CN114285418A - Improved decoding method for polarization code EPC-MS-SCL - Google Patents
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Abstract
The invention particularly relates to an improved polar code EPC-MS-SCL decoding method based on an enhanced parity check code. The invention belongs to the technical field of channel coding, and the method comprises the steps of carrying out segmentation processing on an information sequence in a polar code coding stage, adding an enhanced parity check code at the tail end of each segment, carrying out path splitting on a decoder only when elements in a Search Set (SS) are decoded, directly carrying out hard decision decoding on the other elements, immediately checking a segment after decoding the segment, only reserving a path passing the checking, reducing the competition of an error path to a correct path, increasing the probability of reserving the correct path to the end of decoding, and simultaneously reducing the number of decoding lists so as to lower the complexity of decoding. Simulation results show that the improved method for decoding the polarization code EPC-MS-SCL has obvious decoding performance improvement and reduces decoding complexity compared with a method for decoding a path splitting strategy-based auxiliary polarization code serial offset list (PSS-SS-SCL).
Description
Technical Field
The invention belongs to the technical field of channel coding, and relates to an improvement of a PSS-SS-SCL (Power switching sharing selection based on Search Set under the successful Cancellation List) decoding method of polarization codes in channel coding. The method is mainly based on the principle of an enhanced parity check code and a polar code Serial Cancellation List (SCL) decoding method to improve the PSS-SS-SCL decoding method.
Background
The polar code proposed by Arikan is a first kind of code word that can be proven to achieve the channel capacity of binary input memoryless symmetric channels, and is an important technology of a new generation of mobile communication systems. The polar code has successfully selected into the 5G standard, becomes a coding scheme of a control channel in a 5G enhanced mobile broadband scene, and is a research hotspot in the current channel coding field. In addition to the channel capacity reachable property, the polar code has the outstanding advantage that no error floor exists under the serial cancellation decoding algorithm. However, in the case of a code length limited, the Block Error Rate (Block Error Rate BLER) performance of the actual SC decoding algorithm is far worse than that of the Turbo code and the LDPC code due to incomplete channel polarization.
Therefore, researchers have proposed a Sequential Cancellation List (SCL) decoding algorithm capable of retaining multiple decoding paths, and a CA-SCL (CRC Aid SCL) decoding algorithm using a CRC-Polar code concatenated with a Cyclic Redundancy Check (CRC) code. The CA-SCL decoding algorithm selects the code word which passes CRC check and has the optimal path measurement as decoding output when the decoding is finished, improves the decoding performance of the SCL, and is also the mainstream polarization code decoding scheme at present. Under the CA-SCL decoder, compared with the LDPC code with the same code length and code rate, the BLER performance of the polarization code can exceed that of the existing LDPC code. Although CA-SCL has good decoding performance, the algorithm has high decoding complexity O (LNlogN), wherein L is the number of decoder lists and N is the length of the polar code word. In order to reduce the decoding complexity of the CA-SCL, researchers have proposed corresponding improvements. Because of the obvious difference between the reliabilities of different bits of the polarization code, the splitting of all information bits is not needed, and based on the method, the scholars propose a PSS-SS-SCL decoding method based on a path splitting strategy, the method only performs the path splitting when decoding elements in a Search Set (SS), and obtains lower decoding complexity under the condition that the performance of the method is almost the same as that of a CA-SCL. However, the PSS-SS-SCL decoding method based on the path splitting strategy does not consider how to improve the decoding success rate at the split bit position, and therefore, compared with the CA-SCL, the decoding performance is not improved. Aiming at the problem, the invention adds the enhanced Parity Check code before the error-prone position, decodes one section and then immediately checks and prunes, and improves the decoding success rate of the position, thereby providing an EPC-MS-SCL (enhanced Parity Check and Monte Carlo Segment acquired successful Cancellation List) decoding algorithm which not only keeps the characteristic of low splitting times of the PSS-SS-SCL decoding method, but also obtains better decoding performance.
Disclosure of Invention
In view of the above, the present invention provides an improved method for decoding an EPC-MS-SCL. By carrying out segmentation processing on the information sequence in the polar code encoding stage, an enhanced parity check code is added at the tail end of each segment. The decoder only performs path splitting when decoding the elements in the search set, other elements directly execute hard decision decoding, after a section of sequence is decoded, the section is checked, and paths which do not pass the check are cut off, so that the competition of error paths to correct paths is reduced, the probability that the correct paths are reserved until the decoding is finished is increased, the decoding performance is improved, the number of decoding lists is reduced, and the decoding complexity is lower.
