CN114448448A - Polarization code encoding and decoding method based on CA-SCL - Google Patents
Polarization code encoding and decoding method based on CA-SCL Download PDFInfo
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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
- H03M13/13—Linear codes
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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
- H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Abstract
The invention belongs to the technical field of wireless communication, and particularly relates to a polarization code coding and decoding method based on CA-SCL. The method adopts a segmentation mode of front density and back sparse, so that parity check can be performed earlier and more intensively in the early stage of decoding, and an erroneous decoding path is terminated earlier according to a check result, so that subsequent unnecessary calculation is reduced, and the time complexity and the space complexity of decoding are reduced.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a polarization code coding and decoding method based on CA-SCL.
Background
The polarization code is an error correcting code based on the channel polarization phenomenon, and the basic idea is that based on the sub-channels with different reliabilities generated by the channel polarization phenomenon, the sub-channels with high reliability are used for transmitting information bits, and the sub-channels with low reliability are transmitted to realize error-free transmission according to the frozen bits appointed by the transmitter and the receiver in advance; unlike Low Density Parity Check (LDPC) codes and Turbo codes: the LDPC and Turbo codes are only found to approach the Shannon limit through experiments, and cannot theoretically prove that the LDPC and Turbo codes can reach the Shannon limit; while the polar code is the first error correcting code that theoretically proves to be able to reach the shannon limit.
Existing decoding methods can be mainly classified into the following categories: one is SC decoding and various improving methods including SCL decoding, and the like, and the decoding method of the type is difficult to find a good balance between low complexity and low error rate; still another method is Belief Propagation (BP) decoding, which increases the decoding speed and reduces the decoding delay due to its highly parallelized structure, but is unsatisfactory in performance because of the existence of a large number of short defects in the Tanner graph of the polarization code.
Disclosure of Invention
The invention aims to provide a coding and decoding method which is improved and optimizes a polar code decoding method on the basis of a CA-SCL decoding method.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a polarization code coding and decoding method based on CA-SCL comprises the following steps:
step 1: obtaining a bit sequence to be coded, and carrying out coding on a bit sequence u to be coded with the length of k bits1Segmenting according to a mode of front density and back density to obtain m subsections, and storing the m subsections into a newly built storage space of a storage;
step 2: calling m subsections stored in a memory, and carrying out parity check coding on the m subsections;
and step 3: combining the m sub-segments after the parity check coding in the step 2 to obtain a bit sequence u with the length of k + m bits2；
And 4, step 4: for bit sequence u2Performing CRC coding to obtain a bit sequence u3(ii) a Since parity checks can only detect odd-bit errors, local parity checks do not guarantee verificationThe verified result is correct, so that the probability of detecting an error sequence can be further improved by performing overall CRC check on the whole decoding sequence on the basis of the local parity check, and the decoding accuracy is improved.
And 5: for bit sequence u3Polarization coding is carried out to obtain code words c to be sent1；
Step 6: code word c generated after coding1Transmitting through a channel;
and 7: decoding the information output by the channel by using a CA-SCL decoding method;
and 8: combining the segmentation mode in the step 1, performing parity check on each decoding path of CA-SCL decoding when information bits of one sub-segment are decoded; if the parity check is satisfied, the decoding path is reserved; if not, directly removing the path from the decoding list;
and step 9: after completing the parity check of all sub-segment information bits through step 8, performing CRC check on the paths in the decoding list, and selecting the path which meets the CRC check and has the minimum path metric value as a decoding result to be output.
Before the polar code coding is carried out, the information bit sequence is segmented by adopting a segmentation mode of front density and back sparse, a parity check bit is added at the tail end of each end, the segments added with the parity check bits are combined in sequence, and then the combined sequence is subjected to CRC (cyclic redundancy check) coding. When decoding, decoding is performed by adopting the decoding idea of SCL. According to the invention, through a segmentation mode of front secret and rear sparse, once parity check is carried out when one section of information bit decoding is completed, if the check is not passed, the decoding path is directly abandoned, and if the check is passed, the subsequent decoding step is normally carried out; and finally, when all the information bits are decoded, performing CRC (cyclic redundancy check) on the whole information sequence obtained by decoding, selecting a decoding path which can pass the CRC and has the minimum PM (particulate matter) value from a decoding list as a decoding result and outputting the decoding result.
