CN110278002A - Polarization code belief propagation list decoding method based on bit reversal - Google Patents
Polarization code belief propagation list decoding method based on bit reversal Download PDFInfo
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Abstract
The polarization code belief propagation list decoding method based on bit reversal that the invention discloses a kind of, the code word used are the concatenated codes that CRC code and polarization code are formed.Method in the present invention is not in the case where BPL decoding result passes through CRC check, by analyzing the decoding result in BPL interpretation method, construct flip bits set (Flip Bits Set, FBS), (bit reversal in the present invention is realized by setting infinity for the priori log-likelihood ratio for being reversed bit) is overturn to the information bit that polarization code is located in FBS, the mistake in the BPL decoder of part can be corrected, and then improves the bit error rate and frame error rate performance of BPL interpretation method.
Description
Technical Field
The invention relates to a polarization code belief propagation list decoding method based on bit flipping, and belongs to the technical field of channel coding in wireless communication.
Background
The polar code technology is a novel channel coding technology, and when the code length tends to be infinite, the transmission rate can reach the channel capacity of a binary input memoryless symmetrical channel. Currently, there are two types of decoding methods for polar codes, one type of decoding method is based on Serial Cancellation (SC), which includes a Serial Cancellation List (SCL) decoding method based on SC decoding, the SC-based polar code decoding method belongs to sequential decoding, and decoded information bits affect the estimation of subsequent information bits, so that the information bits in a codeword must be estimated one by one, thereby generating a large decoding delay. The other mainstream decoding method of the polarization code is based on a Belief Propagation (BP) decoding method, and comprises a Belief Propagation List (BPL) decoding method, and due to the property of parallel iterative computation of the BP decoding method, the decoding time delay of the BP decoding method is significantly lower than that of an SC decoding method and is insensitive to the length of a code word, so that the BP decoding method is suitable for application scenarios with high requirements on time delay. The traditional BP decoding method has poor error rate and frame error rate performance, the BPL decoding method adopts a plurality of BP decoders based on different factor graphs for decoding, the improvement of the error rate and the frame error rate performance is brought at the cost of higher calculation complexity and hardware requirements on the basis of the BP decoding method, but the error rate and the frame error rate performance of the BPL decoding method are still poor compared with an SCL decoding method added with Cyclic Redundancy Check (CRC). .
Disclosure of Invention
In order to improve the bit error rate and the frame error rate performance of a BPL decoding method, the invention provides a polarization code belief propagation list decoding method based on bit reversal, and a used code word is a cascade code formed by a CRC (cyclic redundancy check) code and a polarization code. In the method, under the condition that the BPL decoding result does not pass CRC (cyclic redundancy check), a Flip Bit Set (FBS) is constructed by analyzing the decoding result in the BPL decoding method, information Bits of a polarization code in the FBS are flipped (bit flipping in the invention is realized by setting a prior log-likelihood ratio of the flipped Bits to be infinite), errors in a part of BPL decoders can be corrected, and the error rate and the frame error rate performance of the BPL decoding method are improved.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a bit-flipping-based polar code belief propagation list decoding method, which comprises the following steps:
the first step, carrying out BPL decoding with CRC check, specifically:
(1) initialization
For a polar code with a code length of N and a length of K of the original information bit sequence, the received signal is recorded asThe list number in the BPL decoding method is marked as L, and the step (2) is carried out; the original information bit sequence is an information sequence which is subjected to CRC coding and is not filled with frozen bits;
(2) starting L BP decoders simultaneously for decoding
