CN113067584A - Coding method for common auxiliary polarization code of CRC (Cyclic redundancy check) code and PC (personal computer) code - Google Patents

Coding method for common auxiliary polarization code of CRC (Cyclic redundancy check) code and PC (personal computer) code Download PDF

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CN113067584A
CN113067584A CN202110310163.XA CN202110310163A CN113067584A CN 113067584 A CN113067584 A CN 113067584A CN 202110310163 A CN202110310163 A CN 202110310163A CN 113067584 A CN113067584 A CN 113067584A
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crc
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polarization
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袁建国
张瑞
李志伟
粱栩珩
张降龙
游薇
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
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Abstract

The invention particularly relates to a coding method for assisting a polarization code by using a CRC code and a PC code together. The invention belongs to the technical field of channel coding, and the method adds a CRC code with higher error detection efficiency in a polarization (PC-polar) code assisted by a parity check code, and optimizes a check function of the PC code through different PC code numbers, positions and five-bit cyclic shift registers, thereby obviously improving the error correction performance of the PC-polar code. Simulation results show that the CRC-PC-polar (CRC8, PC6) code constructed by the algorithm has a block error rate (BLER) of 10‑5When compared with the PC-polar code, the cyclic redundancy check polar code and the segmented cyclic redundancy check polar code, the code has net coding gains of 0.4dB, 0.1dB and 0.2dB respectively.

Description

Coding method for common auxiliary polarization code of CRC (Cyclic redundancy check) code and PC (personal computer) code
Technical Field
The invention belongs to the technical field of channel coding, and relates to a coding method of a polarization code in channel coding. The method is mainly based on the improvement of the codes of the polarization codes by the CRC codes and the PC codes.
Background
The polar code is a novel coding mode, is proposed for the first time in 2008 by professor Arikan of university of turkish bicken, can realize a code construction method of capacity of a symmetric binary input discrete memoryless channel, and is a new star in the coding field. As a channel coding technique which can be theoretically proved to reach the shannon limit and has a practical linear complexity coding and decoding capability, the 3GPP determines a polarization code scheme which is mainly promoted by china companies such as hua shi and the like as a control channel coding scheme of a 5G enhanced mobile broadband scene in the RAN1#87 meeting of 3GPP which ends in lino, nevada, 2016, 18.
The dominant one in all polar code schemes is the CRC code assisted SCL decoding algorithm, which can have comparable performance to the current state-of-the-art low density parity check code. In order to further improve the performance of the coding algorithm of the CRC code assisted polar code (usually abbreviated as CRC-polar code) under high signal to noise ratio, researchers have studied the CRC code, including the SCL algorithm of the adaptive list, the optimal CRC polynomial search algorithm in the polar code, the minimum hamming weight algorithm for reducing the polar code, and so on. However, the above-mentioned polar code schemes have a problem that erroneous bits cannot be detected and corrected during decoding. In order to solve the problem, a segmented CRC (cyclic redundancy check) and discrete CRC code auxiliary polarization code scheme is provided, and both schemes can correct error bits in the decoding process and improve the decoding performance. But the multiple CRC code is less efficient in correcting the erroneous bits than the PC-polar code. Compared with the CRC code, the PC code can provide better error correction performance in decoding, but has the disadvantage of low error detection efficiency, which is mainly reflected in: for the same check function, increasing the number of PC bits does not improve the error correction efficiency; secondly, only the error of odd bits can be detected, but the error of even bits cannot be detected. On the contrary, the error correction performance can be effectively improved by increasing the bit number of the CRC code.