Due to the polarization characteristics of the channel, the sub-channels with better channel quality in the polarization channel are mainly distributed in the later part of the whole, and even if the channel with poor channel quality is used for sending the frozen bit, the sub-channels for sending the information bit still have relatively poor channels and are mainly distributed in the earlier part of the whole. Therefore, the method adopts a segmentation mode of front-dense and back-sparse, parity check can be carried out earlier and more intensively in the early stage of decoding (the front part of decoding is in the early stage of decoding, errors are easier to make, the parity check can only detect the error of an odd digit, the more intensive check can improve the probability of detecting an error sequence), and the decoding path of the error is terminated earlier according to the check result, so that subsequent unnecessary calculation is reduced, and the time complexity and the space complexity of decoding are reduced.
Preferably, the front dense and rear sparse segmentation mode is as follows: bit sequence u of length k bits1After segmentation, the segment length of the front portion is smaller than the segment length of the rear portion. The front part and the rear part are as follows: the segment is a bit sequence u with the length of k bits1The front part is a front part, and the rear part is a rear part.
The present application deals with k-bit sequences u1The front section adopts a segmentation mode of small segment length, more segments, large segment length and less segments in the rear section, so that parity check is performed earlier and more intensively in the early stage of decoding, and an error decoding path is terminated earlier according to a check result, thereby reducing subsequent unnecessary calculation and reducing the time complexity and space complexity of decoding.
Preferably, in step 8, when the information bits of a sub-segment are decoded, the parity check is performed on the information bits of the sub-segment immediately.
After each sub-section information bit is judged, parity check is immediately carried out on the sub-section information bit, so that the decoding path for detecting errors can be terminated in advance, the downward expansion of the error path is terminated, unnecessary decoding calculation is reduced, and the time complexity and the space complexity of decoding are further reduced.
Preferably, in step 2, after parity-check coding is performed on m sub-segments, m check bits are added at the ends of the m information sequence sub-segments.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
due to the polarization characteristics of the channels, the channels with better channel quality in the polarization channels are mainly distributed in the later part of the whole, and even if the channels with poor channel quality are used for sending the frozen bits, the channels for sending the information bits still have relatively poor channels and are mainly distributed in the earlier part of the whole. Therefore, the method adopts a segmentation mode of front-dense and back-sparse, parity check can be carried out earlier and more intensively in the early stage of decoding (the front part of decoding is easier to make mistakes in the early stage of decoding, the parity check can only detect the error of an odd digit, the more intensive check can improve the probability of detecting an error sequence), and the decoding path of the error is terminated earlier according to the check result, so that the subsequent unnecessary calculation is reduced, and the time complexity and the space complexity of decoding are reduced. Meanwhile, the parity check coding is adopted locally, the CRC check coding is adopted integrally, and the local check is carried out firstly and then the integral check is carried out during decoding, so that the probability of detecting an error sequence is further improved, and the decoding accuracy is improved.
Drawings
The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
fig. 1 is a schematic diagram of a parity check code and a CRC check code adding method according to the present invention.
Fig. 2 is a flow chart of a polar code decoding method according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of embodiments of the present application, generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.
