CN110233628B - Self-adaptive belief propagation list decoding method for polarization code - Google Patents
Self-adaptive belief propagation list decoding method for polarization code Download PDFInfo
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- 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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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/13—Linear codes
Abstract
The invention discloses a self-adaptive belief propagation list decoding method of a polarization code, which comprises the steps of firstly determining the maximum list number of the method according to the number of BP decoders owned by a receiving end, obtaining a BP decoding factor graph with better decoding effect through calculation by a Gaussian approximation method, then selecting different BP decoding factor graphs from the BP decoders recorded in the list for decoding, sequencing decoding results, and then performing cyclic redundancy check, if the results passing the cyclic redundancy check exist, successfully decoding and stopping decoding, otherwise, automatically adjusting the size of the list, expanding the list number to twice of the original number, and continuously using the BP decoders in the list for decoding.
Description
Technical Field
The invention relates to a self-adaptive belief propagation list decoding method of a polarization code, belonging 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. At present, two types of decoding methods of polarization codes are mainstream, one type of decoding methods is based on Serial Cancellation (SC) decoding, including Serial Cancellation List (SCL) decoding methods based on SC decoding, the SC-based polarization code decoding method belongs to sequential decoding, and information bits already decoded affect the estimation of subsequent information bits, so that the information bits in a code word 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, including a Belief Propagation List (BPL) decoding method, and due to the parallel iterative computation property of the BP decoding method, the decoding time delay of the BP decoding method is significantly lower than that of the 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. However, the bit error rate and the frame error rate performance of the traditional BP decoding method are poor, and the BPL decoding method improves the bit error rate and the frame error rate performance on the basis of the BP decoding method, but brings higher computational complexity and hardware requirements.
Disclosure of Invention
The invention provides a self-adaptive belief propagation list decoding method of a polarization code, wherein the used code word is a cascade code formed by a Cyclic Redundancy Check (CRC) code and the polarization code. The list of the decoding method of the self-adaptive belief propagation list is used for recording BP decoders capable of decoding simultaneously, the number of the list is defined as the number of the BP decoders in the list, and the maximum number of the list is defined as the upper limit of the number of the BP decoders capable of decoding simultaneously.
The invention provides a self-adaptive belief propagation list decoding method, which comprises the steps of firstly determining the maximum list number of the method according to the number of BP decoders owned by a receiving end, obtaining BP decoding factor graphs with better decoding effect through calculation by a Gaussian approximation method, then selecting different BP decoding factor graphs for decoding the BP decoders recorded in the list, sequencing decoding results, performing cyclic redundancy check, if the results passing the cyclic redundancy check exist, successfully decoding and stopping decoding, and otherwise, automatically adjusting the size of the list, expanding the list number to twice of the original list, and continuously using the BP decoders in the list for decoding.
The existing BP decoding method has poor bit error rate and frame error rate performance, while the BPL decoding method adopts a method of simultaneously decoding a plurality of BP decoders, and improves the bit error rate and the frame error rate performance at the cost of higher computational complexity and hardware energy consumption. Compared with a BP decoding method and a BPL decoding method, the polarization code self-adaptive belief propagation list decoding method has better bit error rate and frame error rate performance, and the number of lists required for completing decoding under the condition of medium and high signal to noise ratio is obviously smaller than that of the BPL decoding method. This shows that the number of BP decoders which need to be started under the condition of medium and high signal-to-noise ratio in the adaptive belief propagation list decoding method of the polarization code is significantly less than that of the BPL decoding method adopting the constant list number, thereby achieving the effects of significantly reducing the computational complexity and reducing the hardware energy consumption.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a self-adaptive belief propagation list decoding method of a polarization code, which comprises the following steps:
the first step is as follows: maximum number of lists allowed for initialization L max Constructing 2L for BP decoding max -1 permutation matrix persistence _ matrix corresponding to the factor graph, specifically:
(1) According to the number of BP decoders owned by the receiving end, the maximum list number L is automatically determined max ；