Therefore, the invention provides a novel coding method for a common auxiliary polarization code of a CRC code and a PC code, aiming at the problem of poor error correction performance caused by low error detection efficiency of the parity check code in the PC-polar code. In order to improve the error detection efficiency of the PC-polar code, ensure that the PC-polar code has the same high-efficiency error detection efficiency of the CRC code and improve the error correction performance of the polar code, firstly, a channel is selected from MHW and sub-MHW sets as a channel set for transmitting PC bits, so that the distance spectrum of an information bit set is as large as possible; then, a check function of the PC code is optimized by using CSR, and bit errors caused by serial decoding of the polarization code are reduced; and finally, a CRC code with higher error detection efficiency is added to improve the error detection efficiency of the PC-polar code, so that the structure of the PC-polar code assisted by the CRC code is obtained. Through simulation verification, when the Signal Noise Ratio (SNR) of the CRC-PC-polar (CRC8, PC6) code constructed by the coding method provided by the invention is 1-3.5 dB, the overall error correction performance is obviously superior to that of the PC-polar code, the CRC-polar code and the segmented-CRC-polar code.
Disclosure of Invention
In view of the above, the present invention provides a coding method of CRC code assisted PC-polar code, which improves the coding method of polar code by CRC code and PC code. The number, the position and the check function of the PC bits are designed through the CSR and the optimized distance spectrum, and then the optimal CRC generator polynomial is combined, so that the proposed polarization code has the advantages of the PC code and the CRC code at the same time, and the error correction performance is obviously improved.
In order to achieve the purpose, the invention provides the following technical scheme:
firstly, reliability estimation is carried out on each channel by utilizing a channel estimation method of confirming the code length of the polarization code to be constructed and combining polarization weight, and sequencing is carried out. Channels are selected from the MHW set and the sub-MHW set of sets of information bits as a set of channels of PC bits such that the distance spectrum of the set of information bits is as large as possible.
Then, a check function of the PC code is designed by utilizing the five-bit CSR, so that bit errors caused by serial decoding of the polarization code are reduced; the CRC code with higher error detection efficiency is added to improve the error detection efficiency of the PC-polar code, and the structure of the common auxiliary polarization code of the CRC code and the PC code is obtained.
And then, the number of proper CRC codes and PC codes is determined by using a control variable method, so that the error correction performance of the polarization code constructed by the method is better.
And finally, under the same simulation environment, carrying out simulation comparative analysis on the coding method of the CRC code and the PC code which jointly assist the polarization code and other coding schemes of the same type.
The invention has the beneficial effects that:
a coding method of a polarization code is assisted by a CRC code and a PC code together. In the method, firstly, a channel is selected from an MHW set and a secondary MHW set of an information bit set as a channel set of PC bits, so that the distance spectrum of the information bit set is as large as possible, and the correct decoding probability of the information bits is improved; secondly, a check function of the PC code is optimized by utilizing a five-bit cyclic shift register, so that the PC-polar code has the following advantages: 1. the method has the advantages that a check function is not required to be designed for each PC bit independently, the complexity of the PC check function is fixed 2, the complexity of the PC check function cannot be changed by changing the number of the PC bits, 3, the check function can be stored in advance, calculation is not required in a coding and decoding stage, 4, the polarization code bit is divided into five parts, and the situation that the first bit is wrong and the second bit and the fourth bit are wrong due to the serial decoding structure of an SCL decoder in the decoding stage can be effectively avoided; and finally, the CRC code with higher error detection efficiency is added, so that the defect of low error detection efficiency of the PC code is overcome, and the error correction performance of the polarization code is improved. As for the calculation complexity and the decoding time delay, the CRC code is added into the base PC-polar code, only the processes of CRC coding and decoding are added in the coding and decoding processes, and the calculation complexity and the decoding time delay are hardly increased. But the error correction performance is obviously improved compared with the PC-polar code, the CRC-polar code and the segmented-CRC-polar code.