The following describes an embodiment of the present invention in detail with reference to fig. 1 and 2;
a polarization code coding and decoding method based on CA-SCL comprises the following steps:
step 1: obtaining a bit sequence to be coded, and carrying out coding on a bit sequence u with the length of k bits to be coded1Segmenting according to a mode of front density and back density to obtain m subsections, and storing the m subsections into a newly built storage space of a storage; the front dense and rear sparse segmentation mode comprises the following steps: bit sequence u of length k bits1After segmentation, the segment length of the front segment portion is smaller than the segment length of the rear segment portion. The application is directed to a bit sequence u with a segment length of k bits1The front section adopts a segmentation mode of small segment length, more segments, large segment length and less segments in the rear section, so that parity check is performed earlier and more intensively in the early stage of decoding, and an error decoding path is terminated earlier according to a check result, thereby reducing subsequent unnecessary calculation and reducing the time complexity and space complexity of decoding.
Step 2: calling m subsections stored in a memory, and carrying out parity check coding on the m subsections; after parity encoding the m subsegments, m check bits are added at the end of the m information sequence subsegments.
And step 3: combining the m sub-segments after the parity check coding in the step 2 to obtain a bit sequence u with the length of k + m bits2；
And 4, step 4: for bit sequence u2Performing CRC redundancy cyclic coding to obtain a bit sequence u3(ii) a Because the parity check can only detect the error of odd number, the partial parity check can not ensure that the result after verification is correct, the whole CRC check is carried out on the whole decoding sequence, and the probability of detecting the error sequence can be further improved on the basis of the partial parity check, thereby improving the accuracy of decoding.
And 5: to pairBit sequence u3Polarization coding is carried out to obtain code words c to be sent1；
Step 6: code word c generated after coding1Transmitting through a channel;
and 7: the receiving end receives the information and decodes the information by using a CA-SCL decoding method;
and step 8: combining the segmentation mode in the step 1, performing parity check on the information bit of each subsection every time the information bit of one subsection is decoded for each decoding path of the CA-SCL decoding, and if the parity check is met, reserving the decoding path; if not, directly removing the path from the decoding list; after each sub-section information bit is judged, parity check is immediately carried out on the sub-section information bit, so that the decoding path for detecting errors can be terminated in advance, the downward expansion of the error path is terminated, unnecessary decoding calculation is reduced, and the time complexity and the space complexity of decoding are further reduced.
And step 9: after completing parity check of information bits of all subsections through step 8, performing CRC check on paths in the decoding list, and selecting the path which meets the CRC check and has the minimum path metric value as a decoding result to be output.
Before the polar code coding, the invention firstly segments the information bit sequence, adds the parity check bit at the tail end of each end, then combines the segments added with the parity check bit in sequence, and then carries out CRC check coding on the combined sequence. When decoding, decoding is performed by adopting the decoding idea of SCL. According to the invention, through a segmentation mode of front secret and back sparse, once parity check is carried out when information bits of one subsection are decoded, if the check is not passed, the decoding path is directly abandoned, and if the check is passed, the subsequent decoding step is normally carried out; and finally, when all the information bits are decoded, performing CRC (cyclic redundancy check) on the whole bit sequence obtained by decoding, selecting a decoding path which can pass the CRC and has the minimum PM (particulate matter) value from a decoding list as a decoding result and outputting the decoding result.
Due to the polarization characteristics of the channels, the channels with better channel quality in the polarization channels are mainly distributed in the later part of the whole, and even if the channels with poor channel quality are used for sending the frozen bits, the channels for sending the information bits still have relatively poor channels and are mainly distributed in the earlier part of the whole. Therefore, the method adopts a segmentation mode of front-dense and back-sparse, parity check can be carried out earlier and more intensively in the early stage of decoding (the front part of decoding is easier to make mistakes in the early stage of decoding, the parity check can only detect the error of an odd digit, the more intensive check can improve the probability of detecting an error sequence), and the decoding path of the error is terminated earlier according to the check result, so that the subsequent unnecessary calculation is reduced, and the time complexity and the space complexity of decoding are reduced.