Estimation of information bit sequence by ith BP decoderCalculating an estimate of the codeword bit sequence by the ith BP decoder as a result of the output of the BP decoderAnd receiving signalsHas an Euclidean distance d betweeniAnd (4) turning to the step (3); wherein i is more than or equal to 1 and less than or equal to L,is the ith BP decoder to the jth bit u in the information bit sequencejJ is more than or equal to 1 and less than or equal to N,is the ith BP decoder to the jth bit x in the codeword bit sequencej(ii) an estimate of (d); the information bit sequence is obtained by filling frozen bits in an original information bit sequence, and the code word bit sequence is generated by encoding the information bit sequence by a polarization code;
(3) sequencing decoding results of L BP decoders
Note the bookSorting the components in the decoded _ u according to the following sorting rule to obtain a new vector decoded _ u _ sorted for the vector formed by the estimation of the information bit sequence by the L BP decoders obtained in the step (2), and turning to a step (4):
wherein,represents the kth in decoded _ u _ sortedmThe number of the components is such that,to representAnd receiving signalsThe euclidean distance between them,to representAnd receiving signalsThe euclidean distance between;
(4) CRC (cyclic redundancy check) is carried out on decoding results of L BP (back propagation) decoders
Performing CRC on the components in the decoded _ u _ sorted one by one, if the components passing the CRC exist, successfully decoding the BPL decoder with the CRC, outputting the components passing the CRC as decoding, and ending the whole decoding process; if the component passing the CRC does not exist, the decoding of the BPL decoder with the CRC fails, and the second step is carried out;
and secondly, constructing a flipping bit set FBS, specifically comprising:
(A) initializing a full zero matrix reczero _ one _ matrix of K rows and 2 columns, wherein an element of a qth row and a qth column in the reczero _ one _ matrix is recorded as recp,qP is more than or equal to 1 and less than or equal to K, and q is more than or equal to 1 and less than or equal to 2; recording the number of elements in the FBS as T, wherein T is more than or equal to 0 and less than or equal to K, and transferring to the step (B);
(B) according to the decoding result of the BPL decoding method in the first step, updating the reczero _ one _ matrix according to the following updating rule, and proceeding to step (C):
therein, indexpIs the bit index of the p-th bit in the original information bit sequence with the length of K in the information bit sequence after filling the frozen bits, and is more than or equal to 1 indexj≤N；
(C) Calculating the ratio of each bit in the original information bit sequence to be translated into 0 and 1
If recp,1≤recp,2Then recp,1And recp,2Ratio of smaller value to larger valueIf recp,1＞recp,2Then, thenTurning to step (D);
(D) selecting FBS from information bit set
For set Index _ U ═ Index1,index2,...,indexKSorting the elements in the FBS according to the following sorting rule, selecting the first T elements from the set obtained by sorting to construct the FBS, and turning to the third step:
wherein, Index _ UsortedRepresents the sorted set of Index _ U,represents Index _ UsortedW of (1)aThe number of the elements is one,
thirdly, decoding a polarization code belief propagation list based on bit flipping, specifically:
①, initializing t to 1, and going to step ②;
②, if T is larger than T, the bit-reversal-based BPL decoding method fails to decode, and the whole decoding process is finished, if T is less than or equal to T, go to step ③;
③ BPL decoder of BP method indexes into information bit sequenceBit flipping and proceeding to step ④, wherein each BP decoder in BPL method corresponds to a size of N x (1+ log)2N), the first column of R is used to store the prior log-likelihood ratios of the information bits, the rule of bit flipping is: if the ith BP decoder is in the first step, the step (2) decodes the obtained information bit sequenceEstimation of individual bitsIf the BP decoder is 1, the corresponding R in the BP decoder is the secondThe row first column element is assigned a positive infinity; if it isIf the value is 0, the BP decoder is set to the corresponding RAssigning the first row element to negative infinity, and assigning the values of the other elements in the R according to a BP decoding method;
④ using R obtained in step ③, starting L BP decoders to decode at the same time, and going to step ⑤;
⑤ sequencing the decoding results of the L BP decoders in step ④ according to the sequencing rule in step (3) in the first step, and turning to step ⑥;
⑥, CRC check is performed on the sorted decoding results in step ⑤ one by one, if there is a decoding result passing CRC check, bit flipping decoding is successful, the decoding result passing CRC check is output as decoding, the whole decoding process is ended, if there is no component passing CRC check, t is made t +1, and step ② is performed.
