CN114421974A - Polar code BPL decoding method with improved factor graph selection mode - Google Patents

Polar code BPL decoding method with improved factor graph selection mode Download PDF

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CN114421974A
CN114421974A CN202111503469.3A CN202111503469A CN114421974A CN 114421974 A CN114421974 A CN 114421974A CN 202111503469 A CN202111503469 A CN 202111503469A CN 114421974 A CN114421974 A CN 114421974A
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arrangement
factor
decoding
factor graph
bpl
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白宝明
高瑞雪
王博昱
李秉豪
周沈洋
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Xidian University
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
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Abstract

The invention discloses a polar code BPL decoding method with an improved factor graph selection mode, which comprises the following steps: s1: acquiring an arrangement factor graph adopted during the decoding of the polarization code BPL; s2: transmitting the encoded symbols of the polarization code by using the permutation factor graph, wherein the step S1 specifically includes: calculating the error probability of N sub-channels of the polarization code; selecting K sub-channels with the minimum error probability to form an information bit set; aiming at all arrangement factor graphs obtained through layer arrangement, acquiring corresponding binary vectors pi according to arrangement conditions of the arrangement factor graphs; II, traversing pi corresponding to all the arranged factor graphs, and calculating the upper bound of the error probability corresponding to each factor graph; and selecting the least L arrangement factor graphs corresponding to the upper bound of the error probability as factor graphs during decoding. The invention combines the upper error probability bound corresponding to the arrangement factor graph and the error probability of each subchannel, protects the subchannel with poor performance on the original factor graph by using the additional arrangement factor graph, and improves the whole decoding performance.

Description

Polar code BPL decoding method with improved factor graph selection mode
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a polar code BPL decoding method with an improved factor graph selection mode.
Background
The 5G mobile communication system is an important content of current research in the field of mobile communication. The current 4G mobile communication system has been hard to afford explosively increasing mobile data and new traffic demands. The international telecommunication union radio communication department defines three typical application scenarios of 5G for various aspects of problems, namely an enhanced mobile broadband (eMBB) scenario, a large-scale machine communication (mtc) scenario and an ultra-high-reliability low-latency communication (urrllc) scenario. In 2016, the third generation partnership project adopted polarization codes (Polar codes) as the coding scheme for control channels in the 5GeMBB scenario at the RAN 87 conference.
However, with the development of technology and the reform and progress of scientific technology, more and more devices have started to be directly connected to the internet, which makes the situation of "everything interconnection" gradually developing. Further demands have been placed on low-latency, highly reliable communications by more and more industries, such as future unmanned systems, military and civilian unmanned fleet, vehicle traffic planning in transportation systems, remote monitoring and diagnostics in the medical industry, and VR games. These various types of communication demands require ultra-high, low latency communications. This makes it difficult for the critical techniques for polarization codes in the 5G eMBB scenario to be applicable in the scenario described above. Therefore, intensive research on a high-reliability and low-delay decoding algorithm of Polar codes is needed. The decoding algorithm of the Serial Cancellation List (SCL) adopted in the 5G scheme is limited by the decoding structure, so that high throughput and low latency are difficult to achieve, and the Belief Propagation (BP) decoding algorithm just can meet the above requirements, the BP decoding algorithm of the polarization code achieves updating, transferring and iteration of information through the factor graph of the coding structure, the Belief Propagation List (BPL) decoding algorithm first generates different factor graph structures by changing the scheduling sequence of the factor graph, generates a List set of the factor graph, and then decodes by using all the factor graphs in the set, so that a correct decoding result is selected from the decoding results of the multiple factor graphs.
The BPL decoding method of the polarization code uses a plurality of factor graphs for decoding, so that the decoding performance of BP is improved. Meanwhile, the performance of the BP decoding algorithm is improved, and the practicability of the BP decoding algorithm is greatly improved. For the BPL decoding algorithm of the polar code, different factor graphs are used for decoding, so that different decoding performances can be obtained, but at present, the factor graph selection scheme of the BPL decoding algorithm of the polar code has no optimal solution.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a method for decoding a BPL with improved factor graph selection. The technical problem to be solved by the invention is realized by the following technical scheme:
one aspect of the present invention provides a polar code BPL decoding method with an improved factor graph selection mode, including:
s1: acquiring an arrangement factor graph adopted during the decoding of the polarization code BPL;
s2: transmitting the encoded symbols of the polarization code using the permutation factor map,
wherein, the S1 specifically includes:
s1.1: calculating the error probability P of the N sub-channels of the polarization codei；
S1.2: choosing error probability P from original factor graphiThe smallest K subchannels constitute the set of information bits
Figure BDA0003402543040000021
Wherein the information bits are collected
Figure BDA0003402543040000022
Each element in (1) is the serial number of the selected subchannel;
s1.3: aiming at all arrangement factor graphs obtained through layer arrangement, acquiring corresponding binary vectors pi according to arrangement conditions of the arrangement factor graphs;
s1.4: II, traversing pi corresponding to all the arrangement factor graphs, and respectively calculating the upper bound of the error probability corresponding to each arrangement factor graph;
s1.5: pick the minimum L upper bounds of error probability PB,ΠCorresponding arrangementThe factor graph is used for decoding.