In order to achieve the purpose, the invention provides the following technical scheme:
firstly, selecting the length N of a polarization code to be designed, the number k of information bits, the number m of enhanced parity check code bits and the number w of CRC (cyclic redundancy check) codes, calculating the reliable measurement value of each channel by using a Gaussian approximation method, and obtaining a split channel position index value sequence after sequencing from high to low
And determining a set of frozen bits AcAnd a set of unfrozen bits a and a search set SS.
Then, the Monte Carlo simulation experiment is used for carrying out error rate statistics on SS set elements, and the first m elements with the highest error rate are selected to be sequentially placed and enhancedType check code completion pair information sequence
Is segmented to obtain a sequence
Will be sequenced
Performing CRC coding to obtain a sequence
Handlebar stem rethreshing sequence
Inputting the non-frozen bit set into a polar code encoder to obtain a polar code word P1 NAnd putting the code word into a channel for transmission.
And then, a corresponding decoding method is adopted at a receiving end, namely, the decoder performs path splitting only when SS set elements are decoded, immediately checks all current paths after a section of sequence is decoded, and cuts off paths which do not pass the checking.
And finally, under the same simulation environment, carrying out simulation comparative analysis on the improved decoding method of the polarization code EPC-MS-SCL, which is provided by the patent, and other decoding methods of the same type.
The invention has the beneficial effects that:
an improved method for decoding an EPC-MS-SCL is provided. In the method, firstly, the information sequence is segmented in the stage of polar code coding, then an enhanced parity check code is added at the tail of each segment, a decoder only performs path splitting when decoding elements in a search set, other elements directly perform hard decision decoding, and immediately check a segment after the decoding of the segment is finished, and only paths passing the check are reserved. So that the method has the following advantages: 1. the competition of the error path to the correct path is reduced, the probability of the correct path from the reservation to the end of decoding is increased, and the decoding performance is improved; 2. the number of decoding lists is reduced, so that the decoding complexity is lower; 3. during decoding, check can be carried out, and when no path passes the check, the subsequent unnecessary decoding operation of the decoder can be stopped.
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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 roadmap for the process of the invention;
FIG. 2 is a diagram of a binary tree with a code length of 16 for a polar code;
FIG. 3 is a diagram of an enhanced parity check code with a check sequence length of 8 and a check code length of 2;
FIG. 4 is a block diagram of a 8-bit enhanced parity check code with a length of 256 for a polarization code and a length of 128 for an information sequence, and an 8-bit CRC code;
FIG. 5 is a diagram of comparing bit error rate performance of four polar code decoding methods;
FIG. 6 shows the total number of decoded average decoding lists for different decoding methods;
FIG. 7 shows the mean split times for decoding with different decoding methods;
FIG. 8 shows the average decoding rank of different decoding methods.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
(1) With reference to fig. 1, an improved method for decoding an EPC-MS-SCL is specifically implemented as follows:
in the coding stage of the polarization code, firstly, the length N of the polarization code to be designed is determined, the reliability measurement parameter of each split channel is calculated by using a Gaussian approximation method, all split channels are sequenced from high to low according to the channel reliability, and the sequenced split channel position index value sequence is obtained
The first k + m + w split channels with the highest reliability are selected, i.e.
The split channels corresponding to the first k + m + w index values are used as a non-frozen bit set A, and the rest N-k-m-w split channels are used as a frozen bit (usually set to be 0) set AcWhere k is the number of information bits contained in a codeword, m represents the number of bits in which the enhanced parity check code is selected, and w represents the number of bits of the added CRC. Based on the non-frozen bit set A and the frozen bit set AcThereby obtaining the distribution of R1 nodes, and selecting the first element of each R1 node to obtain an SS set.
At the receiving end, the value of the received signal is first converted into a log-likelihood ratio (LLR), as shown in equation (3).
Y in formula (3)iRepresenting the received signal value, σ, of each bit2Representing the variance of the channel noise.
Each path then obtains a decision LLR for each bit by performing a corresponding f and g operation.
