Polarization code performance analysis and construction method and device based on expansion density evolution

Abstract

The invention discloses a polarization code performance analysis and construction method and device based on extended density evolution. The method comprises the following steps: calculating an error rate lower bound of a polarization code under a serial offset list decoding algorithm according to an extended density evolution algorithm; and determining a polarization code information bit set according to the lower bound of the bit error rate of the serial offset list decoding algorithm. According to the polarization code performance analysis and construction method and device based on extended density evolution disclosed by the invention, the error performance lower bound of each bit can be determined by using the extended density evolution method, and the bit error rate lower bound of the polarization code under a serial offset list decoding algorithm is calculated by using the bit error performance lower bound; and the polarization code information bit set is determined according to the bit error rate lower bound, so that the polarization code error performance is improved, the bit error rate is reduced, and the high-reliability and high-spectrum-efficiency communication requirements are met.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a method and a device for analyzing and constructing polarization code performance based on extended density evolution. Background Art

[0002] As the most basic wireless access technology, channel coding is one of the important research objects to meet the needs of 5G communication. After Shannon's theory was proposed, scholars from various countries have been committed to finding a coding method that can reach the Shannon limit while having relatively low complexity.

[0003] Polar code is currently the only channel coding technology that can be theoretically proven to reach the Shannon limit and has practical linear complexity coding capabilities. Polar code scheme is used as the control channel coding scheme for 5G enhanced mobile broadband (eMBB) scenarios.

[0004] The process of determining the information bit set based on the information bit length and the length of the coded codeword is called the polarization code sequence construction process. At present, the existing construction technology is based on the upper bound of serial cancellation (SC) decoding, and has the best performance in the serial cancellation decoder. However, the construction of serial cancellation list (SCL) decoding is the main decoding algorithm currently used in 5G. The construction method based on the SC upper bound cannot construct the optimal polarization code under the SCL decoder, and cannot meet the communication requirements of high reliability and high spectral efficiency. Summary of the invention

[0005] In view of this, the purpose of the present invention is to propose a polar code performance analysis and construction method and device based on extended density evolution (EDE), and to construct the optimal polar code under the SCL decoder by using the extended density evolution method to improve the error performance of the polar code, reduce the bit error rate, and meet the communication requirements of high reliability and high spectral efficiency.

[0006] The performance analysis and construction method of polar codes based on extended density evolution includes the following steps:

[0007] 1) Calculate the lower bound of the bit error rate of the polar code in the serial cancellation list (SCL) decoding algorithm based on the extended density evolution algorithm;

[0008] 2) Determine the polar code information bit set according to the lower bound of the bit error rate of the SCL decoding algorithm.

[0009] The step 1) comprises the following steps:

[0010] 1.1) determining a partial minimum Hamming weight of each polarization subchannel, and calculating a maximum likelihood performance bound of the polarization code based on the partial minimum Hamming weight and a set of polarization code information bits;

[0011] 1.2) Based on the Gaussian approximation algorithm and the extended density evolution algorithm, the lower bound of the partial path loss probability of polar codes under serial cancellation list decoding is calculated;

[0012] 1.3) The lower bound of the bit error rate of the serial cancellation list decoding algorithm is calculated based on the maximum likelihood performance bound and the lower bound of the serial cancellation list decoding path loss probability.

[0013] The step 1.2) comprises the following steps:

[0014] 1.2.1) According to the Gaussian approximation algorithm, the equivalent noise variance of the i-th polarization subchannel of the polar code is calculated:

[0015] 1.2.2) Let a k Represents a set of information bits The kth smallest element in And a1<a2<…<a K ; Let L represent the list size of the SCL decoding algorithm, given m = log2L; let the polar code information bit sequence be and

[0016] Then the SCL decoding path is at v k , the lower bound of the probability of loss at k>m is:

[0017]

[0018] Among them, P m+1 The extended density evolution method is used to calculate the P0 to P m The calculation formula is:

[0019] P0=P(L k-m ≥0,L k-m+1 ≥0,…,L k ≥0)

