates completion The second polarization transition Each channel, based on the LLR mean value in step 2. Iterative calculation formula and initial value calculation method To obtain the channel The mean of the generated LLR values The channel can be obtained using the following formula. Transmission error probability of the information bits carried on ： ;in, The function is defined as superscript in the formula The range of values ​​is Step 4: Based on the error probability in Step 3 The calculation method will The probability of an error Sort the values ​​in ascending order, and select the top-ranked values ​​from the sorted sequence. The polarization subchannel corresponding to each error probability The index bit is used as the information bit. This represents the set of information bits, thus completing the polar code construction; Step 5: [The channel is then...] Channel capacity This indicates that when the channel capacity For set The Middle When the element is large, the channel capacity can also be expressed as ,in That is, its capacity sequence number, number 1 A pair of channels in step polarization transition and Can be derived from the first A pair of channels generated by step polarization transition and By constructing the above, without loss of generality, we assume that the capacity index in the channel polarization transition satisfies the following conditions: 、 Then there is Step 6: In independent and identically distributed channels, the polarization effect is entirely determined by the coding tree structure of the polar codes. The physical channel is altered through interleaving. Sorting, Channel Capacity serial number The physical channel of the under-dense meteoroid trail described in step 1 will not change. The polarization effect is influenced not only by the coding tree structure of the polar codes, but also by the physical channel of the under-dense meteoroid trail. The ordering of the meteor trails is affected, therefore the physical channel of the sparse meteoroid trails is altered by interleaving. Sorting, and thus changing the channel Capacity serial number Step 7: Change a channel by interleaving. Capacity serial number Specifically, the following steps are used to obtain the interleaving pattern that can achieve the lowest error rate. S1: For the channel parameter Perform enumeration, where S2: For each fixed Value, generating to maximize channel improvement Interlacing pattern of channel capacity S3: The results obtained during the enumeration process of steps S1 and S2 Interwoven pattern The block error rates are compared, and the interleaving pattern that results in the lowest block error rate is selected. As the final interwoven pattern And output; Step 8: Define the physical channel of the under-dense class stream-residual channel. The capacity sort vector is ， That is, in step 7, S2, in order to maximize Interlacing pattern designed for channel capacity ,use Indicates the first Capacity sorting vector after polarization transformation The number of elements in is ,use Indicates completion Capacity sorting vector after secondary polarization transformation The number of elements in the fixed value is 1. After the value, superscript Do after subtracting one Expanding the binary representation, we get the binary expansion formula. ,in For the most significant bit, use express The number of 0s in the middle, then Step 9: Based on the results obtained in Step 8 and Recursively generate underdense class flow co-channel physical channel Capacity sorted vector ,use express The subsequence, according to and generate Specifically There are four possible scenarios for its generation: A: When At that time, The generation method is as follows: ； ;in, ， ， and The expressions are respectively 、 B: When At that time, first The elements in the vector are arranged in descending order to obtain the vector. sum vector ,satisfy ,but The generation method is as follows: ； ； ;in, ， and The expressions are respectively 、 C: When At that time, first The elements in the vector are arranged in descending order to obtain the vector. sum vector ,satisfy ,but The generation method is as follows: ； ； ;in, ， and The expressions are respectively 、 D: When And at times When bits 0 and 1 are randomly distributed, then The generation method is as follows: ； ;in, ， and The expressions are respectively 、 Step 10: Recursively obtain the capacity sorting vector according to the recursive process described in Step 9. That is, the interlaced pattern described in step 7, S2. , this As in step 2 If used, the channel is obtained according to steps 2 and 3. Transmission error probability of the information bits carried on The information bit set is obtained according to step 4. The following formula is used to calculate the interlaced pattern. Theoretical error rate resulting from this ： Step 11: Given that S3 in step 7 requires S1 and S2 to be enumerated during the process... Compare the theoretical block error rates corresponding to the interlacing patterns, and repeat steps 8 to 10 to obtain... Choose the theoretical block error rate that results in the lowest theoretical block error rate. As the final interwoven pattern and will use The set of information bits corresponding to interleaving As the final set of information bits 。

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