In one embodiment of the present invention, the S1.3 includes:
s1.31: carrying out layer arrangement on the original factor graphs to obtain a plurality of arrangement factor graphs;
s1.32: and acquiring a binary vector pi of the corresponding arrangement factor graph according to the arrangement condition of the arrangement factor graph.
In one embodiment of the present invention, the S1.5 includes:
s1.51: order set
Figure BDA0003402543040000031
Collection
Figure BDA0003402543040000032
Figure BDA0003402543040000033
Representing an empty set;
s1.52: from the collection
Figure BDA0003402543040000034
Selecting the sequence number k with the maximum error probability of the bit channel, traversing pi corresponding to all the arranged factor graphs, and dividing the upper bound P of the error probability corresponding to all the factor graphsB,ΠSorting from small to large, and then selecting again in the factor graphs corresponding to the upper bounds of the first 2L error probabilitiesΠ(k)Putting the vector pi corresponding to the selected factor graph into a set
Figure BDA0003402543040000035
And from the set, the sequence number k
Figure BDA0003402543040000036
Removing;
s1.53: repeat step 1.52 until the set is traversed
Figure BDA0003402543040000037
All the serial numbers in (1) satisfy the condition
Figure BDA0003402543040000038
S1.54: will be assembled
Figure BDA0003402543040000039
The arrangement factor graphs corresponding to all the elements in the sequence are used as the arrangement factor graphs adopted in decoding.
In an embodiment of the present invention, the S2 includes:
s2.1: transmitting the coded symbols to a receiving end;
s2.2: the receiving end sends the received LLR value as soft information to a decoder;
s2.3: respectively carrying out BP decoding by using the arrangement factor graph generated in S1.54 to obtain L candidate code words;
s2.4: selecting candidate code words meeting iteration termination conditions from the L candidate code words;
s2.5: and selecting the code word with the minimum Euclidean distance from the candidate code words obtained in the S2.4 as a final decoding result.
Another aspect of the present invention provides a storage medium, in which a computer program is stored, the computer program being configured to execute the steps of the polar code BPL decoding method according to any one of the above embodiments.
In another aspect, the present invention provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the polar code BPL decoding method according to any one of the above embodiments when calling the computer program in the memory.
Compared with the prior art, the invention has the beneficial effects that:
the invention has the advantages that the polar code BPL decoding method with the improved factor graph selection mode is combined with the upper bound P of the error probability corresponding to the arrangement factor graphB,ΠAnd the error probability P of each subchanneliTo select a factor graph, using an additional permutation factor graph to protect the sub-channels with poor performance on the original factor graph, and for L-1 permutation factor graphs, at least L-1 sub-channels can be protected, so that the wholeThe decoding performance of the body is obviously improved.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
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FIG. 1 is a flow chart of a factor graph selection process provided by an embodiment of the present invention;
fig. 2 is a factor graph of a polar code when the subchannel N is 8 according to an embodiment of the present invention;
fig. 3 is a mapping relationship between a factor graph arrangement and a codeword position arrangement of a polarization code when a subchannel N is 8 according to an embodiment of the present invention;
FIG. 4 is a block diagram of a flow chart of an implementation of a method for decoding a BPL with a polar code having an improved factor graph selection according to an embodiment of the present invention;
FIG. 5 is a graph comparing FER obtained using different decoding methods;
FIG. 6 is a comparison graph of FER performance under different factor graph selection methods of BPL;
FIG. 7 is a comparison graph of average number of iterations of BPL under different factor graph selection methods.