[0020] P i =P(L k-m ≥0,…,L k-i ≥0,-ln(β i )≤L k-i+1 <0),i=1,2,…,m

[0021] Among them, L k Indicates v k The bit log-likelihood ratio at , and

[0022] 1.2.3)P m+1 It is expressed as:

[0023]

[0024] in, Represents a random variable The probability density function of Indicates v k-1 =1 condition, v k The log-likelihood ratio of

[0025] 1.2.4) Calculation using the extended density evolution method

[0026] The step 1.2.4) comprises the following steps:

[0027] 1.2.4.1) Given the binary representations of the (k-1)th polarization subchannel and the kth polarization subchannel respectively:

[0028] b k-1 =b(k-2)=[b0(k-2),b1(k-2),…,b n-1 (k-2)]

[0029] b k =b(k-1)=[b0(k-1),b1(k-1),…,b n-1 (k-1)]

[0030] Among them, b0(k-2) represents the lowest bit of binary expansion, b n-1 (k-2) represents the most significant bit of the binary expansion;

[0031] 1.2.4.2) For i = n-1, ..., 0, find the first i (k-2)≠b i (k-1) i, and given k d =i;

[0032] 1.2.4.3) Given the channel noise variance is σ 2 The initial log-likelihood ratio follows the mean The variance is The Gaussian distribution of is, and the corresponding probability density function is:

[0033]

[0034] 1.2.4.4) For parameter j = 0, ..., n-1, first determine whether j is equal to k d , if equal, execute 1.2.4.5), otherwise execute 1.2.4.6);

[0035] 1.2.4.5) Given parameter p j,1 (x) = p j (x)ε(x) and p j,-1 (x) = p j (x)ε(-x), ε(x) represents the step function, p0(x) represents the initial probability density function, p1(x), j=1,…,n-1 represents the intermediate probability density function of the extended density evolution calculation, and Normal(p j,1 (x)*p j,-1 (-x)+p j,1 (-x)*p j,-1 (x)) is assigned to p j+1 (x), where Normal(·) means normalizing the function, and * means convolution;

[0036] 1.2.4.6) Determine b j (k-1) is 0 or 1, if it is 0, then p j (x)⊙p j (x) is assigned to p j+1 (x), if it is 1, then p j (x)*p j (x) is assigned to p j+1 (x), where ⊙ represents the calculation process of the upper branch in the traditional density evolution method;

[0037] 1.2.4.7) Set p n (x) is assigned to Calculate P m+1 .

[0038] The step 1.3) comprises the following steps:

[0039] 1.3.1) The lower bound of partial path loss probability of polar code under serial cancellation list decoding P loss for

[0040]

[0041] in, And P i , i=0,…,m+1;

[0042] 1.3.2) Serial cancellation list decoding algorithm bit error rate lower bound P LB is the maximum likelihood performance bound P ML The sum of the lower bound of the probability of decoding path loss of the serial cancellation list is

[0043] P LB =P ML +P loss .

[0044] The step 2) comprises the following steps:

[0045] 2.1) determining an initial information bit set according to a polarization sequence based on a distance spectrum;

[0046] 2.2) grouping polarimetric subchannels according to partial minimum Hamming weights;

[0047] 2.3) Determine the polar code information bit set based on the initial information bit set and the lower bound of the bit error rate of the serial cancellation list decoding algorithm.

[0048] The step 2.2) comprises the following steps:

[0049] 2.2.1) Group the polarization subchannels according to their partial minimum Hamming weights to obtain a grouping set Among them, the rth group is the row weight 2 n-r The set of polarization channel indices, r = 0, 1, ..., n, that is,

[0050]

[0051] 2.2.2) For Find the parameter c such that and Assign the value of c-1 to parameter a, and assign the value of c to parameter b.