As a further technical solution of the present invention,the value is 0 or 1.
As a further technical scheme of the invention, the value of T can be autonomously determined by an information receiver according to the channel condition.
As a further technical solution of the present invention,
advantageous effects
The polarization code belief propagation list decoding method based on bit inversion can construct an inversion bit set for identifying unreliable information bit judgment by performing data analysis on a failure decoding result under the condition that the decoding of a polarization code BPL decoding method fails, set the prior log likelihood ratio of the unreliable information bit as an infinite value, correct errors in the BPL decoding method in a tentative decoding mode and improve the frame error rate performance of the polarization code under the BPL decoding method. In the interval of medium and high signal-to-noise ratio, compared with a BPL decoding method, the method can improve the frame error rate by one order of magnitude, and meanwhile, the average decoding time delay of the decoding method is similar to that of the BPL decoding method, which shows that the method can obtain the gain of the bit error rate performance at the cost of smaller decoding time delay.
Drawings
Fig. 1 is a flowchart of a polar code belief propagation list decoding method based on bit flipping.
Detailed Description
In the invention, an information sequence with the length of K and subjected to CRC coding and unfilled frozen bits is recorded as an original information bit sequence, an information sequence with the length of N and obtained by filling frozen bits in the original information bit sequence with the length of K is recorded as an information bit sequence, and a bit sequence generated after the information bit sequence is subjected to polarization code coding is called a code word bit sequence.
The bit flipping-based polarization code belief propagation decoding method in the present invention is described by taking a polarization code with a code length N of 256 and an original information bit sequence length K of 136 (including a cyclic redundancy check code length r of 8) as an example. The construction method of the polarization code in this example is gaussian approximation, the code word construction signal-to-noise ratio is 2.5 db, and the cyclic redundancy check code generating polynomial is g (x) ═ x8+x6+x3+x2+1。
As shown in fig. 1, the method comprises the following steps:
the first step is as follows: and carrying out BPL decoding with CRC check. The method comprises the following steps:
(1) and (5) initializing. For a polar code with a code length of N and a length of K of the original information bit sequence, the received signal is recorded asIn this example N is 256. The list number in the BPL decoding method is denoted by L (the BPL decoding method is an existing method, and the list number L indicates that L BP decoders using different factor graphs are used for decoding in the BPL decoding method), where L is 32 in this example. And (4) transferring to the step (2).
(2) And starting L BP decoders for decoding at the same time. Note the bookFor the estimation of the information bit sequence by the ith BP decoder, i is more than or equal to 1 and less than or equal to L as the output result of the BP decoder, whereinIs the ith BP decoder to the jth bit u in the information bit sequencejIs estimated by the estimation of (a) a,the value is 0 or 1. Note the bookEstimation of codeword bit sequence for the ith BP decoder, whereinIs the ith BP decoder to the jth bit x in the codeword bit sequencejIs estimated. BP decoding is performed simultaneously using L BP decoders. Calculating an estimate of the codeword bit sequence obtained by the ith BP decoderAnd receiving signalsHas an Euclidean distance d betweeni，And (4) transferring to the step (3).
(3) And sequencing the decoding results of the L BP decoders. Note the bookA vector formed of estimates of the information bit sequence for the L BP decoders obtained in step (2), whichIs an estimate of the information bit sequence by a BP decoder. Sorting the components in the decoded _ u according to the following rules to obtain a new vector decoded _ u _ sorted:
represents the kth in decoded _ u _ sortedmComponent, kmIndicating the change in index caused by the sorting. Then, the process proceeds to step (4).
