CN114448448B - CA-SCL-based polarization code encoding and decoding method - Google Patents
CA-SCL-based polarization code encoding and decoding method Download PDFInfo
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- 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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- 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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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 with front and rear dense and sparse, so that parity check can be carried out more densely at the early stage of decoding, and the error decoding path is terminated more early according to the check result, thereby reducing subsequent unnecessary calculation and reducing the time complexity and the space complexity of decoding.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a polarization code encoding and decoding method based on CA-SCL.
Background
The polarization code is an error correction code based on the channel polarization phenomenon, the basic idea is to transmit information bits by using sub-channels with high reliability based on sub-channels with different reliability generated by the channel polarization phenomenon, and the sub-channel transmission with low reliability realizes error-free transmission according to frozen bits agreed in advance by the transceiver; unlike low density parity check (Low Density Parity Check, LDPC) codes and Turbo codes are: LDPC and Turbo codes only find that they approach shannon limit through experiments, and cannot prove that they can reach shannon limit in theory; and the polarization code is the first error correction code that has theoretically been demonstrated to reach the shannon limit.
The existing decoding methods can be mainly divided into the following categories: one is SC decoding and its various improved methods including SCL decoding, which are difficult to find a good balance between low complexity and low bit error rate; the other is a belief propagation (Belief Propagation, BP) decoding method, which accelerates the decoding speed and reduces the decoding delay due to its highly parallelized structure, but is unsatisfactory in performance due to the large number of short breaks in the Tanner graph of the polar code.
Disclosure of Invention
The invention aims to provide a coding and decoding method for improving the CA-SCL decoding method and optimizing the polarization code decoding method.
In order to solve the technical problems, the invention adopts the following technical scheme:
a polarization code encoding and decoding method based on CA-SCL comprises the following steps:
step 1: acquiring a bit sequence to be encoded, and for a bit sequence u to be encoded with a length of k bits 1 Segmenting according to a front-secret and rear-sparse mode to obtain m subsections, and storing the m subsections into a newly built storage space of a memory;
step 2: calling m sub-segments stored in a memory, and performing parity check coding on the m sub-segments;
step 3: merging the m sub-segments subjected to parity check coding in the step 2 to obtain a bit sequence u with the length of k+m bits 2 ；
Step 4: for bit sequence u 2 CRC encoding is performed to obtain a bit sequence u 3 The method comprises the steps of carrying out a first treatment on the surface of the Since the parity check can only detect the error of the odd bit, the local parity check cannot ensure that the verified result is correct, and therefore, on the basis of the local parity check, the whole CRC check is performed on the whole decoding sequence, the probability of detecting the error sequence can be further improved, and the decoding accuracy is improved.
Step 5: for bit sequence u 3 Performing polarization coding to obtain codeword c to be transmitted 1 ；
Step 6: codeword c generated after encoding 1 Transmitting through a channel;
step 7: decoding the information output by the channel by using a CA-SCL decoding method;
step 8: combining the segmentation mode in the step 1, performing parity check on each decoding path of CA-SCL decoding after decoding information bits of one sub-segment; if the parity check is satisfied, reserving the decoding path; if not, the path is directly removed from the decoding list;
step 9: and 8, after the parity check of all sub-segment information bits is finished, performing CRC check on paths in the decoding list, and selecting a path which meets the CRC check and has the minimum path metric value as a decoding result to be output.
Before coding the polarization code, the invention firstly segments the information bit sequence by adopting a front-secret and rear-sparse segmentation mode, adds a parity check bit at the tail end of each end, sequentially combines the segments added with the parity check bit, and then carries out CRC (cyclic redundancy check) coding on the combined sequence. In decoding, the SCL decoding concept is adopted for decoding. The invention carries out parity check once every time a section of information bits are decoded by a segmentation mode of front encryption and rear decryption, if the parity check is not passed, the decoding path is directly abandoned, and if the parity check is passed, the subsequent decoding step is normally carried out; and finally, when the decoding of all the information bits is completed, CRC checking is carried out on the whole information sequence obtained by decoding, and a decoding path which can pass the CRC checking and has the minimum PM value is selected from a decoding list to be used as a decoding result and output.
Due to the characteristics of channel polarization, sub-channels of a polarized channel with better channel quality are mainly distributed in the rear part of the whole, and even if channels with poor channel quality are used for transmitting frozen bits, relatively worse channels still exist in sub-channels for transmitting information bits and are mainly distributed in the front part of the whole. Therefore, the method adopts a segmentation mode with front and rear sparse, so that parity check can be carried out more densely at the front stage of decoding (the front stage of decoding is the front part of decoding, errors are more prone to occur, the parity check can only detect errors of odd digits, the denser check can improve the probability of error sequences being detected), and the decoding path of errors is terminated more early according to the checking result, thereby reducing subsequent unnecessary calculation and reducing the time complexity and the space complexity of decoding.
Preferably, the front-close and rear-open segmentation mode is as follows: bit sequence u of length k bits 1 After segmentation, the front part has a segment length smaller thanThe section of the rear portion is long. The front and rear portions are: bit sequence u with the segment being k bits long 1 The two sections are divided, wherein one section positioned at the front is a front part, and the other section positioned at the rear is a rear part.