[0052] The step 2.3) comprises the following steps:

[0053] 2.3.1) Initialization Assign to Will Assign to Assign it to infinity, Assign a value of 0;

[0054] 2.3.2) If Then execute 2.3.3), otherwise execute 2.3.8);

[0055] 2.3.3) Calculation And assign the result to the collection calculate That is, collection Reduce Set And assign the result to the collection

[0056] 2.3.4) Calculation And assign the result to i max ,Will Assign to

[0057] 2.3.5) Calculation And assign the result to i min ,Will Assign to

[0058] 2.3.6) Assigning to a collection And calculate the lower bound of the bit error rate of the serial cancellation list decoding algorithm

[0059] 2.3.7) If Then Assigning to a collection Will Assign to And execute step 2.3.2); otherwise, execute 2.3.2 directly;

[0060] 2.3.8) If a=0 and b=n at this time, execute step 2.3.10), otherwise execute step 2.3.9);

[0061] 2.3.9) Assign max(a-1,0) to a, assign min(b+1,n) to b, and execute step 2.3.1);

[0062] 2.3.10) Get the polar code information bit set at this time

[0063] Polar code performance analysis and construction device based on extended density evolution, including:

[0064] A sequence construction module, used to construct a sequence according to the polar code based on the distance spectrum, determine a required sequence, and determine an initial information bit set;

[0065] A polarization sub-channel grouping module, used for grouping the polarization sub-channels according to some minimum Hamming weights of the polarization sub-channels;

[0066] A serial cancellation list performance lower bound calculation module is used to calculate the performance lower bound of the serial cancellation list decoding algorithm;

[0067] Serial cancellation list information bit construction module: used to determine the polar code information bit set according to the lower bound of the serial cancellation list decoding algorithm performance.

[0068] A polar code performance analysis and construction device based on extended density evolution comprises a memory and a processor: the memory is used to store a computer program; the processor is used to implement the polar code performance analysis and construction method based on extended density evolution when executing the computer program.

[0069] The present invention has the following beneficial effects and advantages:

[0070] The present invention uses the extended density evolution method to construct the optimal polar code under the SCL decoder to improve the error performance of the polar code, reduce the bit error rate, and meet the communication requirements of high reliability and high spectral efficiency. The method of the present invention is particularly suitable for application in actual communication systems and has a good practical prospect. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 A flow chart of the polar code performance analysis and construction method based on extended density evolution provided by the present invention;

[0072] Figure 2 A schematic diagram of a process of calculating the lower bound of the bit error rate of polar codes under the SCL decoding algorithm according to the extended density evolution algorithm of the present invention;

[0073] Figure 3 A schematic diagram of a process for determining a polar code information bit set according to a lower bound of a bit error rate of an SCL decoding algorithm according to the present invention;

[0074] Figure 4 This is a flow chart of determining the polar code information bit set according to the initial information bit set and the lower bound of the bit error rate of the SCL decoding algorithm in the present invention;

[0075] Figure 5 A schematic diagram of the structure of a polar code performance analysis and construction device based on extended density evolution provided by the present invention;

[0076] Figure 6 This is a performance diagram of the polarization code bit error rate curve of the present invention with a code length of 128 and a code rate of 0.5. DETAILED DESCRIPTION

[0077] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0078] In order to make the objectives, technical solutions and advantages of the present disclosure more clearly understood, the present disclosure is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0079] Unless otherwise defined, technical or scientific terms used in one or more embodiments of the present specification should have the common meanings understood by a person having ordinary skills in the field to which the present disclosure belongs.

[0080] It should be noted that for a code length of N = 2 n , the polar code with information bit length K has the following coding structure: in Denotes the Kronecker product. Polar code construction is the process of selecting K sub-channels with the greatest reliability from N polarization sub-channels to form an information bit set.

[0081] In this specification, lowercase bold (such as a) indicates a column vector; uppercase bold (such as A) indicates a matrix; and handwriting (such as ) represents a set, Representing a collection The number of elements in ; represents the Kronecker product; a←b means assigning the value of b to a.

