CN106803759A - Polar yards of effective adaptive decoding method based on Gauss construction - Google Patents
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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
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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
- H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
Abstract
The invention discloses a kind of Polar yard effective adaptive decoding method based on Gauss construction, introducing Gauss judgement is divided and combines effective adaptive decoding algorithm carrying out path under conditions of being constructed based on Gauss.The present invention calculates the posterior probability for obtaining each information bit under Gaussian channel using Gauss construction, and the decoding in this, as each information bit reliability, each information bit decoding reliability is applied to continuously delete sequential decoding, if the decoding of current bit position（It is translated into 0 or 1）Reliability more than can with the reliability of correct decoding when, directly enter row decoding, if be unsatisfactory for, still keep path to divide, by it is this path division is carried out based on bit reliability after obtain all active paths of current bit and enter row decoding in conjunction with effective adaptive decoding algorithm.Numerical simulation experiment shows, under equal conditions, of the invention in the case of keeping performance constant, with lower complexity.
Description
Technical field
The present invention relates to a kind of Polar yards of effective adaptive decoding method based on Gauss construction, belong to Error Correction of Coding skill
Art field.
Background technology
Polar yards is a kind of new Error Correction of Coding proposed by Arikan, for binary symmetric channel, in theory
Prove up to shannon limit, and with relatively low encoding and decoding complexity.Due to Polar yards of excellent specific property, academia is caused
Very big concern, be applied to message sink coding, channel coding, Joint Source/channel Coding Design, tapping channel coding, and code
In rate compatibility.
Polar yards of common decoding algorithm deletes (Successive Cancellation, SC) decoding algorithm for continuous,
It is proposed first by Arikan.The algorithm using bit channel likelihood probability hard-decision values output coding sequence, and according to
The fractionation of channel is iterated calculating.It has decoding simple but the features such as time delay is larger, handling capacity is not high.
In order to reduce the complexity of SC decodings, some decoding algorithms, such as A.Alamdar-Yazdi et al. profits have been occurred in that
Recursive structure in being decoded with SC, simplifies the treatment to information bit, it is proposed that a simplified SC decoder.It is not influenceing
The time delay of SC decoders is considerably reduced on the premise of decoding performance, decoding performance is improve.But because simplified SC is decoded
Device can not improve the bit error rate, therefore I.Tal and A.Vardy et al. propose continuous deletion sequence (Successive in succession
Cancellation List, SCL) decoding algorithm.It is different from SC algorithms, in SCL decoding algorithms, when information bit is translated, no
It is again selection possibility preferable path, but retains the extension that two kinds of possible values (" 0 " and " 1 ") carry out path simultaneously,
When path is expanded more than default L, the maximum L paths of selection wherein possibility proceed decoding below.The algorithm
In the case where certain decoding complexity is sacrificed, it is obtained in that closely polarization code is in maximum likelihood (Maximum-
Likelihood, ML) decoding under performance.
Then, Niu Kai et al. has carried out further improvement to SCL algorithms, it is proposed that with CRC (Cyclic
Redundancy Check, CRC) auxiliary SCL decoding algorithms, because CRC check false dismissal probability is very low, therefore this scheme
The decoding performance for obtaining will be better than maximum-likelihood decoding.
A kind of adaptation scheme is proposed in order to reduce the complexity of SCL decoding algorithms, B.Li et al., the program first will be pre-
If value L is set to less value, if can decode and receive by CRC check, if L can not gradually be increased by verification
Value be further continued for decoding, until successfully decoded.But in the algorithm, if not over CRC check, to restart to translate
Code algorithm, therefore decoding delay will increase.
On this basis, Chuan Zhang et al. propose a kind of efficient adaptive algorithm, in the algorithm, setting
One threshold value of path metric value, when the difference of the metric of two most middle paths is more than this threshold value, deletes remaining
A semipath, if less than threshold value, then still retain all of path.The algorithm is effective on the premise of error performance is not influenceed
Reduce decoding complexity.But when the condition of setting is unsatisfactory for, decoding path does not change, therefore to the reduction of complexity
Also limit.