The present application is directed to k-bit sequences u 1 The front section of the decoder adopts a segmentation mode with small section length, more sections and less sections, so that the parity check is carried out more densely and earlier in the earlier stage of decoding, and the wrong decoding path is terminated more quickly according to the checking result, thereby reducing the subsequent unnecessary calculation and reducing the time complexity and the space complexity of decoding.
Preferably, in the step 8, when the information bit of one sub-segment is decoded, the parity check is performed on the information bit of the sub-segment immediately.
After each sub-segment information bit is judged, parity check is immediately carried out on the sub-segment information bit, so that the error decoding path 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 the step 2, after parity encoding is performed on the m sub-segments, m check bits are added to the end of the m information sequence sub-segments.
In summary, due to the adoption of the technical scheme, the beneficial effects of the invention are as follows:
because of the characteristics of channel polarization, channels with better channel quality in polarized channels are mainly distributed in the rear part of the whole, and even if channels with poor channel quality are used for transmitting frozen bits, relatively worse channels still exist in channels for transmitting information bits and are mainly distributed in the front part of the whole. Therefore, the method adopts a segmentation mode with front and rear sparse, so that parity check can be carried out more densely at the front stage of decoding (the front part of decoding is more prone to error at the front stage of decoding, the parity check can only detect errors of odd digits, the denser check can improve the probability of detecting error sequences), and the decoding path of the errors is terminated more early according to the checking result, thereby reducing subsequent unnecessary calculation and reducing the time complexity and the space complexity of decoding. Meanwhile, as parity check coding is adopted locally and CRC check coding is adopted wholly, partial check is performed firstly and then the whole check is performed during decoding, the probability of detecting the error sequence is further improved, and the accuracy of decoding is improved.
Drawings
The invention will now be described by way of example and with reference to the accompanying drawings in which:
fig. 1 is a schematic diagram of the addition of parity check codes and CRC check codes according to the present invention.
Fig. 2 is a flow chart of a polar code decoding method according to the present invention.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, 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 apparent that the described embodiments are only some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, which are 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, as provided in the accompanying drawings, is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present application without making any inventive effort, are intended to be within the scope of the present application.
Embodiments of the present invention are described in detail below with reference to fig. 1 and 2;
a polarization code encoding and decoding method based on CA-SCL comprises the following steps:
step 1: acquiring a bit sequence to be encoded, and for a bit sequence u to be encoded with a length of k bits 1 Segmenting according to a front-secret and rear-sparse mode to obtain m subsections, and storing the m subsections into a newly built storage space of a memory; the front-dense and rear-sparse segmentation mode is as follows: bit sequence u of length k bits 1 After the segmentation, the processing unit is used for processing the data,the front section has a smaller section length than the rear section. The present application is directed to a bit sequence u with a segment length of k bits 1 The front section of the decoder adopts a segmentation mode with small section length, more sections and less sections, so that the parity check is carried out more densely and earlier in the earlier stage of decoding, and the wrong decoding path is terminated more quickly according to the checking result, thereby reducing the subsequent unnecessary calculation and reducing the time complexity and the space complexity of decoding.
Step 2: calling m sub-segments stored in a memory, and performing parity check coding on the m sub-segments; after parity encoding the m sub-segments, m check bits are added at the end of the m information sequence sub-segments.
Step 3: merging the m sub-segments subjected to parity check coding in the step 2 to obtain a bit sequence u with the length of k+m bits 2 ；
Step 4: for bit sequence u 2 Performing CRC redundancy cyclic coding to obtain a bit sequence u 3 The method comprises the steps of carrying out a first treatment on the surface of the Because the parity check can only detect the error of the odd bit, the local parity check cannot ensure that the verified result is correct, and the whole CRC check is carried out on the whole decoding sequence, the probability of detecting the error sequence can be further improved on the basis of the local parity check, thereby improving the decoding accuracy.
Step 5: for bit sequence u 3 Performing polarization coding to obtain codeword c to be transmitted 1 ；
Step 6: codeword c generated after encoding 1 Transmitting through a channel;
step 7: the receiving end receives the information and decodes the information by using a CA-SCL decoding method;
step 8: combining the segmentation mode in the step 1, immediately carrying out parity check on the information bits of one sub-segment after decoding each decoding path of CA-SCL decoding and decoding the information bits of the sub-segment, and if the parity check is met, reserving the decoding path; if not, the path is directly removed from the decoding list; after each sub-segment information bit is judged, parity check is immediately carried out on the sub-segment information bit, so that the error decoding path 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.
Step 9: and 8, after the parity check of the information bits of all the subsections is finished, CRC check is carried out on paths in the decoding list, and paths which meet the CRC check and have the minimum path metric value are selected to be output as decoding results.