(4) And performing CRC on the decoding results of the L BP decoders. Performing CRC on the components in the decoded _ u _ sorted one by one, if the components passing the CRC exist, successfully decoding the BPL decoder with the CRC, outputting the components passing the CRC as decoding, and ending the whole decoding process; if no component passing the CRC check exists, the decoding of the BPL decoder with the CRC check fails, tentative bit reversal decoding needs to be carried out, and the step is shifted to the second step.
The second step is that: a flip bit set FBS is constructed. The method comprises the following steps:
(1) and (5) initializing. Initializing the all-zero matrix reczero _ one _ matrix of K rows and 2 columns for counting the BPL decoding result in the first step, in this example, K is 136. The element in the p-th row and the q-th column in the reczero _ one _ matrix is denoted as recp,qP is more than or equal to 1 and less than or equal to K, and q is more than or equal to 1 and less than or equal to 2. The number of elements in the FBS is recorded as T, T is more than or equal to 0 and less than or equal to K, T represents the bit number which can be used for overturning, and the value of the T can be autonomously determined by an information receiver according to the channel condition. In this example, T is 4. And (4) transferring to the step (2).
(2) And counting the decoding result of the BPL decoding method in the first step, and writing the decoding result into the matrix reczero _ one _ matrix. Note indexjIs that the jth bit in the original information bit sequence with the length of K is in the information bit sequence after filling the frozen bitBit index, j is more than or equal to 1 and less than or equal to K, and index is more than or equal to 1jN is less than or equal to N. The update rule of reczero _ one _ matrix is as follows:
thus, recp,1Recording the index of the information bit sequence in the L BP decoderspThe number of decoders, rec, for each bit to be 0p,2Recording the index of the information bit sequence in the L BP decoderspThe number of decoders for which a bit is 1. And (4) transferring to the step (3).
(3) The ratio of 0 to 1 for each bit in the original information bit sequence is calculated. Defining ratiopAnd p is more than or equal to 1 and less than or equal to K is recp,1And recp,2Ratio of smaller value to larger value in order to ensure ratiopThe value of (a) does not exceed 1, facilitating the sequencing of subsequent steps. The calculation rule is if recp,1≤recp,2Then, thenIf recp,1＞recp,2Then, thenratiopThe larger the bit rate is, the larger thepThe larger the difference in decoding of the individual bits, the greater the probability of decoding error occurring in the information bit. And (4) switching to the step.
(4) The FBS is selected from the set of information bits. Let set Index _ U ═ Index1,index2,...,indexKAnd the K original information bits are set by bit indexes in the information bit sequence after the frozen bits are filled. Sorting the elements in the Index _ U according to the following sorting rule:
Index_Usortedrepresents the sorted set of Index _ U,represents Index _ UsortedW of (1)aElement of waIndicating the change in index caused by the sorting. From sorted set Index _ UsortedThe first T elements of the medium selection are constructedFBS in this example is {6,7,13,20 }.
The third step: and decoding the polarization code belief propagation list based on bit flipping. The method comprises the following steps:
(1) and (5) initializing t to 1, counting the number of times of trial bit reversal decoding by using t, and switching to the step (2).
(2) If T is larger than T, the bit flipping-based BPL decoding method fails in decoding, and the whole decoding process is finished; if T is less than or equal to T, the step (3) is carried out.
(3) In the BPL method, L BP decoders all index into information bit sequence asThe bit of (the t-th element in the FBS set) is bit flipped. Each BP decoder in the BPL decoding method corresponds to a matrix R, wherein R is a matrix with the size of N (1+ log)2N), where N is the length of the polarization code. The first column of R is used to store the a priori log likelihood ratios of the information bits. The rule of bit flipping is: if the ith BP decoder is in the first step, the step (2) decodes the obtained information bit sequenceEstimation of individual bits1, the first matrix of the R matrix corresponding to the BP decoderThe row first column element is assigned a positive infinity; if it is0, the first R matrix corresponding to the BP decoderThe row first column element is assigned a negative infinity. The values of the other elements in R are still assigned according to the traditional BP decoding method. And (4) switching to the step.