The content of the invention
In order to further reduce Polar yards of decoding complexity, the present invention is using the reliability of information bit as path
Division criterion, referred to as Gauss judge that the information bit larger to decoding correctness does not implement division, and it is less to decode correctness
Information bit just enters line splitting, and the sequence after division again by resulting l bars decoding path according to reliability from big to small is laggard
The effective adaptive selection of row, i.e. difference and default value to l/2 and the reliability of l/2+1 paths is compared, such as
Really its difference is more than default value, then l/2 paths, all retain if less than then all paths before only retaining, and obtain a kind of base
In Polar yards of effective adaptive decoding algorithm of Gauss construction.
The technical problems to be solved by the invention are to provide a kind of Polar yards of effective adaptive decoding based on Gauss construction
Method, reduces the Polar yards of continuous complexity for deleting decoding algorithm.The method Gauss construction under conditions of, based on different
The reliability of information bit carries out path division, only just enters line splitting to the decoding less information bit of correctness, and decoding is correct
Property larger information bit do not divide, and combine effective adaptive algorithm, obtain lower average path number, further reduce
Polar yards of decoding complexity.
The present invention uses following technical scheme to solve above-mentioned technical problem：
The present invention provides a kind of Polar yards of effective adaptive decoding method based on Gauss construction, and the method includes following
Specific steps：
Step 1：For code length be N, information bit is k Polar yards, channel is the Gaussian channel of binary system, Polar
Code is split into N number of subchannel, preliminary log likelihood ratio L (yi) obeyGaussian Profile, its
In, yiRepresent i-th output of subchannel, i=1,2 ..., N, σ2It is the variance of white Gaussian noise；I-th Gaussian distributed
Subchannel averageObtained by following recurrence formula：
Wherein,U expects for interchannel noise；
Step 2：Calculate i-th error probability P of subchannele(ui), choose the small subchannel transmission of subchannel error probability
Information bit, completes Gauss construction, wherein,
Step 3：It is sky to put sequence, and sequence number is 0, i=1, and path maximum number is Lmax, path difference threshold is τ, i-th
Sub-channels decoding error probability Pe(ui)；
Step 4：SCL decoding algorithms are carried out, when ith bit is information bit, ifThen i-th compares
Special decoding valuation is 0, ifThe then decoding valuation of ith bit is 1, otherwise carries out path division；
When i-th bit in all paths all decodes completion, the reliability to gained path is ranked up, and obtains number of path L；Its
In,It is the log-likelihood ratio of ith bit in l paths, l=1,2 ..., L；
Step 5：If L ＞ Lmax, then the larger L of reliability is retainedmaxPaths；If less than Lmax, then L paths are all
Retain, and take the metric in L/2 and L/2+1 paths and be compared, the less L/2 roads of metric are deleted if difference is more than τ
Footpath, otherwise still all retains；
Step 6：If i ＜ N, i=i+1 is made, return to step 2 otherwise selects in the decoding path that step 5 is obtained
Output is once used as by the path of CRC check；If all paths can not select most reliable path by CRC check
That is the maximum path of metric is used as outgoing route.
As further prioritization scheme of the invention, in step 1It is reduced to
Used as further prioritization scheme of the invention, modulation system is BPSK.
As further prioritization scheme of the invention, i-th decoding metric of the l paths of bit in step 5 It is j-th decoding valuation of bit,For l paths logarithm seemingly
So compare.
Used as further prioritization scheme of the invention, the value for walking N is 512.
The present invention uses above technical scheme compared with prior art, with following technique effect：
1st, the present invention is it is contemplated that the decoding correct probability of different information bits is different, with based on decoding bit reliability
Property method, insecure information bit is entered into line splitting, reliable information bit is directly decoded, reduce splitpath；
2nd, the present invention can be from path reliability to from the aspect of the influence for decoding result, according to the reliability of decoding path
Size carry out the selection in punctured path, decoding complexity is further optimized, more applicability.
Brief description of the drawings
Fig. 1 is that N-bit is based on the Polar yards of continuous deletion sequential decoding schematic diagram that Gauss judges.