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In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a technical flow chart of the algorithm of the present invention;
FIG. 2 is a block diagram of a five-bit circular shift register;
FIG. 3 is a performance diagram of different PC bit numbers for the polar code constructed by the proposed algorithm;
FIG. 4 is a comparison of four polar code structures;
fig. 5 is a graph comparing the performance of four polarization codes when m is 6 and f is 6;
fig. 6 is a graph comparing the performance of four polarization codes when m is 8 and f is 6;
fig. 7 is a graph comparing the performance of four polarization codes when m is 10 and f is 7;
fig. 8 is a comparison graph of the performance of three polar codes constructed by the proposed algorithm.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
(1) Referring to fig. 1, a specific implementation method of a coding method of a common auxiliary polarization code of a CRC code and a PC code is as follows:
in the PC-polar code, K information bits and f PC bits are transmitted through K + f most reliable channels, an index set of the K information bits is defined as a,
Figure BDA0002989304290000031
where N is the total number of channels and N is limited to 2nN is a positive integer; the index set of f PC bits is defined as Apc(ii) a The remaining N-K-f unreliable channels are used to transmit the frozen bits, and the index set of the frozen bits is defined as AcThe values of the freeze bits are normally all set to 0. The code rate of the polar code is R ═ K/N.
The generator matrix of the polarization code can be defined as:
Figure BDA0002989304290000032
b in formula (1)NIs a bit-reversal matrix, and
Figure BDA0002989304290000033
represents the n-fold kronecker product of F. The coding sequence of the polarization code can be obtained by the formula (2)
Figure BDA0002989304290000034
Figure BDA0002989304290000035
In the formula (2)
Figure BDA0002989304290000036
Is all information bits uA＝(uiI ∈ A), PC bits
Figure BDA0002989304290000037
And freeze the bit
Figure BDA0002989304290000038
A vector formed by the set of (a).
Polarization weight channel reliability estimation method, for a given subchannel index i, its binary extension is B ═ Bn-1,K,b1,b0) The corresponding polarization weights are defined as:
Figure BDA0002989304290000041
in the formula (3), beta is 21/4. Calculating the polarization weight value of each channel through a formula (3), thereby sequencing the reliability of the channels; wherein a higher polarization weight value represents a higher channel reliability.
Figure BDA0002989304290000042
Figure BDA0002989304290000043
D in formula (4) and formula (5)mAnd dsRespectively MHW and sub-MHW of non-frozen bit channels in the polar code,
Figure BDA0002989304290000044
is GNHamming weight value of row i. PC bit slave set AmAnd AsThe distance spectrum of the information bits is selected to be as large as possible, so that the path metric value difference between different paths is as large as possible, and the real path is easy to select.
The specific algorithm for selecting the PC bit number and the position is as follows: 1. determining the reliability of all channels according to a formula (3), and sequencing; 2. selecting the most reliable K + f channels as an information bit set and a PC bit set respectively, and taking the rest channels as a frozen bit set; 3. if A ismIf the number of middle bits is greater than f, the least reliable f channels are selected as the PC bit set ApcIf A ismIf the number of the middle bits is less than f, selecting AmAll channels in and AsMiddle f-A |mI least reliable channels as PC bit set ApcWherein | AmL is AmThe number of medium bits.
The PC bit check function herein is constructed using a five-bit CSR, which is shown in fig. 2, and the specific PC bit function construction algorithm is as follows:
output initial data, including information bit vector
Figure BDA0002989304290000045
Apc，A，Ac。
Secondly, initializing CSR, wherein all values are 0, initializing j is 1, and j is an information bit index.
Recording i as the operation times of the CSR, and operating the CSR, namely assigning the value of the first bit of the register to the fifth bit, the value of the second bit to the first bit, the value of the third bit to the second bit, the value of the fourth bit to the third bit, and the value of the fifth bit to the fourth bit; if i ∈ A and
Figure BDA0002989304290000046
then u will bej(ujRepresenting a vector
Figure BDA0002989304290000047
J) and the value of the first bit in the CSR, and saves the result in the first bit CSR, and performs j ∈ j +1 if i ∈ a and j ∈ apcThen the value of the first bit CSR is assigned to ujAnd j is executed as j + 1.
Executing step (c) until i is equal to N.
Output data
Figure BDA0002989304290000048
Will be provided with
Figure BDA0002989304290000049
Feeding into a CRC encoder to obtain
Figure BDA00029893042900000410
Where m is the number of bits of the CRC code. Finally will be
Figure BDA00029893042900000411
Sent to a polar code encoder to obtain
Figure BDA0002989304290000051
An encoding algorithm for the CRC code and the PC code jointly assisted polarization code is summarized as follows:
inputting data N, K, f and m;
secondly, confirming the reliability of all channels according to the formula (3) and sequencing.