The following description will be made by taking a polar code with a code length N of 1024 and an information bit number K of 512 as an example, in which Additive White Gaussian Noise (AWGN) channels are modulated by binary phase shift keying (bpsk):
the method of the invention is illustrated in fig. 2, and specifically comprises the following steps:
adding parity bits in segments: the original 512-bit information bit sequence is divided into 6 segments by means of front dense and rear sparse, the length of the first 4 segments is 64, the length of the rear 2 segments is 128, each segment is added with parity check bits and then combined to obtain a 518-bit information sequence
Adding a CRC check code: the present embodiment adopts a generator polynomial g (x) x4+x3CRC check code of +1, pair
CRC operation is carried out to obtain a 522-bit long bit sequence
Selecting the position of the information bit and coding the polarization code: estimating polarized sub-channels by adopting a Gaussian approximation method, and screening the first 522 sub-channels with the highest reliability for transmitting 522 bits
The remaining 502 subchannels are used to transmit the frozen bits, thereby constructing an input sequence 1024 bits long
Finally will be
Multiplying the generated matrix of the polarization code to obtain the sequence after the polarization code coding
Decoding the received signal:
after transmission through AWGN channel, becomes the receiving sequence of receiving end
Let the size of the decoding list at the decoding end be L-4, and adopt SCL decoding method to
Performing decoding when
When the (i.e. parity check bit) is decoded, the parity check is performed on the current alternative decoding path, and if the parity check does not pass, the path is directly discarded. After all bits are decoded, performing CRC check on all the alternative paths in the decoding list, and selecting the path with the minimum PM value from the alternative paths passing the check as a final decoding result to be output.
On the basis of CA-SCL decoding, the invention achieves the purpose of terminating the error decoding path in advance by adding parity check bits in a segmented manner, thereby realizing the reduction of decoding time delay.
The above embodiments only express specific embodiments of the present application, and the description is specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for those skilled in the art, without departing from the technical idea of the present application, several changes and modifications can be made, which are all within the protection scope of the present application.
Claims (4)
1. A polarization code coding and decoding method based on CA-SCL is characterized by comprising the following steps:
step 1: obtaining a bit sequence to be coded, and carrying out coding on a bit sequence u to be coded with the length of k bits1Segmenting according to a mode of front density and back density to obtain m subsections, and storing the m subsections into a newly built storage space of a storage;
step 2: calling m subsections stored in a memory, and carrying out parity check coding on the m subsections;
and step 3: combining the m sub-segments after the parity check coding in the step 2 to obtain a bit sequence u with the length of k + m bits2；
And 4, step 4: for bit sequence u2Performing CRC coding to obtain a bit sequence u3；
And 5: for bit sequence u3Polarization coding is carried out to obtain code words c to be sent1；
Step 6: code word c generated after coding1Transmitting through a channel;
and 7: decoding the information output by the channel by using a CA-SCL decoding method;
and 8: combining the segmentation mode in the step 1, performing parity check on each decoding path of CA-SCL decoding when information bits of one sub-segment are decoded; if the parity check is satisfied, the decoding path is reserved; if not, directly removing the path from the decoding list;
and step 9: after the parity check of the information bits of all the subsections is completed through the step 8, the CRC check is carried out on the paths in the decoding list, and the path which meets the CRC check and has the minimum path metric value is selected as the decoding result to be output.
2. The CA-SCL-based polar code coding method according to claim 1, wherein the preceding-dense-and-following-sparse segmentation manner is: bit sequence u of length k bits1After segmentation, the segment length of the front portion is smaller than the segment length of the rear portion.
3. The CA-SCL-based polar code encoding and decoding method according to claim 1, wherein in step 8, when information bits of a sub-segment are decoded, parity check is immediately performed on the information bits of the sub-segment, and when list decoding pruning is performed at the position, the size of the path selection value is not judged, and pruning is performed directly according to the result of the parity check.
4. The CA-SCL-based polar code encoding and decoding method according to claim 1, wherein in step 2, when parity-check coding is performed on m sub-segments, m parity check bits are added at the end of m information sequence sub-segments, respectively.
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