Fig. 2 is that the continuous deletion sequential decoding algorithm and original effect adaptive decoding algorithm of CRC auxiliary are proposed with the present invention
Scheme FER (frame error rate, FER) curve ratio relatively scheme (N=512).
Specific embodiment
Technical scheme is described in further detail below in conjunction with the accompanying drawings：
In the present invention, path division depends on the decoding reliability of each information bit.The present invention is used under Gaussian channel
Gauss construction calculates the posterior probability for obtaining each information bit, and the decoding in this, as each information bit reliability, will be each
Information bit decoding reliability be applied to continuously delete sequential decoding, if current bit position decoding (being decoded as 0 or 1) can
By property more than can with the reliability of correct decoding when, directly enter row decoding, if be unsatisfactory for, still keep path to divide, pass through
This all active paths for obtain after the division of path current bit based on bit reliability are translated in conjunction with effective self adaptation
Code algorithm enters row decoding.Numerical simulation experiment shows, under equal conditions, compared with original effect adaptive approach, based on Gauss
The effective adaptive decoding algorithm of Polar yards of construction keep performance it is constant in the case of, with lower complexity.
The method of the present invention is fallen into a trap based on Polar yards of Gauss structural theory in continuous sequential decoding process of deleting
Calculate the error probability P of each bit channel decodinge(ui), so as to obtain decoding reliability, sentenced as path division using reliability
According to referred to as Gauss judges, the information bit larger to decoding correctness does not implement division, and decodes the less information ratio of correctness
Spy just enters line splitting.Gauss is judged that formula is combined with effective adaptive algorithm by the method for the present invention, to obtained by each bit
Path carries out punctured again.
The present invention for different information bits, decodes result correctness from from the aspect of the influence of decoding bit reliability
Probability it is different, on this basis, can be judged carry out path division with Gauss with the probability of correct decoding according to subchannel.
If using Pe(ui) represent in all possible inputOn the basis of estimate i-th subchannel uiMistake it is general
Rate (It is the bit stream that channel receiving terminal is obtained,It is preceding i-1 bit value)：
Wherein, X represents input, and Y represents output,Represent i-th decoding valuation of bit, Pe(ui) it is information uiIn preceding i-
In the case of 1 information bit is properly decoded, subchannelThe probability of decoding error estimation.Once obtain
Pe(ui), also just obtain i-th possibility of subchannel correct decoding, i.e., will not be less than 1-Pe(ui).In other words, 1-Pe
(ui) can be used to represent that i-th subchannel is capable of the reliability of correct decoding.
Generally, for channel WN:XN→YN,I-th subchannel turns when representing that code length is N
Probability (obtaining exporting the transition probability of bit when being now 0 for i-th subchannel transmission), and code length are moved for N then thinks channel
N number of subchannel is split into, i-th subchannel transmits i-th bit.Y is receiving terminal bit stream, such asIt is then receiving terminal the 1st
To N number of bit.Assuming that preceding i-1 bit is all correctly translated, i-th bit u of subchanneliThe probability that decoding makes a mistake
For：
But because the complexity for calculating this formula is higher, can be calculated with Gaussian approximation.It is assumed that inputIt is
Full null sequence, according to receiving terminal bit yiThe distribution of obedience can be calculated preliminary log likelihood ratioObeying average isVariance isGaussian Profile.Such that it is able to be calculated the average of the log-likelihood ratio of each Gaussian distributedTherefore the P that formula (2) is representede(ui) can be calculated with following formula：
Wherein
Know that log-likelihood ratio can be iterated with following two formula to be calculated：
WhereinLog-likelihood ratioThe subscript N of middle L represents number of subchannels, subscript
The 2i-1 bit is represented, in bracketIt is the decoding valuation (0 or 1) of ith bit, such asRepresent the 1st to the strange of 2i-2 bits
Numerical digit,The 1st even bit for arriving 2i-2 bits is represented, y is receiving terminal bit stream, such asIt is then receiving terminal the 1st to N/2
Bit.