Before coding the polarization code, the invention segments the information bit sequence, adds the parity check bit at the end of each end, combines each segment added with the parity check bit in sequence, and then carries out CRC check coding on the combined sequence. In decoding, the SCL decoding concept is adopted for decoding. The invention carries out parity check once every time an information bit of a sub-segment is decoded by a segmentation mode of front encryption and rear decryption, if the parity check is not passed, the decoding path is directly abandoned, and if the parity check is passed, the subsequent decoding step is normally carried out; and finally, when the decoding of all the information bits is completed, CRC checking is carried out on the whole bit sequence obtained by decoding, and a decoding path which can pass the CRC checking and has the minimum PM value is selected from a decoding list to be used as a decoding result and output.
Because of the characteristics of channel polarization, channels with better channel quality in polarized channels are mainly distributed in the rear part of the whole, and even if channels with poor channel quality are used for transmitting frozen bits, relatively worse channels still exist in channels for transmitting information bits and are mainly distributed in the front part of the whole. Therefore, the method adopts a segmentation mode with front and rear sparse, so that parity check can be carried out more densely at the front stage of decoding (the front part of decoding is more prone to error at the front stage of decoding, the parity check can only detect errors of odd digits, the denser check can improve the probability of detecting error sequences), and the decoding path of the errors is terminated more early according to the checking result, thereby reducing subsequent unnecessary calculation and reducing the time complexity and the space complexity of decoding.
The following description uses a polarization code with a code length of n=1024 and an information bit number of k=512 for example, where binary phase shift keying modulation is used in an additive white gaussian noise (Additive White Gaussian Noise, AWGN) channel:
the method of the invention is as shown in fig. 2, and is specifically as follows:
segmentation adds parity bits: dividing the original 512-bit information bit sequence into 6 sections by adopting a front-secret and rear-sparse mode, wherein the length of the first 4 sections is 64, the length of the second 2 sections is 128, adding parity check bits to each section, and merging to obtain an information sequence with 518 bits
Adding a CRC check code: the present embodiment uses a generator polynomial of G (x) =x 4 +x 3 +1 CRC check code pairPerforming CRC operation to obtain 522 bit sequence +.>
Selecting the position of the information bit and carrying out polarization code coding: estimating polarized sub-channel by Gaussian approximation, screening out 522 first sub-channels with highest reliability for transmitting 522 bitsThe remaining 502 sub-channels are used for transmitting frozen bits, thereby constructing an input sequence 1024 bits long>Finally will->Multiplying the generated matrix of the polarization code to obtain the sequence after the encoding of the polarization code +.>
For received signalsDecoding:after transmission through AWGN channel, it becomes a receiving sequence of receiving endLet the decoding list of decoding end be l=4, use SCL decoding method to do +.>Decoding when When decoded (i.e., parity bits), the current alternate decoding path is parity checked, and if the check fails, the path is discarded directly. After all bits are decoded, CRC check is carried out on all alternative paths in the decoding list once, and the path with the minimum PM value is selected from the checked alternative paths to be output as a final decoding result.
The invention achieves the purpose of stopping the error decoding path in advance by adding the parity check bit in a segmentation way on the basis of CA-SCL decoding, thereby realizing the reduction of decoding delay.
The foregoing examples merely represent specific embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the present application. It should be noted that, for those skilled in the art, several variations and modifications can be made without departing from the technical solution of the present application, which fall within the protection scope of the present application.
Claims (2)
1. A polarization code encoding and decoding method based on CA-SCL is characterized by comprising the following steps:
step 1: acquiring bit sequences to be encodedA column of length ofkBit sequence of bits to be encodedSegmenting according to a front dense and rear sparse mode to obtainmSub-segment and willmThe sub-segments are stored in a newly built storage space of the memory;
step 2: calling stored in memorymSub-segment pairmParity check coding is carried out on each sub-segment;
step 3: merging the parity check codes in the step 2mSub-segments of lengthk+mBit sequence of bits；
Step 4: for bit sequencesPerforming CRC encoding to obtain bit sequence +.>；
Step 5: for bit sequencesPerforming polarization coding to obtain code word +.>；
Step 6: codeword generated after encodingTransmitting through a channel;
step 7: decoding the information output by the channel by using a CA-SCL decoding method;
step 8: combining the segmentation mode in the step 1, performing parity check on each decoding path of CA-SCL decoding after decoding information bits of one sub-segment; if the parity check is satisfied, reserving the decoding path; if not, the path is directly removed from the decoding list;
step 9: after the information bit parity check of all the subsections is finished through the step 8, CRC check is carried out on paths in the decoding list, and paths which meet the CRC check and have the minimum path metric value are selected to be output as decoding results;
the front-dense and rear-sparse segmentation mode is as follows: length ofkBit sequence of bitsAfter segmentation, the segment length of the front part is smaller than that of the rear part;
in the step 2, formWhen each sub-segment is subjected to parity check coding, the sub-segment is subjected to parity check codingmThe check bits of the parity check are respectively added tomThe end of the information sequence sub-segment.
2. The method of claim 1, wherein in step 8, when each sub-segment information bit is decoded, parity check is immediately performed on the sub-segment information bit, and when the list decoding pruning is performed there, the pruning is performed directly according to the parity check result without determining the size of the path selection value.
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