Selecting the most reliable K + f + m channels, and selecting the m channel indexes with the largest indexes as a set A of CRC codescrc。
Determining PC bit set A according to the algorithm selected by the PC bit number and the positionpc。
Randomly generating information bit vector
Figure BDA0002989304290000052
Sixth, algorithm pair is constructed according to PC bit function
Figure BDA0002989304290000053
Is coded to obtain
Figure BDA0002989304290000054
Seventhly, in CRC precoder
Figure BDA0002989304290000055
Coding to obtain
Figure BDA0002989304290000056
Will
Figure BDA0002989304290000057
Sent to a polar code encoder to obtain
Figure BDA0002989304290000058
Ninthly output data
Figure BDA0002989304290000059
(2) The determination of the number of two check codes is described with reference to fig. 3, which is as follows:
because two kinds of check bits are redundant for information bits, the more the number of check bits is, the better the provided error correction performance is, and the greater the redundancy is, the lower the error correction performance is, so there is a trade-off between redundancy and the number of check bits, and it is necessary to find a proper number of check bits, so that the error correction performance of the polar code is improved as much as possible.
Because two check codes are adopted, the bit quantity of the two check codes is selected by adopting a control variable method. As shown in fig. 3, when the length of the polar code is 512, R is 1/2, and the SNR is 3.2dB, the performance of the CRC error correction performance is better for the three CRC bit numbers 6, 8, and 10 with different PC code bit numbers. The simulation conditions adopted by the invention are as follows: binary phase shift keying modulation, an additive white gaussian noise channel, SCL decoding, a list width L of 16, and when the number of CRC codes is 6, 8, and 10, the selected generator polynomial is: g (x) ═6x+5x+4x+、g(x)＝x8+x7+x6+x5+x4+x3+1 and g (x) x10+x9+x8+x7+x4+x2+1。
As can be seen from fig. 3, when the CRC code bit numbers are 6, 8, and 10, the performance is optimal when the PC code bit numbers are 6, and 7, respectively, so the check code bit numbers of the three combinations are selected: 1. m is 6 and f is 6, 2, m is 8 and f is 6, 3, m is 10 and f is 7.
(3) The structure diagram of four polarization codes is explained with reference to fig. 4:
wherein the CRC-polar code is a CRC code auxiliary polar code structure proposed by the document [1] "ZHANG Q, LIU A, PAN X, et al.CRC code design for list decoding of polar codes [ J ]. IEEE Communication Letters,2017,21(6):1229 + 1232", the PC-polar code is a PC code auxiliary polar code structure proposed by the document [2] "ZHANG H, LI R, WANG J, et al.Party-check polar code for 5G and beyond [ C ]//2018IEEE International Conference Communication, Kansas City, MO: IEEE,2018: 1-7." PC code auxiliary polar code structure proposed by the document [3] "Liqiong, Aronia, thinking cleaner, and continuous coding code based on Segmented redundancy cycle J." and adaptive decoding of continuous coding codes [ J ]. sub.1578, the Segmented CRC-polar code structure proposed by the document [3] "JL.," JO.J.: 1578, 1578 auxiliary polar code structure, the CRC-PC-polar code is a common auxiliary polar code structure of the CRC and PC codes provided by the invention.
(4) The advantages of the proposed coding method are described with reference to fig. 5, 6, 7, and 8, which are as follows:
as shown in fig. 5, the CRC-PC-polar code proposed herein has m-6, f-6, and Block Error Rate (BLER) of 10-5When compared with document [1]]Proposed CRC-polar code, document [2]]Proposed PC-polar code and literature [3]The proposed Segmented-CRC-polar codes have net gains of about 0.2dB, 0.3dB, and 0.4dB, respectively.
As can be seen from fig. 6, the CRC-PC-polar code proposed herein has m-8, f-6, BLER-10-5When compared with document [1]]Proposed CRC-polar code, document [2]]Proposed PC-polar code and literature [3]The proposed Segmented-CRC-polar codes have net gains of about 0.1dB, 0.4dB, 0.2dB, respectively.