As can be seen from the above equation, computational length for N log-likelihood ratio (logarithmic likelihood ratio,
LLR it is the LLR of N/2, i.e. likelihood pair that) can be converted into and calculate two lengthCan turn
It is changed to calculating likelihood pairObtain, similarly respectively with (4) formula and (5)
Formula continues recursion can be converted to calculating likelihood pairSo as to be converted to
Computational length is the LLR of N/4, and the recurrence relation can go on until length is 1 always.When length is 1, LLR's
Value can be directly by formulaIt is calculated.
Similarly,Can also be obtained by following recurrence：
Wherein,Can be used during emulation
Approximately.Initial valueσ is channel noise variance.
Code length said before is split into N number of subchannel for Polar yards of N, thus in above formula the subscript N of L be can be with table
Show subchannel number, subscript i represents i-th subchannel.In above formula, it can be seen thatCalculating point odd-even channel meter
Calculate, for example：Calculate the value of the 2nd sub-channels in 8 channels altogetherSubscript 2 is even number, then with (7) formula meter
Calculate, i.e.,Continue recursive calculation(equivalent to the 1st sub-channels calculated in 4 channels), subscript
1 is odd number, therefore is calculated with (6) formulaIt can be seen that to obtainValue,
Need to continue recursive calculationSimilarly calculated with (6) formula For
Known initial value, therefore can directly be calculatedValue, so as to calculateFinally obtain's
Value.
It is calculated Pe(ui) after, you can the selection of information bit is carried out, Polar yards of Gauss construction is completed, while preserving Pe
(ui) value carries out Gauss judgement to facilitate during decoding.
Decoding path reliable value represents the correct probability of current decoding path, for i-th l paths of bit, road
Footpath metric is：
There is division accurate by after the threshold value that path reliability was substituted into and can obtain correct decoding is calculated
Then：
Represent known reception terminal sequence in actual calculatingValuation with preceding i-1 bit is
On the basis of uiThe path metric value P obtained when=0l(ui).If meeting the criterion, l paths do not divide, otherwise the l articles
Path is split into two paths.For example, when (9) formula meets, can directly be translated intoAccording to Bayes' theorem, can be by
Above-mentioned (9) and (10) formula are reduced to
Polar yards of effective adaptive decoding process based on Gauss construction of the bit of one embodiment of the invention 5, such as Fig. 1 institutes
Show, wherein, the deleted path of the path representation with vertical line, dashed path represented and do not divide：
Step 1：When decoding bit is information bit, the code word and channel log-likelihood ratio and decoding error obtained by transmission
Probability is compared, it is assumed here that the 1st bit is unsatisfactory for the condition directly decoded in (11) formula, therefore directly carries out path point
Split；
Step 2：Obtain two paths and to carry out path with effective self adaptation punctured, by comparing after two paths all enter
Row retains；
Step 3：Gained path is proceeded continuously to delete sequential decoding, ibid, four paths retain the 2nd bit,
The decoding of the 3rd bit is carried out, wherein the first pathsWith Article 4 pathMeet direct decoding condition, do not enter line splitting, four paths all complete translating for the 3rd bit
Carry out being further continued for decoding after effective Adaptive Path is punctured after code；
Step 4：The decoding of the 4th, 5 bit, decoding knot must be proceeded after punctured to path by effective adaptive algorithm
CRC check is carried out after beam as the path to obtained by, selection first is used as decoding output, decodes result by the path for verifying
Path reliability in above-mentioned steps 3 according to decoding bit has carried out effective adaptive algorithm, wherein effectively adaptive
Answer algorithmic method as follows：
Reliability to most middle two paths in decoding gained path is compared, if its difference is more than default
It is worth, then a punctured remaining semipath, if it is less, all paths all retain, i.e.,：Assuming that current path number is l, if full
Sufficient Pl/2(ui)-Pl/2+1(ui) ＞ τ, then retain the semipath of reliability highest one, if be unsatisfactory for, all paths all retain.