Detailed Description
To further illustrate the technical means and effects of the present invention adopted to achieve the predetermined object, the following describes a method for decoding BPL with improved factor graph selection according to the present invention in detail with reference to the accompanying drawings and the detailed description.
The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings. The technical means and effects of the present invention adopted to achieve the predetermined purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only and are not used for limiting the technical scheme of the present invention.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or device that comprises a list of elements does not include only those elements but may include other elements not expressly listed. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of additional like elements in the article or device comprising the element.
The invention provides a polar code BPL decoding method, which aims to provide a factor graph selection mode suitable for a BPL decoding algorithm of a polar code and is used for further improving the performance of the polar code BPL decoding. The technical idea of the embodiment of the invention is as follows: in the process of selecting the arrangement factor graph, not only the upper bound P of the error probability corresponding to the arrangement factor graph is consideredB,ΠAnd the error probability P of each sub-channel is taken into accounti. Each additional permutation factor map is used to protect a sub-channel with poor performance on the original factor map. Thus, at least L-1 sub-channels can be protected for L-1 permutation factor graphs, so that the whole decoding performance is improved, wherein L represents the maximum search path number set according to the path metric value.
In this embodiment, the method for decoding the BPL includes:
s1: and acquiring an arrangement factor graph adopted during decoding of the polarization code.
Specifically, referring to fig. 1, fig. 1 is a flowchart of a factor graph selection process according to an embodiment of the present invention, and step S1 includes:
s1.1: for a polar code with the code length of N, calculating the error probability P of N subchannels of the polar codei：
Specifically, in using a Gaussian approximation construct, let
Figure BDA0003402543040000061
Representing log-likelihood ratios corresponding to the ith polarized channel of the polarized code
Figure BDA0003402543040000062
Is determined by the probability density function of (a),
Figure BDA0003402543040000063
denotes the ith polarization channel, let z-N (0, σ)2) For additive white gaussian noise on the original channel W, assuming that all-zero codewords are sent without loss of generality, the following calculation relationship is given:
Figure BDA0003402543040000064
log-likelihood ratio received from channel W
Figure BDA0003402543040000065
Order to
Figure BDA0003402543040000066
Representing a probability density function
Figure BDA0003402543040000067
Is measured. Due to SC decoding
Figure BDA0003402543040000068
The calculation method of (b) is substantially the same as the calculation method of BP decoding of LDPC code, and it can be inferred that
Figure BDA0003402543040000069
This can be done by calculating the mean value
Figure BDA00034025430400000610
To replace
Figure BDA00034025430400000611
And (4) calculating.
Function of probability density
Figure BDA00034025430400000612
Can be obtained by the following two formulas:
Figure BDA00034025430400000613
Figure BDA00034025430400000614
the initial condition of the recursion is
Figure BDA00034025430400000615
(probability density function in case of one channel alone), symbol |, and symbol |, respectively represent convolution operations of check node and variable node on the polar code factor graph.
Mean value of same
Figure BDA0003402543040000071
It can also be derived by recursive calculations, namely:
Figure BDA0003402543040000072
Figure BDA0003402543040000073
initial value
Figure BDA0003402543040000074
Wherein the content of the first and second substances,
Figure BDA0003402543040000075
further, in the above-mentioned case,
Figure BDA0003402543040000076
the function can be simplified into
Figure BDA0003402543040000077
Wherein α -0.4527, β -0.86, and λ -0.0218.
Obtained by a recursive manner
Figure BDA0003402543040000078
Mean value of
Figure BDA0003402543040000079
Then, the error probability approximation can be obtained as:
Figure BDA00034025430400000710
wherein the content of the first and second substances,
Figure BDA00034025430400000711
s1.2: according to the set information bit length K and the error probability P of the sub-channeliChoosing the error probability P from the original factor graphiThe smallest K subchannels constitute the set of information bits
Figure BDA00034025430400000712
Wherein the information bits are collected
Figure BDA00034025430400000713
Each element in (a) is a sequence number of the selected subchannel.
Assuming that the required information bit length K is 5, the error probability P of N sub-channelsiThe smaller five sub-signals with the sequence numbers 1, 3, 5, 6 and 8 respectively, then
Figure BDA00034025430400000714
S1.3: and aiming at all the arrangement factor graphs obtained by layer arrangement, acquiring corresponding binary vectors pi according to the arrangement conditions of the arrangement factor graphs.