L≈sign(L1)sign(L2)min{|L1||L2|} (4)
L＝(1-2U1)L1+L2 (5)
Equation (4) represents f operation convenient for hardware implementation, and equation (5) represents g operation; wherein L represents the LLR of the operation output; l is1，L2LLR, U representing input operation1Representing the decoded estimate of the previous bit of the input operation.
If the current bit belongs to AcThen each path translates the bit value to 0 directly; if the current bit belongs to the SS set, each path directly executes hard decision decoding; otherwise, normal SCL decoding is performed. After a section of sequence is decoded, the information sequence of the section is checked immediately through the enhanced parity check code of the section, only a pass check path is reserved, and if no path passes the check, the decoding failure is declared. Finally, after the decoding is finished, the CRC is selected to pass the checkAnd the path of the optimal path metric value is used as a decoding output result.
(2) The selection of the search set is illustrated in connection with FIG. 2:
the polar code can be regarded as being composed of a plurality of sub-polar code blocks, wherein a sub-block only containing information bits is called a Rate-1 node, a white node in the figure is a frozen bit node, a gray node is a mixed node, a black node is an information bit node, an R1 node is { A, B, C, D, E }, and the first element of the node is taken to form an SS set { u, D, E }1,u2,u3,u5,u6}。
(3) The structure of the enhanced parity check code is explained with reference to fig. 3:
the enhanced parity check code uses a plurality of check bits, wherein one check bit is the parity check of some bits in the information sequence, and the value of the first check bit is determined by the sequence
All elements are obtained by traditional parity check coding, and the value of the second bit check bit is obtained by parity check coding of odd bits in the check sequence of the first bit check code; and for the value of the nth check bit, carrying out parity check coding on odd bits in the (n-1) th check sequence. For the analysis of the error detection capability of the enhanced parity check code, taking a two-bit parity check code as an example:
1) when the sequence is
Odd errors occur in the data, and can be detected through a first check bit;
2) when the sequence is
In which an even number of errors occur, is now divided into sequences
The odd number of errors and the even number of errors occur in the middle and even numbers respectively, and the former case can be detected through the second bit check bit.
Therefore, the two-bit enhanced parity check code can detect all odd errors and half of even errors (assuming that the probability of the error occurring in the odd bits and the even bits is the same), where the error detection capability is:
for an n-bit enhanced parity check code, the error detection capability is derived as:
(n is the number of bits of the check code).
(4) Segmenting information sequence and adding check code will be explained with reference to fig. 4
The elements in the SS set were error rate estimated by Monte Carlo simulation experiments: in decoding split set elements SiThen, if the correct path exists before decoding and S is decodediIf the correct path exists later, the decoding is recorded in SiIf S is decoded, then S is decodediIf no correct path exists, the decoding is recorded in SiAnd (4) processing failure, and finally counting to obtain the decoding failure probability of each element. Then selecting the first m bits with higher error rate (m is the total number of the enhanced parity check codes), then arranging the m bits according to the ascending order of the channel position, judging the number of the front information bits of the position by the first element, and skipping the element if no information bit exists in the front; if the number of the information bits is less than 5, 1 check bit is placed in the first section; in other cases 2 check bits are placed. Comparing the difference between the other elements and the previous element, and skipping the current element if the difference is equal to 1; if the number of the check bits is less than 5, 1 check bit is placed at the tail of the information sequence; otherwise, 2 check bits are placed at the end of the information sequence until the m check bits are placed, and then the information sequence is finished
Adding enhanced parity check codes in sections and obtaining sequences
Then the sequence is processed
Sending the data into a CRC encoder to obtain an added sequence
Will be provided with
Inputting the non-frozen bit sequence into a polar code encoder to obtain a polar code word P1 NAnd inputting the code word into a channel for transmission.