As can be seen from fig. 7, the CRC-PC-polar code proposed herein has m-10, f-7, BLER-10-6When compared with document [1]]Proposed CRC-polar code, document [2]]Proposed PC-polar code and literature [3]The proposed Segmented-CRC-polar codes have net gains of about 0.2dB, 0.4dB, and 0.3dB, respectively.
Comparing the performance of the three polar codes presented herein results in figure 8. As shown in FIG. 8, both CRC-PC-polar (CRC8, PC6) and CRC-PC-polar (CRC10, PC7) codes can achieve a BLER of 10 at an SNR of about 3.1dB-6And the CRC-PC-polar (CRC8, PC6) code has better performance in a low signal-to-noise ratio region, so the comprehensive performance of the CRC-PC-polar (CRC8, PC6) code is optimal in the three proposed polar code structures.

Claims (3)

1. A coding method of a common auxiliary polarization code of a CRC code and a PC code is characterized in that: aiming at the problem that error detection efficiency is low and error correction performance is poor in Parity Check (PC) code assisted polarization codes (PC-polar codes for short), Cyclic Redundancy Check (CRC) codes with high error detection efficiency are added, Check functions of the PC codes are designed by combining with five-bit Cyclic Shift Registers (CSRs), and distance spectrums of the polarization codes are optimized, so that the improvement of the error correction performance of the polarization codes constructed by the provided coding method is facilitated.
2. The coding method of the jointly auxiliary polarization code of the CRC code and the PC code according to claim 1, comprising the following steps:
the method comprises the following steps: and estimating the reliability of the channel. Selecting a code length N and a code rate R of a polarization code to be designed, estimating the reliability of each channel by using a polarization weight channel estimation method, wherein the higher the polarization weight value is, the more reliable the channel is, and sequencing all channels according to the channel reliability.
Step two: a non-frozen bit channel is determined. Selecting front K + f + m reliable channels as non-frozen bit channels, wherein K is the number of information bits, f is the number of PC bits, and m is the number of CRC bits; the remaining N-K-f-m serves as a channel for transmitting the frozen bits.
Step three: a set of acknowledgement information bits, PC bits, and CRC bits. Firstly, selecting m channels with the largest indexes from non-frozen bit channels as channels of CRC bits; then determining Minimum Hamming Weight (MHW) and a second Minimum Hamming Weight set of the non-frozen bit channels, and selecting f channels from the two sets as the channels of the PC bit set; the last remaining channel transmits a set of information bits.
Step four: the check function of the PC bits is constructed using CSR. Firstly, the core idea of the five-bit CSR is to divide the non-frozen bit channel into 5 parts, wherein the value of the 1 st bit is set in the 1 st bit CSR, the value of the 2 nd bit is set in the 2 nd bit CSR, the value of the 3 rd bit is set in the 3 rd bit CSR, and so on (the value of the 6 th bit is set in the 1 st bit CSR); secondly, performing modulo two addition on the bit value in the same CSR and storing the bit value in the CSR; and finally, constructing an odd check function for the value in the CSR by utilizing the PC bit.
Step five: and performing CRC coding. And placing the code word sequence constructed by the PC function into a CRC encoder to obtain a CRC code with m bits, and placing the CRC code with m bits into the code word sequence constructed by the PC function to obtain a code word sequence with the length of K + f + m.
Step six: and (5) encoding the polarization code. Putting the code word sequence with the length of K + f + m into a polarization code encoder to obtain a polarization code sequence c1 N。
3. The coding method of the co-aided polarization code of the CRC code and the PC code according to claim 2, wherein the specific method for selecting the PC bits in the third step is:
if the number of bits in the MHW set is greater than f, the least reliable f channels are selected as the PC bit set ApcIf the number of bits in the MHW set is less than f, all channels in the MHW set are selected, and the remaining channels are selected from the least reliable channels in the secondary MHW set.
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Application publication date: 20210702