[0082] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0083] like Figure 1 As shown in FIG. 1 , the polar code performance analysis and construction method based on extended density evolution includes the following basic steps:

[0084] Step 1: Calculate the lower bound of the bit error rate of the polar code under the SCL decoding algorithm based on the extended density evolution algorithm:

[0085] Step 2: Determine the polar code information bit set according to the bit error rate lower bound of the SCL decoding algorithm.

[0086] Figure 2 The process of calculating the lower bound of the bit error rate of the polar code under the SCL decoding algorithm according to the extended density evolution algorithm of the present invention includes:

[0087] S201: Determine a partial minimum Hamming Weight (MWD) of each polarization subchannel, and calculate a polar code ML performance bound based on the partial MWD and a set of polar code information bits:

[0088] (11) For the i-th polarization subchannel, i = 1, 2, …, N, the corresponding monomial is f(i-1), and the binary representation of i-1 is b(i-1) = [b0(i-1), b1(i-1), …, b n-1 (i-1)], then where a j (i-1)=1-b j (i-1), j=0,1,…,n-1;

[0089] (12) The i-th row of the generator matrix G corresponding to the i-th polarization subchannel has a row weight d i Expressed as

[0090] (13) The weight of the i-th polarimetric subchannel pair is d i The distance spectrum of the influence of is defined as follows: For the monomial Given a collection Assume the degree of f(i-1) is Impact is defined as

[0091] (14) Then the partial MWD of the i-th polarization subchannel is expressed as (d i ,A i ),in

[0092] (15) The ML performance bound of the i-th polariton channel is

[0093]

[0094] Among them, Q(·) represents the right tail function of the standard normal distribution, E s / N0 represents the bit signal-to-noise ratio.

[0095] S202: Calculate the lower bound of the partial path loss probability of the polar code under SCL decoding based on the Gaussian approximation algorithm;

[0096] (21) According to the Gaussian approximation algorithm, the equivalent noise variance of the i-th polarization subchannel of the polar code is calculated:

[0097] (22) Let a k Represents a set of information bits The kth smallest element in And a1<a2<…<a K ; Let L represent the list size of the SCL decoding algorithm, given m = log2L; let the polar code information bit sequence be and

[0098] Then the SCL decoding path is at v k , the lower bound of the probability of loss at k>m is

[0099]

[0100] Among them, P m+1 The extended density evolution method is used to calculate the P0 to P m Calculate according to the following formula:

[0101] P0=P(L k-m ≥0,L k-m+1 ≥0,…,L k ≥0) (3)

[0102] P i =P(L k-m ≥0,…,L k-i ≥0,-ln(β i )≤L k-i+1 <0),i=1,2,…,m (4)

[0103] Lk Indicates v k The bit log-likelihood ratio at , and

[0104] S203: Calculate the lower bound of partial path loss probability of polar code under SCL decoding based on the extended density evolution algorithm;

[0105] (31)P m+1 Expressed as

[0106]

[0107] in, Represents a random variable The probability density function of Indicates v k-1 =1 condition, v k The log-likelihood ratio of

[0108] (32) Calculated using the extended density evolution method The details are as follows:

[0109] (321) Given that the binary representations of the (k-1)th polarimetric subchannel and the kth polarimetric subchannel are

[0110] b k-1 =b(k-2)=[b0(k-2),b1(k-2),…,b n-1 (k-2)] (6)

[0111] b k =b(k-1)=[b0(k-1),b1(k-1),…,b n-1 (k-1)] (7)

[0112] (322) For i = n-1, ..., 0, find the first i (k-2)≠b i (k-1) i, and given k d =i;

[0113] (323) Given the channel noise variance is σ 2 The initial log-likelihood ratio follows the mean The variance is The Gaussian distribution of

[0114]

[0115] (324) For j = 0, ..., n-1, first determine whether j is equal to k d , if equal, execute (325), if not equal, execute (326);

[0116] (325) Given p j,1 (x) = p j (x)ε(x) and p j,-1 (x) = p j (x)ε(-x), ε(x) represents a step function, then p j+1 (x)←Normal(p j,1 (x)*p j,-1 (-x)+p j,1 (-x)*p j,-1 (x)), where Normal(·) means normalizing the function, and * means convolution;

[0117] (326) Judge b j (k-1) is 0 or 1, if it is 0, execute p j+1 (x)←p j (x)⊙p j (x), if it is 1, execute p j+1 (x)←p j (x)*p j (x), where ⊙ represents the calculation process of the upper branch in the traditional density evolution method;

[0118] (327) Given According to formula (5), P m+1 .