Specifically, the original factor graphs are firstly subjected to layer arrangement to obtain a plurality of arrangement factor graphs, and then binary vectors corresponding to the arrangement factor graphs are obtained according to arrangement conditions of the arrangement factor graphs. Referring to fig. 2, fig. 2 shows an embodiment of the present invention when the subchannel N is 8The factor graph of the polarization code, wherein, the left graph (a) is the original factor graph corresponding to the polarization code BP decoding algorithm when the code length N is 8, (b) is each calculation unit module in the BP decoding, and wherein L isi，jRepresenting left-hand propagation information in the decoding process, Ri，jRepresenting the right-hand propagation information in the decoding process.
Referring to fig. 3, fig. 3 is a mapping relationship between a factor graph arrangement and a codeword position arrangement of a polar code when a subchannel N is 8 according to an embodiment of the present invention. In particular, with vector { l }n-1，...，l0The layer of the polarization code factor graph is represented by a vector
Figure BDA0003402543040000081
Representing the binary form of the integer j.
Figure BDA0003402543040000082
Factor number on the representative factor graph
Figure BDA0003402543040000083
Subchannel sum in { ln-1，...，l0The first on the factor graph represented by
Figure BDA0003402543040000084
The subchannels are identical, j represents the number of rows in the factor graph, pi: { 0., n-1} → { 0., n-1} is a permutation. For brevity, denoted by pi (j)
Figure BDA0003402543040000085
In the decimal form of (1), N Π (j) constitute a vector Π. For example in FIG. 2
Figure BDA0003402543040000086
Represented is the 2 nd subchannel on the left factor graph and in { l }n-1，...，l0The {0, 1, 0} th, i.e., the 3 rd sub-channel on the original factor graph represented by the } is identical.
S1.4: traversing pi corresponding to all the arrangement factor graphs, and respectively calculating the upper bound of the error probability corresponding to each arrangement factor graph:
Figure BDA0003402543040000087
s1.5: pick the minimum L upper bounds of error probability PB，ΠThe corresponding factor graph is used as the factor graph used in decoding.
The S1.5 specifically includes:
s1.51: order set
Figure BDA0003402543040000088
Collection
Figure BDA0003402543040000089
Figure BDA00034025430400000810
Representing an empty set;
s1.52: from the collection
Figure BDA00034025430400000811
Selecting the sequence number k with the maximum error probability of the bit channel, traversing pi corresponding to all the arranged factor graphs, and dividing the upper bound P of the error probability corresponding to all the factor graphsB,ΠSorting from small to large, and then selecting again in the factor graphs corresponding to the upper bounds of the first 2L error probabilitiesΠ(k)The vector pi corresponding to the selected factor graph is put into a set
Figure BDA0003402543040000091
And from the set, the sequence number k
Figure BDA0003402543040000092
Is removed.
E.g. the current set
Figure BDA0003402543040000093
Then the slave set
Figure BDA0003402543040000094
In the selection pairThe rank k with the highest error probability is 8.
S1.53: repeat step 1.52 until the set is traversed
Figure BDA0003402543040000095
All the serial numbers in (1) satisfy the condition
Figure BDA0003402543040000096
S1.54: will be assembled
Figure BDA0003402543040000097
The arrangement factor graphs corresponding to all the elements in the sequence are used as the arrangement factor graphs adopted in decoding.
S2: and transmitting the coded symbols of the polarization code by using the permutation factor graph.
Specifically, S2 includes:
s2.1: and sending a coded symbol to a receiving end, wherein the coded symbol comprises information bits and frozen bits.
In this embodiment, the transmitting end transmits a coded symbol with a code rate of 0.5 to the receiving end.
S2.2: the receiving end sends the received LLR value as soft information to a decoder;
s2.3: respectively carrying out BP decoding by using the arrangement factor graph generated in the step 1.54 to obtain L candidate code words;
referring to fig. 2, the information updating process for a computing unit is shown as follows:
Figure BDA0003402543040000098
Figure BDA0003402543040000099
Figure BDA00034025430400000910
Figure BDA00034025430400000911
wherein the content of the first and second substances,
Figure BDA00034025430400000912
before the BP decoding starts, the following initialization is performed:
Figure BDA0003402543040000101
Figure BDA0003402543040000102
where i represents the number of layers in the factor graph and n represents the number of the rightmost layer in the factor graph.