(2) Narrowing the search of the desired permutation factor graph: for code length N =2 n The polar code of (2) needs to pass through n coding stages l during coding 0 ,...,l n-1 Factor graph adopted during decoding and L = { L = } 0 ,l 1 ,...,l n-1 The elements in the Chinese character are arranged in a one-to-one mapping relationship; defining a parameter k, so that k satisfies the condition: (n-k)! Not less than L max Noting that a subset of the set L is L h ＝{l k ,l k+1 ,...,l n-1 Get set L h (n-k) of the Medium element! Arranging the seeds completely, and adding the first k encoding stages (l) with unchanged sequence before each arrangement 0 ,l 1 ,...,l k-1 Get (n-k)!of all elements in the set L! Arranging, obtaining corresponding (n-k)!according to the one-to-one mapping relation between the factor graph and the element arrangement in L! Seed factor graph, thereby reducing the search range of the replacement factor graph to (n-k)! Seed growing;
(3) Selecting a required factor graph from the search range of the replacement factor graphs: (n-k)!for all elements in the set L obtained in step (2)! Arranging, respectively calculating frame error rate obtained by corresponding factor graph under Gaussian approximation method, and selecting 2L with minimum frame error rate max -1 factor graph;
(4) Configuration 2L max -1 permutation matrix probability _ matrix corresponding to the factor graph: construct 2L max -1 row and n columns of permutation matrix multiplication _ matrix, each row of multiplication _ matrix corresponding to 2L selected in step (3) max -1 one of a full permutation of sets L;
secondly, decoding a self-adaptive belief propagation list of the polarization code, specifically comprising the following steps:
(A) Initialization: initializing the number l =1 of BP decoders which can simultaneously carry out belief propagation decoding of the polarization codes at present;
(B) BP decoding is carried out simultaneously by using l independent BP decoders, each BP decoder independently carries out BP decoding respectively by adopting factor graphs corresponding to 1 line element which is not used yet in the simulation _ matrix, and the output result of the BP decoder is
And
calculating estimates of codewords from each decoder
And receiving signals
The euclidean distance d therebetween, wherein,
is to the information bit u i Is estimated by the estimation of (a) a,
is to the information bit u i Code word bit x obtained after cascade coding i Estimate of (a), y i An ith bit representing a received signal;
(C) Estimating the I groups of information bits obtained in the step (B) according to the corresponding sorting rule that d is from small to large
Sorting;
(D) Estimating the I groups of information bits ordered in step (C)
And (3) performing cyclic redundancy check one by one: if the current decoding result to be checked
If the cyclic redundancy check is met, the decoding of the self-adaptive belief propagation list decoding method is successful, the decoding result is returned, and the whole decoding process is finished; otherwise, estimating the next group of information bits
Performing cyclic redundancy check if the l groups of information bits are estimated
If the cyclic redundancy check fails, the step (E) is carried out;
(E) If L is greater than or equal to L max Outputting the ordered first set of estimates of the information bits of step (C)
As a decoding result, the entire decoding flow ends; otherwise let l =2l, proceed to step (B).
As a further optimization scheme of the invention, the value of k in the step (1) is automatically determined by the receiving end according to the self computing capability and the time delay requirement.
As a further preferred embodiment of the present invention, in step (B)
Compared with the prior art, the invention adopting the technical scheme has the following technical effects: the self-adaptive belief propagation list decoding method of the polarization code sets the list number to be a smaller value, then carries out cyclic redundancy check on the decoding result in the existing list, and increases the list number to continue decoding after the cyclic redundancy check fails. Compared with the traditional BP decoding method, the self-adaptive belief propagation list decoding method of the polarization code obviously improves the bit error rate and the frame error rate, and the average decoding time delay and the calculation complexity in a middle-high signal-to-noise ratio interval are only slightly higher than that of the traditional BP decoding method. Compared with the existing BPL decoding method, the self-adaptive belief propagation list decoding method of the polarization code improves the bit error rate and the frame error rate performance, avoids a large amount of unnecessary calculation and hardware energy consumption in the BPL decoding method by gradually increasing the number of lists, can reduce the calculation complexity by one order of magnitude in an interval of medium and high signal to noise ratio, and obtains the bit error rate performance exceeding the BPL decoding method by approaching the calculation complexity and hardware energy consumption cost of the traditional BP decoding method. This shows that the method of the present invention can obtain the gain of the bit error rate performance and the simplification of the calculation complexity at the cost of smaller decoding time delay.
Drawings
FIG. 1 is a flow chart of a method for adaptive belief propagation list decoding of polar codes;
FIG. 2 shows a code length of 8, comprising 3 encoding stages (l) 0 、l 1 、l 2 ) Schematic representation of the 3 different factor graphs of (a), wherein (a) is a sequence through l 2 、l 0 、l 1 The factor graph of (b) is sequentially passed through l 1 、l 2 、l 0 Is sequentially passed through l 1 、l 0 、l 2 Factor graph of (a).