[0119] S204: Calculate the lower bound of the bit error rate of the SCL decoding algorithm based on the ML performance bound and the lower bound of the SCL decoding path loss probability:

[0120] (41) The lower bound of the partial path loss probability of polar code under SCL decoding is

[0121]

[0122] in, And P i , i=0,…,m+1 is calculated according to S202 and S203;

[0123] (42) The lower bound of the bit error rate of the SCL decoding algorithm is the sum of the ML performance bound and the lower bound of the SCL decoding path loss probability, that is,

[0124] P LB =P ML +P loss (10)

[0125] Figure 3 The process of determining the polar code information bit set according to the lower bound of the bit error rate of the SCL decoding algorithm of the present invention includes:

[0126] S301: Determine an initial information bit set according to a polarization sequence based on a distance spectrum

[0127] According to the polarization sequence based on the distance spectrum Determine a polarization sequence of length N, and, where represents the reliability of the th polarization subchannel, and calculate the lower bound of the performance of the SCL decoding algorithm according to the determined information bit set;

[0128] S302: Grouping polarization sub-channels according to partial MWD

[0129] (21) The polarization subchannels are grouped according to their partial MWD, where the rth group is the group with a row weight of 2. n-r The set of polarization channel indices, r = 0, 1, ..., n, that is,

[0130]

[0131] (22) For r=0,1,…,n, find c such that and And given a←c-1 and b←c;

[0132] S303: Determine the polar code information bit set according to the initial information bit set and the lower bound of the bit error rate of the SCL decoding algorithm. The corresponding flow chart is as follows: Figure 4 Shown

[0133] (31) Initialization

[0134] (32) If Execute (33), otherwise execute (38);

[0135] (33) Calculation and

[0136] (34) Calculation and

[0137] (35) Calculation and

[0138] (36) And calculate the lower bound of the bit error rate of the SCL decoding algorithm based on S201 to S204

[0139] (37) If implement and And execute (32), otherwise execute (32) directly;

[0140] (38) If a=0 and b=n, execute (310), otherwise execute (39);

[0141] (39) a←max(a-1,0) and b←min(b+1,n), execute (31);

[0142] (310) Determine the polar code information bit set for the SCL decoder

[0143] In the above-mentioned embodiments of the present invention, the polarization code construction method for the serial cancellation list decoder provided by the embodiment of the present invention is introduced from the perspective of constructing an information bit set. It can be understood that the above-mentioned method can be implemented in various network elements. In order to realize the above-mentioned functions, each network element, such as a terminal, a base station, a control node, etc., includes a hardware structure and / or a software module corresponding to each function. It should be easily appreciated by those skilled in the art that, in combination with the units and algorithm steps of each example described in the embodiments disclosed herein, the present invention can be implemented in the form of hardware or a combination of hardware and computer software. Whether a function is executed in the form of hardware or computer software driving hardware depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention.

[0144] Figure 5 The polar code construction device for the serial cancellation list decoder provided by the present invention comprises:

[0145] Transceiver S401: transmitter and receiver, used for sending and receiving signals;

[0146] Modem processor S402: used for polar code modulation, demodulation and decoding;

[0147] Storage S403: used to store the polar code construction sequence based on the distance spectrum;

[0148] The controller / processor S404 is configured to read a construction sequence having the same length as the encoding code length of the polar code sequence to be constructed from the construction sequence, and determine a polar code information bit set according to the present invention;

[0149] The communication interface S405 is used to support the apparatus for constructing a polar code information bit set to communicate with other network entities.