(4) And (4) carrying out BPL decoding by using the matrix R assigned according to the step (3).For the estimation of the information bit sequence by the ith BP decoder, i is more than or equal to 1 and less than or equal to L as the output result of the BP decoder, whereinIs the ith BP decoder to the jth bit u in the information bit sequencejIs estimated by the estimation of (a) a,the value is 0 or 1.Estimation of codeword bit sequence for the ith BP decoder, whereinIs the ith BP decoder to the jth bit x in the codeword bit sequencejIs estimated. BP decoding is performed simultaneously using L BP decoders. Calculating the codeword estimate from the ith BP decoderAnd receiving signalsHas an Euclidean distance d betweeni，And (5) switching to the step.
(5) And sequencing the decoding results of the L BP decoders. Note the bookAnd (4) forming a vector by the estimates of the L BP decoders on the information bits obtained in the step (4), wherein each component is the estimate of a BP decoder on the information bit sequence. And sequencing the components in the decoded _ u according to the formula (1) to obtain a new vector decoded _ u _ sorted. And (6) switching to the step.
(6) And performing CRC on the decoding results of the L BP decoders. Performing CRC on the components in the decoded _ u _ sorted one by one, if the components passing the CRC exist, successfully decoding the bit by turning, outputting the components passing the CRC as decoding, and ending the whole decoding process; if there is no component that passes the CRC check, let t be t +1, and proceed to step (2).
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (4)
1. The polar code belief propagation list decoding method based on bit reversal is characterized by comprising the following steps of:
the first step, carrying out BPL decoding with CRC check, specifically:
(1) initialization
For a polar code with a code length of N and a length of K of the original information bit sequence, the received signal is recorded asThe list number in the BPL decoding method is marked as L, and the step (2) is carried out; the original information bit sequence is an information sequence which is subjected to CRC coding and is not filled with frozen bits;
(2) starting L BP decoders simultaneously for decoding
Estimation of information bit sequence by ith BP decoderCalculating an estimate of the codeword bit sequence by the ith BP decoder as a result of the output of the BP decoderAnd receiving signalsHas an Euclidean distance d betweeniAnd (4) turning to the step (3); wherein i is more than or equal to 1 and less than or equal to L,is the ith BP decoder to the jth bit u in the information bit sequencejJ is more than or equal to 1 and less than or equal to N,is the ith BP decoder to the jth bit x in the codeword bit sequencej(ii) an estimate of (d); the information bit sequence is obtained by filling frozen bits in an original information bit sequence, and the code word bit sequence is generated by encoding the information bit sequence by a polarization code;
(3) sequencing decoding results of L BP decoders
Note the bookFor the vector formed by the estimation of the L BP decoders on the information bit sequence obtained in the step (2), the components in the decoded _ u are sorted according to the following sorting rule to obtain a new vector decodeed _ u _ sorted, proceed to step (4):
wherein,represents the kth in decoded _ u _ sortedmThe number of the components is such that,to representAnd receiving signalsThe euclidean distance between them,to representAnd receiving signalsThe euclidean distance between;
(4) CRC (cyclic redundancy check) is carried out on decoding results of L BP (back propagation) decoders
Performing CRC on the components in the decoded _ u _ sorted one by one, if the components passing the CRC exist, successfully decoding the BPL decoder with the CRC, outputting the components passing the CRC as decoding, and ending the whole decoding process; if the component passing the CRC does not exist, the decoding of the BPL decoder with the CRC fails, and the second step is carried out;
and secondly, constructing a flipping bit set FBS, specifically comprising:
(A) initializationThe all-zero matrix reczero _ one _ matrix of K row and 2 columns, the element of the qth row and the qth column in the reczero _ one _ matrix is denoted as recp,qP is more than or equal to 1 and less than or equal to K, and q is more than or equal to 1 and less than or equal to 2; recording the number of elements in the FBS as T, wherein T is more than or equal to 0 and less than or equal to K, and transferring to the step (B);
(B) according to the decoding result of the BPL decoding method in the first step, updating the reczero _ one _ matrix according to the following updating rule, and proceeding to step (C):
therein, indexpIs the bit index of the p-th bit in the original information bit sequence with the length of K in the information bit sequence after filling the frozen bits, and is more than or equal to 1 indexj≤N；
(C) Calculating the ratio of each bit in the original information bit sequence to be translated into 0 and 1
If recp,1≤recp,2Then recp,1And recp,2Ratio of smaller value to larger valueIf recp,1＞recp,2Then, thenTurning to step (D);
(D) selecting FBS from information bit set
For set Index _ U ═ Index1,index2,...,indexKSorting the elements in the FBS according to the following sorting rule, selecting the first T elements from the set obtained by sorting to construct the FBS, and turning to the third step:
wherein, Index _ UsortedRepresents the sorted set of Index _ U,represents Index _ UsortedW of (1)aThe number of the elements is one,
thirdly, decoding a polarization code belief propagation list based on bit flipping, specifically:
①, initializing t to 1, and going to step ②;
②, if T is larger than T, the bit-reversal-based BPL decoding method fails to decode, and the whole decoding process is finished, if T is less than or equal to T, go to step ③;
③ BPL decoder of BP method indexes into information bit sequenceBit flipping and proceeding to step ④, wherein each BP decoder in BPL method corresponds to a size of N x (1+ log)2N), the first column of R is used to store the prior log-likelihood ratios of the information bits, the rule of bit flipping is: if the ith BP decoder is in the first step, the step (2) decodes the obtained information bit sequenceEstimation of individual bitsIf the BP decoder is 1, the corresponding R in the BP decoder is the secondThe row first column element is assigned a positive infinity; if it isIf the value is 0, the BP decoder is set to the corresponding RAssigning the first row element to negative infinity, and assigning the values of the other elements in the R according to a BP decoding method;
④ using R obtained in step ③, starting L BP decoders to decode at the same time, and going to step ⑤;
⑤ sequencing the decoding results of the L BP decoders in step ④ according to the sequencing rule in step (3) in the first step, and turning to step ⑥;
⑥, CRC check is performed on the sorted decoding results in step ⑤ one by one, if there is a decoding result passing CRC check, bit flipping decoding is successful, the decoding result passing CRC check is output as decoding, the whole decoding process is ended, if there is no component passing CRC check, t is made t +1, and step ② is performed.
2. The bit flipping-based polar code belief propagation list decoding method of claim 1,the value is 0 or 1.
3. The bit flipping-based polar code belief propagation list decoding method of claim 1, wherein the value of T is autonomously determinable by an information receiver according to channel conditions.
4. The bit flipping-based polar code belief propagation list decoding method of claim 1,
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| CN110492974A (en) * | 2019-08-19 | 2019-11-22 | 北京邮电大学 | A kind of parallel polarization code coding method and device |
| CN110620588A (en) * | 2019-10-25 | 2019-12-27 | 网络通信与安全紫金山实验室 | BPL decoding method and device based on polarization code |
| CN110798284A (en) * | 2019-11-25 | 2020-02-14 | 安徽大学 | Polarization code transmission method based on double BP decoding graph parallel decoding technology |
| CN110932824A (en) * | 2020-02-11 | 2020-03-27 | 网络通信与安全紫金山实验室 | Polarization code belief propagation algorithm based on two-way graph with bit reversal |
| CN111416624A (en) * | 2020-03-27 | 2020-07-14 | 网络通信与安全紫金山实验室 | Polarization code belief propagation decoding method, equipment and storage medium |
| CN111446973A (en) * | 2020-04-17 | 2020-07-24 | 北京交通大学 | Polarization code belief propagation decoding method based on multi-flip bit set |
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