Fig. 2 is the FER Performance comparision curves of each decoding scheme.Wherein, code length N is 512, and code check k is 0.5, Lmax=4.From
Can take a fancy in figure, in different signal to noise ratios, interpretation method proposed by the present invention is continuous with original CRC auxiliary to delete decoding calculation
Method and effective adaptive decoding algorithm have almost identical decoding performance, that is to say, that set forth herein interpretation method will not be right
The bit error rate of decoding is impacted.Table 3 is that interpretation method proposed by the present invention is average with the path of effective adaptive decoding method
Number comparison diagram.Wherein, code length N=512, Lavg=(L1+L2+L3+...+LN)/N.It can be seen that with effective self adaptation
Method is compared, and Polar yards of effective adaptive decoding algorithm based on Gauss construction proposed by the present invention is obtained in that relatively low road
Footpath number, because decoding complexity and decoding path number are into positive correlation, therefore scheme complexity proposed by the present invention is lower, and performance is more
Plus it is superior.Understood with reference to Fig. 2 and table 3, on the one hand Polar yards of effective adaptive decoding algorithm based on Gauss construction can make decoding
Lower complexity is obtained, the error performance of decoding is not on the other hand interfered with yet.
The path average comparison diagram of the interpretation method proposed by the present invention of table 3 and effective adaptive decoding method
The above, the only specific embodiment in the present invention, but protection scope of the present invention is not limited thereto, and appoints
What be familiar with the people of the technology disclosed herein technical scope in, it will be appreciated that the conversion or replacement expected, should all cover
It is of the invention include within the scope of, therefore, protection scope of the present invention should be defined by the protection domain of claims.
Claims (5)
1. the Polar yards of effective adaptive decoding method for being constructed based on Gauss, it is characterised in that the method includes walking in detail below
Suddenly：
Step 1：For code length be N, information bit is k Polar yards, channel is the Gaussian channel of binary system, Polar yards of quilt
It is split into N number of subchannel, preliminary log likelihood ratio L (yi) obeyGaussian Profile, wherein, yi
Represent i-th output of subchannel, i=1,2 ..., N, σ2It is the variance of white Gaussian noise；I-th son of Gaussian distributed
The average of channelObtained by following recurrence formula：
Wherein,U expects for interchannel noise；
Step 2：Calculate i-th error probability P of subchannele(ui), choose the small subchannel transmission information of subchannel error probability
Position, completes Gauss construction, wherein,
Step 3：It is sky to put sequence, and sequence number is 0, i=1, and path maximum number is Lmax, path difference threshold is τ, i-th son
Channel decoding error probability Pe(ui)；
Step 4：SCL decoding algorithms are carried out, when ith bit is information bit, ifThen ith bit
Decoding valuation is 0, ifThe then decoding valuation of ith bit is 1, otherwise carries out path division；Work as institute
I-th bit for having path all decodes completion, and the reliability to gained path is ranked up, and obtains number of path L；Wherein,It is the log-likelihood ratio of ith bit in l paths, l=1,2 ..., L；
Step 5：If L ＞ Lmax, then the larger L of reliability is retainedmaxPaths；If less than Lmax, then L paths all retain,
And take the metric in L/2 and L/2+1 paths and be compared, the less L/2 paths of metric are deleted if difference is more than τ, it is no
Then still all retain；
Step 6：If i ＜ N, i=i+1 is made, return to step 2 is selected for the first time otherwise in the decoding path that step 5 is obtained
Output is used as by the path of CRC check；If all paths can not select most reliable path i.e. degree by CRC check
The maximum path of value is used as outgoing route.
2. it is according to claim 1 based on Gauss construction Polar yards of effective adaptive decoding method, it is characterised in that
In step 1It is reduced to
3. it is according to claim 1 based on Gauss construction Polar yards of effective adaptive decoding method, it is characterised in that
Modulation system is BPSK.
4. it is according to claim 1 based on Gauss construction Polar yards of effective adaptive decoding method, it is characterised in that
I-th decoding metric of the l paths of bit in step 5 It is j-th
The decoding valuation of bit,It is the log-likelihood ratio of l paths.
5. it is according to claim 1 based on Gauss construction Polar yards of effective adaptive decoding method, it is characterised in that N
Value be 512.
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