[0150] The polar code information bit set construction device provided by the present invention can execute the method steps of the previous embodiment, which will not be described in detail here.

[0151] The functions of the controller / processor S404 can be implemented by circuits or by general hardware executing software codes. When the latter is adopted, the memory S403 is also used to store program codes that can be executed by the controller / processor S404. When the controller / processor S404 runs the program codes stored in the memory S403, the aforementioned functions are executed.

[0152] Further, the apparatus for constructing a polar code sequence may also include an encoder S4021, a modulator S4022, a demodulator S4023, and a decoder S4024.

[0153] The encoder S4021 is used to obtain data / signaling that the network side device is about to send to the terminal or the terminal is about to send to the network side device, and encode the data / signaling. The modulator S4022 modulates the data / signaling encoded by the encoder S4021 and transmits it to the transceiver S401, which is sent to the terminal or other network side devices by the transceiver S401. The demodulator S4023 is used to obtain the data / signaling sent by the terminal or other network side devices and demodulate it. The decoder S4024 is used to decode the data / signaling demodulated by the demodulator S4023.

[0154] The encoder S4021, modulator S4022, demodulator S4023 and decoder S4024 can be implemented by the synthesized modulation and demodulation processor S402. These units perform processing according to the radio access technology (for example, access technology of LTE, 5G or other evolved systems) adopted by the radio access network.

[0155] Understandably, Figure 5 Only a simplified design of a polar code information bit set device is shown. In practical applications, the device may include any number of transceivers, processors, controllers / processors, memories, and / or communication interfaces.

[0156] The present invention has been tested and simulated for many times. The following is a detailed description of the implementation process and performance analysis of the present invention based on the test results of the simulation embodiment:

[0157] Table 1 is a distance spectrum-based polar code construction table with a code length of 1024, which can directly determine the distance spectrum-based polar code construction sequence.

[0158] In the present invention, assuming that the polar code length is 128, the polarization sequence determined according to the construction table of 1024 is as follows:

[0159] {0,1,2,4,8,16,32,64,3,5,6,9,10,17,12,18,33,20,34,65,24,36,66,40,68,48,72,80,96,7,11,13,19,14,21,35,22,25,37,67,26,38,41,69,28,42,49,70,73,44,50,74,81,52,76,82,97,56,84,98,88,100,104,112,15,23,27,39,29,4 3,71,30,45,51,75,46,53,77,83,54,57,78,85,99,58,86,89,101,60,90,102,105,92,106,113,108,114,116,120,31,47,55,79,59,87,61,91,103,62,93,107,94,109,115,110,117,118,121,122,124,63,95,111,119,123,125,126,127}.

[0160] Table 1

[0161]

[0162]

[0163]

[0164]

[0165]

[0166] Figure 6 This is the bit error rate curve of the polar code with a code length of 128 and a code rate of 0.5.

[0167] from Figure 6 It can be seen that compared with the existing Gaussian approximation (GA) construction method, the polar code performance analysis and construction method based on extended density evolution proposed in the present invention has obvious performance gain. Specifically, at a bit error rate of 0.1, there is a performance gain of about 0.2dB.

[0168] In a specific implementation, the above-mentioned device may be a terminal or a network-side device, which may be a base station or a control node.

[0169] The controller / processor of the above-mentioned base station, terminal, or control node in the present invention can be a central processing unit (CPU), a general processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, transistor logic devices, hardware components or any combination thereof. It can implement or execute various exemplary logic blocks, modules and circuits described in conjunction with the disclosure of the present invention. The processor can also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, and the like.

[0170] The steps of the method or algorithm described in conjunction with the disclosure of the present invention can be implemented in hardware or by a processor executing software instructions (e.g., program code). The software instructions can be composed of corresponding software modules, and the software modules can be stored in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, register, hard disk, mobile hard disk, CD-ROM or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC. In addition, the ASIC can be located in a terminal. Of course, the processor and the storage medium can also be present in the terminal as discrete components.