Then, the BP decoder starts iterative decoding, and when the maximum iteration number T is reachedmaxOr satisfy an iteration termination condition (typically
Figure BDA0003402543040000103
) Stopping decoding, and judging by BP decoder to obtain estimated sequence
Figure BDA0003402543040000104
Figure BDA0003402543040000105
S2.4: selecting candidate code words meeting iteration termination conditions from the L candidate code words;
s2.5: and selecting the code word with the minimum Euclidean distance from the candidate code words obtained in the S2.4 as a final decoding result.
Referring to fig. 4, fig. 4 is a flowchart illustrating an implementation of a polar code BPL decoding method with an improved factor graph selection according to an embodiment of the present invention. Specifically, a headFirstly, utilizing the mapping relation between factor graph arrangement and code word position to obtain L vectors pii. The information sequence u passes through an encoder to obtain a code word sequence x, then passes through a channel to obtain a receiving value y, and a vector piiInterleaving y as interleaving pattern, inputting into BP decoder for decoding to obtain estimated sequence
Figure BDA0003402543040000106
And finally, obtaining a proper estimation sequence as output according to the L estimation sequences according to a certain output criterion.
The following describes the effect of the polar code BPL decoding method according to the embodiment of the present invention with reference to a simulation experiment:
(1) simulation conditions and contents:
the transmission bit error rate comparison simulation is performed on the existing method and the method of the embodiment of the present invention under the windows10 system by using the Visual Studio 2012 with reference to the simulation experiment parameters in table 1, and the result is shown in fig. 5.
TABLE 1 simulation experiment parameters
Figure BDA0003402543040000111
(2) And (3) simulation result analysis:
in FIG. 5, this embodiment shows the use of different decoders
Figure BDA0003402543040000112
(code length is 1024, information sequence length is 512) FER (Frame Error Rate). The BPL with L-32 uses the improved factor map selection method in this embodiment, which has the same decoding performance as the 5G scheme with L-8, but the FER of the improved BPL is still 0.2dB different from that of the 5G uplink scheme with L-32. In addition, it can be seen that the BPL decoding performance of the polarization code in 5G is inferior to that of the polarization code constructed by using RM16 GA. Since the CRC selection path fails in the BPL decoding, the traditional construction method only considering the polarization effect is not friendly to the BPL decoding, which also indicates that it is very important to find a construction method suitable for the BPL decoding.
Fig. 6 compares FER of polar coordinate codes when different permutation factor graph selection methods are used, where L is set to 10, and a Cyclic Shift permutation (Cyclic Shift), a Random permutation (Random) and a method (Improved) of an embodiment of the present invention are shown in fig. 6. It can be seen that the method proposed by the embodiment of the present invention is superior to other methods. Meanwhile, it can be seen that under low signal-to-noise ratio, cyclic shift permutation and random permutation have almost no performance gain, but the method of the embodiment of the invention can still bring considerable gain. At FER of 10-3Compared with cyclic shift permutation, the method of the embodiment of the invention can obtain the gain of 0.25 dB.
Referring to fig. 7, fig. 7 is a comparison graph of average number of iterations of BPL under different factor graph selection methods, and fig. 7 shows the average number of iterations required when L is 10, and gradually approaches the number of iterations required for BP decoding as the SNR increases. As indicated in fig. 4, the corresponding block error probability limits are different for different permutation factor graphs. Using cyclic shifts and random selection will result in a larger margin for the selected factor graph. These factor graphs often require a large number of iterations in the decoding process to reach the decoding termination condition, which also results in an increase in the number of iterations required on average in the BPL decoding process. The method of the embodiment of the invention directly considers the decoding performance of the factor graph, thereby avoiding various problems brought by selecting the factor graph with poor performance.
TABLE 2 clock cycle comparison
Figure BDA0003402543040000121
Table 2 shows the different signal-to-noise ratios Eb/N0(EbRepresenting the bit energy of the signal, NoRepresenting noise power spectral density) under
Figure BDA0003402543040000122
The number of clock cycles required for different decoding methods. It can be seen that in Eb/N0When 2.25, compared with the conventional BPL decoding, the polarization code BPL decoding method of the embodiment of the present inventionThe number of clocks required for the decoding process is reduced by 89.34%. With the increase of the signal-to-noise ratio, the polar code BPL decoding method of the embodiment of the invention can obtain the same decoding delay as BP decoding. When L is 32, the method for decoding the polarization code BPL according to the embodiment of the present invention is performed at FER 10-4Only the number of clocks required for approximately 2.26% SCL decoding is required.