(5) The advantages of the proposed decoding method are demonstrated in conjunction with fig. 5, 6, 7, and 8, which are as follows:
the CA-SCL Decoding method is the scheme proposed in the document [1] "NIU K, CHEN K.CRC-Aided Decoding of Polar Codes [ J ]. IEEE Communications Letters,2012,16(10): 1668-;
the PSS-SS-SCL decoding method is a scheme proposed by the document [2] "GAO C, LIU R, DAI B, HAN X. Path Splitting Selecting Linear-aid subsequent decoding List Algorithm for Polar Codes [ J ]. IEEE Communications Letters,2019,23(3): 422-;
the Segment-CRC Decoding method is the scheme proposed in the document [3] "ZHOU H, ZHANG C, SONG W, Xu S, YOU X, Segmented CRC-air SC List Polar Decoding [ C ]// 201683 rd temporal Technology Conference (VTC Spring).: IEEE,2016: 1-5.";
the simulation initial condition sets the length N of the polar code to be 256, K to be 128 and the code rate
The decoding method of decoding list number L of 8, CA-SCL, PSS-SS-SCL adopts 16-bit CRC check code g16(x)＝x16+x15+x2+ 1; the segment-CRC decoding method divides the information sequence into 4 segments uniformly, and each segment adopts 4-bit CRC check code g4(x)＝x4+ x + 1; EPC-MS-SCL decoding method adopts 8-bit PC and 8-bit CRC check code g8(x)＝x8+x5+x4+1, the channel is additive white gaussian noise channel (AWGN). As shown in fig. 5, the EPC-MS-SCL decoding method provided by the present invention has improved performance compared to the other three decoding methods, wherein the BLER of the EPC-MS-SCL decoding method is 10-3Compared with the CA-SCL and PSS-SS-SCL decoding methods, the gain is improved by about 0.12dB and 0.2dB respectively; at BLER of 10-4Compared with the CA-SCL and PSS-SS-SCL decoding methods, the gain is improved by about 0.1dB and 0.22dB respectively. As can be seen from FIG. 6, the EPC-MS-SCL decoding method proposed herein has a lower average total number of primary decoding lists than the conventional CA-SCL and PSS-SS-SCL decoding methods, and is only slightly higher than the Segment-CRC decoding method. When L is 32, the EPC-MS-SCL decoding method is reduced by about 5% compared with the total number of one-time decoding lists of the traditional CA-SCL and PSS-SS-SCL decoding methods. As shown in FIG. 7, the EPC-MS-SCL and the PSS-SS-SCL have almost the same splitting times, and compared with the CA-SCL, the Segment-CRC decoding method reduces the splitting times by about 70%. The reason that the splitting times are slightly lower than the PSS-SS-SCL when the L is 2 is that the segmentation check has an early termination function, and after a certain section of decoding is finished, if no path passes the check, the subsequent decoding step is stopped. As shown in FIG. 8, the average sorting frequency of the EPC-MS-SCL decoding method is reduced by about 79% compared with the conventional CA-SCL decoding method, and is lower than the Segment-CRC and PSS-SS-SCL decoding methods, and has the least sorting frequency. In summary, compared with the PSS-SS-SCL decoding method, the EPC-MS-SCL decoding method provided by the invention not only retains the advantages of low splitting times and low sequencing times, but also obviously improves the decoding performance of the PSS-SS-SCL decoding method.
Claims (3)
1. An improved decoding method for an EPC-MS-SCL, which is characterized in that: aiming at the problem of insufficient performance of a decoding method based on a Path Splitting Strategy assisted serial Cancellation List (PSS-SS-SCL) in a polar code, an information sequence is segmented at the coding stage of the polar code, an Enhanced Parity Check code (EPC) is added at the tail end of each segment, a decoder performs Path Splitting only when decoding elements in a Search Set (Search Set, SS), other elements directly perform hard decision decoding, and immediately Check a segment after decoding the segment, and only paths passing the Check are reserved. Therefore, the competition of the error path to the correct path is reduced, the probability that the correct path is reserved until the decoding is finished is increased, the decoding performance is improved, and the number of decoding lists is reduced, so that the decoding complexity is lower.
2. The improved method of claim 1, wherein the method comprises the following steps:
the method comprises the following steps: and estimating the reliability of the channel. Selecting the code length N of the polarization code to be designed, calculating the reliability measurement parameter of each split channel by using a Gaussian approximation method, sequencing all split channels according to the channel reliability from high to low to obtain a sequenced split channel position index value sequence
Step two: determining a non-frozen bit set A, a frozen bit set AcAnd a search set SS. The first k + m + w split channels with the highest reliability are selected, i.e.
The split channels corresponding to the first k + m + w index values are used as a non-frozen bit set A, and the rest N-k-m-w split channels are used as a frozen bit (usually set to be 0) set AcWhere k is the number of information bits included in a codeword, m represents the number of bits of the selected enhanced parity Check code, and w represents the number of bits of the added Cyclic Redundancy Check (CRC). Based on the non-frozen bit set A and the frozen bit set AcAnd determines the search set SS.