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings as follows:
the adaptive belief propagation list decoding method of the polarization code in the invention is explained by taking the code length N =2048, the information bit number K =1024 and the length r =8 of the cyclic redundancy check code 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 generator polynomial of the cyclic redundancy check code is g (x) = x 8 +x 6 +x 3 +x 2 +1。
As shown in fig. 1, the method comprises the following steps:
the first step is as follows: maximum number of lists allowed for initialization L max (in this example L max = 4), construct 2L for BP decoding max -1 (2L in this example) max -1= 7) permutation matrix probability _ matrix corresponding to the factor graph. The method comprises the following steps:
(1) According to the number of BP decoders owned by the receiving end, the maximum is determined autonomouslyNumber of lists L max . And (3) switching to the step (2).
(2) The search range of the desired substitution factor graph is narrowed (the substitution factor graph is an existing concept, and the construction method is briefly described in this step). For code length N =2 n The polar code of (2) needs to pass through n coding stages l during coding 0 ,...,l n-1 In the set L = { L = } 0 ,l 1 ,...,l n-1 }. The factor graph used in decoding and the full arrangement of the elements in L are in a one-to-one mapping relationship, for example, fig. 2 shows three different factor graphs when n = 3. The total arrangement of elements in the set L is n! Species, and therefore n! Different coding factor graphs are described. Defining a parameter k so that k satisfies the condition: (n-k)! Not less than L max And (k is related to the size of the factor graph search range, and the specific value can be automatically determined by the receiving end according to the self computing capability and the time delay requirement). Let a subset of the set L be L h ，L h ＝{l k ,l k+1 ,...,l n-1 }. Obtaining a set L h (n-k) of the Medium element! Arranging the seeds completely, and adding the first k encoding stages { l ] with unchanged sequence before each arrangement 0 ,l 1 ,...,l k-1 Thus, get (n-k)!of all elements in the set L! Arranging, and obtaining corresponding (n-k)!according to the one-to-one mapping relation between the factor graph and the element arrangement in L! A seed factor graph. This completes the search of the permutation factor graph from the original n! The seed is reduced to the present (n-k)! And (4) seed selection. And (4) transferring to the step (3).
(3) And selecting a required factor graph from the search range of the replacement factor graphs. (n-k)!for all elements in the set L obtained in step (2)! Arranging, respectively calculating frame error rate obtained by corresponding factor graph under Gaussian approximation method, and selecting 2L with minimum frame error rate max -arrangement of all elements in the set L corresponding to 1 factor graph. And (5) switching to the step (4).
(4) And constructing a permutation matrix permatation _ matrix corresponding to the required factor graph. Construct the size of 2L max -1 row and n columns of permutation matrix multiplication _ matrix, each row of multiplication _ matrix corresponding to 2L selected in step (3) max One of 1 full permutation of sets L. The process is ended. In this exampleThe persistence _ matrix of (1) is a matrix of size 7 rows and 11 columns as follows:
the second step: and carrying out adaptive belief propagation list decoding of the polarization code. The method comprises the following steps:
(1) And (5) initializing. Note that the number of BP decoders capable of simultaneously performing belief propagation decoding of polarization codes is l. Initialization parameter l =1, and the received signal is recorded as
And (4) transferring to the step (2).
(2) And simultaneously starting the BP decoders to decode according to different factor graphs. Note the book
And
is the output result of the BP decoder, wherein
Refers to the information bit u i Is estimated by the estimation of (a) a,
is a code word bit x obtained by cascade coding information bits i Is estimated. And carrying out BP decoding simultaneously by using l independent BP decoders, wherein each BP decoder respectively and independently carries out BP decoding by adopting a factor graph corresponding to 1 line element which is not used in the permatation _ matrix. Calculating estimates of codewords from each decoder
And receive the signal
Has a Euclidean distance d between，
And (4) transferring to the step (3).
(3) Estimating the l groups of information bits obtained in the step (2)
And (6) sorting. Estimating the l groups of information bits obtained in the step (2) according to the corresponding sorting rule that d is from small to large
And (6) sorting. And (4) switching to the step.