The present embodiment of the method for decoding the polarization code BPL with the improved factor graph selection combines the upper bound P of the error probability corresponding to the permutation factor graphB,ΠAnd the error probability P of each subchanneliThe factor graph is selected, the subchannel with poor performance on the original factor graph is protected by using the additional permutation factor graph, and at least L-1 subchannels can be protected for L-1 permutation factor graphs, so that the overall decoding performance is obviously improved.
Another embodiment of the present invention provides a storage medium having stored therein a computer program for executing the method steps of the polar code BPL decoding method described in the above embodiment. Yet another aspect of the present invention provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the polar code BPL decoding method according to the above embodiment when calling the computer program in the memory. Specifically, the integrated module implemented in the form of a software functional module may be stored in a computer readable storage medium. The software functional module is stored in a storage medium and includes several instructions to enable an electronic device (which may be a personal computer, a server, or a network device) or a processor (processor) to execute some steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (6)

1. A method for decoding a polar code BPL with an improved factor graph selection mode is characterized by comprising the following steps:
s1: acquiring an arrangement factor graph adopted during the decoding of the polarization code BPL;
s2: transmitting the coded symbols of the polarization code by using the permutation factor graph;
wherein, the S1 specifically includes:
s1.1: calculating the error probability of N sub-channels of the polarization code;
s1.2: selecting K sub-channels with the minimum error probability from an original factor graph to form an information bit set, wherein each element in the information bit set is the serial number of the selected sub-channel;
s1.3: aiming at all arrangement factor graphs obtained through layer arrangement, acquiring corresponding binary vectors pi according to arrangement conditions of the arrangement factor graphs;
s1.4: II, traversing pi corresponding to all the arrangement factor graphs, and respectively calculating the upper bound of the error probability corresponding to each arrangement factor graph;
s1.5: and selecting the least L arrangement factor graphs corresponding to the upper bound of the error probability as factor graphs adopted in decoding.
2. The method of claim 1, wherein the S1.3 comprises:
s1.31: carrying out layer arrangement on the original factor graphs to obtain a plurality of arrangement factor graphs;
s1.32: and acquiring a binary vector pi of the corresponding arrangement factor graph according to the arrangement condition of the arrangement factor graph.
3. The method of claim 1, wherein the S1.5 comprises:
s1.51: order set
Figure FDA0003402543030000011
Collection
Figure FDA0003402543030000012
Figure FDA0003402543030000013
Representing an empty set;
s1.52: from the collection
Figure FDA0003402543030000014
Selecting the sequence number k with the maximum error probability of the bit channel, traversing pi corresponding to all the arranged factor graphs, and dividing the upper bound P of the error probability corresponding to all the factor graphsB,ΠSorting from small to large, and then selecting again in the factor graphs corresponding to the upper bounds of the first 2L error probabilitiesΠ(k)Putting the vector pi corresponding to the selected factor graph into a set
Figure FDA0003402543030000021
And from the set, the sequence number k
Figure FDA0003402543030000022
Removing;
s1.53: repeat step 1.52 until the set is traversed
Figure FDA0003402543030000023
All the serial numbers in (1) satisfy the condition
Figure FDA0003402543030000024
S1.54: will be assembled
Figure FDA0003402543030000025
The arrangement factor graphs corresponding to all the elements in the sequence are used as the arrangement factor graphs adopted in decoding.
4. The method for BPL decoding with improved factor graph selection as claimed in claim 3, wherein said S2 comprises:
s2.1: transmitting the coded symbols to a receiving end;
s2.2: the receiving end sends the received LLR value as soft information to a decoder;
s2.3: respectively carrying out BP decoding by using the arrangement factor graph generated in S1.54 to obtain L candidate code words;
s2.4: selecting candidate code words meeting iteration termination conditions from the L candidate code words;
s2.5: and selecting the code word with the minimum Euclidean distance from the candidate code words obtained in the S2.4 as a final decoding result.
5. A storage medium, characterized in that the storage medium has stored therein a computer program for executing the steps of the polar code BPL decoding method according to any of claims 1 to 4.
6. An electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the polar code BPL decoding method according to any one of claims 1 to 4 when calling the computer program in the memory.
CN202111503469.3A 2021-12-09 2021-12-09 Polar code BPL decoding method with improved factor graph selection mode Pending CN114421974A (en)

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CN115622574A (en) * 2022-12-16 2023-01-17 天地信息网络研究院(安徽)有限公司 Polarization code decoding method based on genetic algorithm

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