[0171] Those skilled in the art will appreciate that in one or more of the above examples, the functions described in the present invention may be implemented in hardware, software, firmware, or any combination thereof. When implemented using software, the functions may be stored in a computer-readable medium or transmitted as one or more instructions or codes on a computer-readable medium. Computer-readable media include computer storage media and communication media, wherein communication media include any media that facilitates the transmission of a computer program from one place to another. The storage medium may be any available medium that a general or special-purpose computer can access.

[0172] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method 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 on the basis of the technical solution of the present invention should be included in the scope of protection of the present invention.

Claims

1. A polar code performance analysis and construction method based on extended density evolution, characterized in that: The following steps are involved: 1) Calculate the lower bound of the bit error rate of the polar code in the serial cancellation list (SCL) decoding algorithm based on the extended density evolution algorithm; 2) Determine the polar code information bit set according to the lower bound of the bit error rate of the SCL decoding algorithm.

2. The method for analyzing and constructing polar codes based on extended density evolution according to claim 1, characterized in that: The step 1) comprises the following steps: 1.1) determining a partial minimum Hamming weight of each polarization subchannel, and calculating a maximum likelihood performance bound of the polarization code based on the partial minimum Hamming weight and a set of polarization code information bits; 1.2) Based on the Gaussian approximation algorithm and the extended density evolution algorithm, the lower bound of the partial path loss probability of polar codes under serial cancellation list decoding is calculated; 1.3) The lower bound of the bit error rate of the serial cancellation list decoding algorithm is calculated based on the maximum likelihood performance bound and the lower bound of the serial cancellation list decoding path loss probability.

3. The method for analyzing and constructing polar codes based on extended density evolution according to claim 2, characterized in that: Step 1.2) The following steps are involved: 1.2.1) According to the Gaussian approximation algorithm, the equivalent noise variance of the i-th polarization subchannel of the polar code is calculated: 1.2.2) Let a k Represents a set of information bits The kth smallest element in And a1<a2<…<a K ; Let L represent the list size of the SCL decoding algorithm, given m = log2L; let the polar code information bit sequence be and Then the SCL decoding path is at v k , the lower bound of the probability of loss at k>m is: in, P m+1 The extended density evolution method is used to calculate the P0 to P m The calculation formula is: P0=P(L k-m ≥0,L k-m+1 ≥0,…,L k ≥0) P i =P(L k-m ≥0,…,L k-i ≥0,-ln(β i )≤L k-i+1 <0),i=1,2,…,m Among them, L k Indicates v k The bit log-likelihood ratio at , and 1.2.3)P m+1 It is expressed as: in, Represents a random variable The probability density function of Indicates v k-1 =1 condition, v k The log-likelihood ratio of 1.2.4) Calculation using the extended density evolution method 4. The method for analyzing and constructing polar codes based on extended density evolution according to claim 3, characterized in that: Step 1.2.4) The following steps are involved: 1.2.4.1) Given the binary representations of the (k-1)th polarization subchannel and the kth polarization subchannel respectively: b k-1 =b(k-2)=[b0(k-2),b1(k-2),…,b n-1 (k-2)] b k =b(k-1)=[b0(k-1),b1(k-1),…,b n-1 (k-1)] in, b0(k-2) represents the least significant bit of the binary expansion, b n-1 (k-2) represents the most significant bit of the binary expansion; 1.2.4.2) For i = n-1, ..., 0, find the first i (k-2)≠b i (k-1) i, and given k d =i; 1.2.4.3) Given the channel noise variance is σ 2 The initial log-likelihood ratio follows the mean The variance is The Gaussian distribution of is, and the corresponding probability density function is: 1.2.4.4) For parameter j = 0, ..., n-1, first determine whether j is equal to k d , if equal, execute 1.2.4.5), otherwise execute 1.2.4.6); 1.2.4.5) Given parameter p j,1 (x) = p j (x)ε(x) and p j,-1 (x) = p j (x)ε(-x), ε(x) represents the step function, p0(x) represents the initial probability density function, p1(x), j=1,…,n-1 represents the intermediate probability density function of the extended density evolution calculation, and Normal(p j,1 (x)*p j,-1 (-x)+p j,1 (-x)*p j,-1 (x)) is assigned to p j+1 (x), where Normal(·) means normalizing the function, and * means convolution; 1.2.4.6) Determine b j (k-1) is 0 or 1, if it is 0, then p j (x)⊙p j (x) is assigned to p j+1 (x), if it is 1, then p j (x)*p j (x) is assigned to p j+1 (x), where ⊙ represents the calculation process of the upper branch in the traditional density evolution method; 1.2.4.7) Set p n (x) is assigned to Calculate P m+1 .