(4) Estimating the I groups of information bits sequenced in the step (3)
And performing cyclic redundancy check one by one. If the current decoding result to be checked
If the cyclic redundancy check is satisfied, the decoding of the self-adaptive belief propagation list decoding method is successful, the decoding result is returned, and the whole decoding process is finished. Otherwise, estimating the next group of information bits
A cyclic redundancy check is performed. If l groups of information bit estimates
If the cyclic redundancy check fails, the step (5) is carried out.
(5) If L is greater than or equal to L max Outputting the first set of information bit estimates sorted in step (3)
As a result of the decoding, the entire decoding flow ends. Otherwise l → 2l is updated, i.e. the list is resized adaptively, resizing the list to twice the original list size. And (3) switching to the 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 (3)
1. The self-adaptive belief propagation list decoding method of the polarization code is characterized by comprising the following steps of:
the first step is as follows: maximum number of list allowed by initialization L max Constructing 2L for BP decoding max -1 permutation matrix probability _ matrix corresponding to the factor graph, specifically:
(1) According to the number of BP decoders owned by the receiving end, the maximum list number L is automatically determined max ；
(2) Narrowing the search of the desired permutation factor graph: for code length N =2 n The polar code of (2) needs to pass through n coding stages l 0 ,...,l n-1 Factor graph adopted in decoding and L = { L = } 0 ,l 1 ,...,l n-1 The elements in the Chinese character are arranged in a one-to-one mapping relationship; defining a parameter k so that k satisfies the condition: (n-k)! Not less than L max Noting that a subset of the set L is L h ＝{l k ,l k+1 ,...,l n-1 Get set L h (n-k) of the Medium element! Arranging the seeds completely, and adding the first k encoding stages { l ] with unchanged sequence before each arrangement 0 ,l 1 ,...,l k-1 Thus, get (n-k)!of all elements in the set L! Arranging, obtaining corresponding (n-k)!according to the one-to-one mapping relation between the factor graph and the element arrangement in L! Seed factor graph, thereby reducing the search range of the replacement factor graph to (n-k)! Seed growing;
(3) Selecting a required factor graph from the search range of the replacement factor graphs: (n-k)!for all elements in the set L obtained in step (2)! Arranging, respectively calculating frame error rates obtained by corresponding factor graphs under a Gaussian approximation method, and selecting the 2L with the minimum frame error rate max -1 factor graph;
(4) Configuration 2L max -1 factor graph corresponding permutation matrix persistence _ matrix: construct 2L max -1 row and n columns of permutation matrix multiplication _ matrix, each row of the multiplication _ matrix corresponding to 2L selected in step (3) max -1 one of a full permutation of sets L;
secondly, decoding a self-adaptive belief propagation list of the polarization code, specifically comprising the following steps:
(A) Initialization: initializing the number l =1 of BP decoders which can simultaneously carry out belief propagation decoding on the polarization codes at present;
(B) BP decoding is carried out by using l independent BP decoders, each BP decoder respectively and independently carries out BP decoding by using a factor graph corresponding to 1 line element which is not used yet in the mutation _ matrix, and the output result of the BP decoder is
And
calculating codeword estimates for each decoder
And receive the signal
The euclidean distance d therebetween, wherein,
is to the information bit u i The estimation of (a) is performed,
is to the information bit u i Code word bit x obtained after cascade coding i Estimate of (a), y i An ith bit representing a received signal;
(C) The I groups of letters obtained in the step (B) are sorted according to the corresponding sorting rule that d is from small to largeInformation bit estimation
Sorting;
(D) Estimating the I groups of information bits ordered in step (C)
And (3) performing cyclic redundancy check one by one: if the current decoding result to be checked
If the cyclic redundancy check is met, the decoding of the self-adaptive belief propagation list decoding method is successful, the decoding result is returned, and the whole decoding process is finished; otherwise, estimating the next group of information bits
Performing cyclic redundancy check if the l groups of information bits are estimated
If the cyclic redundancy check fails, the step (E) is carried out;
(E) If L is greater than or equal to L max Outputting the ordered first set of information bit estimates of step (C)
As a decoding result, the entire decoding flow ends; otherwise let l =2l, proceed to step (B).
2. The adaptive belief propagation list decoding method of polar codes according to claim 1, characterized in that the value of k in step (1) is determined by the receiving end itself according to its own computing power and delay requirement.
3. The adaptive belief propagation list decoding method of polarization codes according to claim 1, wherein in step (B)
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