Step three: and carrying out error rate statistics on elements in the SS set. Error rate estimation of elements within the SS set using Monte Carlo simulation experiments: in decoding split set elements SiThen, if the correct path exists before decoding and S is decodediIf the correct path exists later, the decoding is recorded in SiIf S is decoded, then S is decodediIf no correct path exists, the decoding is recorded in SiAnd (4) processing failure, and finally counting to obtain the decoding failure probability of each element.
Step four: for information sequence
Segmenting and adding m-bit enhanced parity check codes to obtain a segmented sequence
Step five: to the sequence
And performing CRC coding. In that
Is used for checking all the previous bits to obtain a sequence
Step six: to the sequence
And carrying out polarization code encoding. Will be sequenced
Inputting the non-frozen bits into a polar code encoder to carry out polar code encoding to obtain a polar code encoded code word P1 NThen P is added1 NThe incoming channel is transmitted.
Step seven: and (5) decoding. And decoding the received signal by adopting a corresponding EPC-MS-SCL decoder at a receiving end.
3. The method of claim 2An improved decoding method for polar code EPC-MS-SCL, wherein the information sequence is segmented and added with enhanced parity check code in the fourth step, and the corresponding EPC-MS-SCL decoder in the seventh step is specifically described as follows: (1) an enhanced parity check code. The check code uses a plurality of check bits, wherein a certain check bit is respectively the parity check of a certain bit in the information sequence. The value of the first check bit of the enhanced parity check code is obtained by carrying out traditional parity check coding on all elements of the checked sequence, and the value of the second check bit is obtained by carrying out parity check coding on odd bits in the checked sequence of the first check code; and for the value of the nth check bit, carrying out parity check coding on odd bits in the check sequence checked by the (n-1) th check code. Setting the sequence to be checked as
At this time, the ith check bit miIs obtained from the formulae (1), (2), (3), wherein [ [ alpha ] ]]Representing a floor function.
For the analysis of the error detection capability of the enhanced parity check code, taking a two-bit parity check code as an example:
1) when the sequence is
In which an odd number of errors occur, can pass through m1Detecting;
2) when the sequence is
In which an even number of errors occur, is now divided into sequences
The odd number of errors and the even number of errors occur respectively in the middle odd number and the even number of the errors respectively, and the former case can pass through m2And (6) detecting.
Therefore, the two-bit enhanced parity check code can detect all odd errors and half of even errors (assuming that the probability of the error occurring in the odd bits and the even bits is the same), where the error detection capability is:
for an n-bit enhanced parity check code, the error detection capability is derived as:
(n is the number of bits of the check code).
(2) Segmentation of the information sequence. Selecting the first m bits (m is the total number of enhanced parity check codes) with higher error rate in the SS set, then arranging the m bits according to the ascending order of the channel position, judging the number of the front information bits of the position by the first element, and skipping the element if no information bit exists in the front; if the number of the information bits is less than 5, 1 check bit is placed in the first section; in other cases 2 check bits are placed. Comparing the difference between the other elements and the previous element, and skipping the current element if the difference is equal to 1; if the number of the check bits is less than 5, 1 check bit is placed in the information sequence; otherwise, 2 check bits are placed in the information sequence until m check bits are placed, and then a segmented sequence is obtained
(3) Corresponding EPC-SS-SCL decoder. The decoder first converts a received signal into a Log Likelihood Ratio (LLR) at a receiving end, and then converts the LLR into a received signalCalculating the decision LLR of each bit, if the current bit belongs to AcThen each path translates the bit value to 0 directly; if the current bit belongs to the SS set, each path directly executes hard decision decoding; otherwise, normal SCL decoding is performed. After decoding a section of sequence, immediately checking the current sequence, only reserving the path passing the check, if no path passes the check, declaring that the decoding fails. After decoding, the decoder selects the Path that passes the CRC check and has the largest Path Metric value (PM) as the decoding output result.
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| CN117176185B (en) * | 2023-10-18 | 2024-02-09 | 苏州元脑智能科技有限公司 | Data encoding and decoding method and device based on polarization code and storage medium |
| CN117792407A (en) * | 2024-02-23 | 2024-03-29 | 南京邮电大学 | Hardware ordering system for decoding polarization code serial offset list |
| CN117792407B (en) * | 2024-02-23 | 2024-05-24 | 南京邮电大学 | Hardware ordering system for decoding polarization code serial offset list |
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