5. The method for analyzing and constructing polar codes based on extended density evolution according to claim 2, characterized in that: The step 1.3) comprises the following steps: 1.3.1) The lower bound of partial path loss probability of polar code under serial cancellation list decoding P loss for in, And P i , i=0,…,m+1; 1.3.2) Serial cancellation list decoding algorithm bit error rate lower bound P LB is the maximum likelihood performance bound P ML The sum of the lower bound of the probability of decoding path loss of the serial cancellation list is P LB =P ML +P loss 。 6. The method for analyzing and constructing polar codes based on extended density evolution according to claim 1, characterized in that: Step 2) The following steps are involved: 2.1) determining an initial information bit set according to a polarization sequence based on a distance spectrum; 2.2) grouping polarimetric subchannels according to partial minimum Hamming weights; 2.3) Determine the polar code information bit set based on the initial information bit set and the lower bound of the bit error rate of the serial cancellation list decoding algorithm.

7. The method for analyzing and constructing polar codes based on extended density evolution according to claim 6, characterized in that: Step 2.2) The following steps are involved: 2.2.1) Group the polarization subchannels according to their partial minimum Hamming weights to obtain a grouping set in, The rth group is the row weight 2 n-r The set of polarization channel indices, r = 0, 1, ..., n, that is, 2.2.2) For Find the parameter c such that and Assign the value of c-1 to parameter a, and assign the value of c to parameter b.

8. The method for analyzing and constructing polar codes based on extended density evolution according to claim 6, characterized in that: The step 2.3) comprises the following steps: 2.3.1) Initialization Assign to Will Assign to Assign it to infinity, Assign a value of 0; 2.3.2) If Then execute 2.3.3), otherwise execute 2.3.8); 2.3.3) Calculation And assign the result to the collection calculate That is, collection Reduce Set And assign the result to the collection 2.3.4) Calculation And assign the result to i max ,Will Assign to 2.3.5) Calculation And assign the result to i min ,Will Assign to 2.3.6) Assigning to a collection And calculate the lower bound of the bit error rate of the serial cancellation list decoding algorithm 2.3.7) If Then Assigning to a collection Will Assign to And execute step 2.3.2); otherwise, execute 2.3.2 directly; 2.3.8) If a=0 and b=n at this time, execute step 2.3.10), otherwise execute step 2.3.9); 2.3.9) Assign max(a-1,0) to a, assign min(b+1,n) to b, and execute step 2.3.1); 2.3.10) Get the polar code information bit set at this time 9. A polar code performance analysis and construction device based on extended density evolution, characterized in that: include: A sequence construction module, used to construct a sequence according to the polar code based on the distance spectrum, determine a required sequence, and determine an initial information bit set; A polarization sub-channel grouping module, used for grouping the polarization sub-channels according to some minimum Hamming weights of the polarization sub-channels; A serial cancellation list performance lower bound calculation module is used to calculate the performance lower bound of the serial cancellation list decoding algorithm; Serial cancellation list information bit construction module: used to determine the polar code information bit set according to the lower bound of the serial cancellation list decoding algorithm performance.

10. A polar code performance analysis and construction device based on extended density evolution, characterized in that: The method comprises a memory and a processor: the memory is used to store a computer program; the processor is used to implement the polar code performance analysis and construction method based on extended density evolution according to any one of claims 1 to 8 when executing the computer program.

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