CN109067410A - A kind of method and interpretation method of determining BP decoding iteration renewal function - Google Patents
A kind of method and interpretation method of determining BP decoding iteration renewal function Download PDFInfo
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- 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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- 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
- H03M13/29—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
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Abstract
The present invention provides a kind of method of determining BP decoding iteration renewal function, and the interpretation method for Polar code.The method of the determining BP decoding iteration renewal function, comprising: a 1) parabolic function ax is found in the range intervals of specified x2, so that the ax in the range intervals2Functional value it is close with the functional value of ln (cosh (x));2) according to the parabolic function ax2Determine the ln (cosh (x)) in the iteration renewal function for BP decoding.
Description
Technical field
The present invention relates to the interpretation methods that Polar code is directed in wireless communication, more particularly to are translated using BP Polar code
The improvement of code mode.
Background technique
In wireless communication procedure, due to the uncertainty of transmission channel, need the effective information to expectation transmission additional
Whether a part of information has been accurately received original effective information with verification.The mode of this additional information transmission is claimed
As channel coding, decoding accordingly is called in the operation that receiving end decodes effective information.
Polar code is a kind of very effective channel coding method.It most proposed earlier than 2009 by Arikan, the volume
If code mode assumes that channel quantity tends to be infinitely great, then at least a part of channel tends to be perfect, and at least one
Channel is divided to tend to pure noise.Based on this it is assumed that can construct and choose in aggregate channel preferable channel to construct Polar
Code.
BP decoding is a kind of mainstream decoded mode for Polar code, and Fig. 1 a schematically shows traditional BP decoding
Factor graph.As shown in Figure 1a, Polar code can realize decoding (n=3 in figure) by the factor iteration in n stage.Fig. 1 b is shown
Processing unit in the factor graph of Fig. 1 a, the factor including one group of connected "+" and "=" and be connected with them 4
A node, wherein indicating the number of node with i and j, N is the dimension of Polar code.
During BP decoding, each node the message L that propagates to the left and is propagated to the right along with two class message
Message R, these two types of message are also referred to as belief messages.Such as Fig. 1 a, when decoding, counted to the right from the node of the leftmost side first
Newest message R is calculated, until propagating to the node of the rightmost side, then calculates newest message L from right to left, until propagating to most
The node in left side propagates one and is counted as an iteration back and forth.After each iteration, it requires to be updated message R and L.
The flow chart that iteration when Fig. 1 c schematically shows BP decoding updates.
With reference to Fig. 1 b, the belief messages R and L of update are separately shown are as follows:
Wherein, 1≤i≤n, 1≤j≤N/2, and iteration renewal function g (x1,x2) are as follows:
The complexity of above-mentioned BP decoding algorithm is very high, especially contains needle in iteration renewal function used in it
Calculating to cosh (x) and ln (x).Thus, in some approximations proposed in the prior art for above-mentioned iteration renewal function
Algorithm and corresponding hardware realization.Wherein more famous one kind is called BP Min-Sum decoding algorithm, proposesApproximate algorithm, thus use approximate iteration renewal function g (x1,x2)≈sgn(x1)sgn(x1)min(|
x1|,|x2|).Such approximate algorithm greatly reduces the complexity of algorithm, however this has very the performance of BP decoding
Big loss.
Summary of the invention
Therefore, it is an object of the invention to overcome the defect of the above-mentioned prior art, a kind of determining BP decoding iteration is provided more
The method of new function, comprising:
1) a parabolic function ax is found in the range intervals of specified x2, so that the ax in the range intervals2's
Functional value is close with the functional value of ln (cosh (x));
2) according to the parabolic function ax2Determine the ln (cosh (x)) in the iteration renewal function for BP decoding.
Preferably, according to the method, wherein step 1) further include:
1-1) determine the parabolic function ax of a variety of candidates with different parameters a2;
1-2) it is directed to current parabolic function ax2, judge whether it meets following Rule of judgment, comprising: first condition:
The ax in the symmetric interval of the successive segmentation point2It is whether similar to ln (cosh (x));
If 1-3) current parabolic function ax2Can satisfy step 1-2) in Rule of judgment then continue step 2), it is no
Then adjust current parabolic function ax2And continue step 1-2).
Preferably, according to the method, wherein step 1) further include:
A successive segmentation point 1-0) is chosen, so that the ln (cosh (x)) when using the successive segmentation point as independent variable
Functional value and | x | the functional value of-ln2 is close, and the successive segmentation point is used to determine the range intervals of the specified x.
Preferably, according to the method, step 1-2) in the Rule of judgment, further includes: second condition: in the company
Ax near continuous cut-point2With | x | whether-ln2 is continuous.
Preferably, according to the method, wherein step 2) includes:
Using the parabolic function ax2Instead of the ln (cosh (x)) in the iteration renewal function that is decoded for BP.
Preferably, according to the method, wherein step 2) includes:
According to the parabolic function ax2With | x |-ln2, determination is used for the iteration of BP decoding more in the form of piecewise function
The piecewise interval of new function, the piecewise function is determined by the successive segmentation point.
Preferably, according to the method, the iteration renewal function g (x1,x2) it is represented as:
Wherein, k is the absolute value of the successive segmentation point.
Preferably, according to the method, wherein step 1-2) include:
By comparing in the symmetric interval of the successive segmentation point, ax2Whether the difference between ln (cosh (x)) is small
In the threshold value of setting, to judge current parabolic function ax2Whether the first condition is met;
When by comparing using the successive segmentation point as independent variable, ax2(| x |-ln2) whether it is less than the threshold value of setting, with
Judge current parabolic function ax2Whether the second condition is met.
Preferably, according to the method, wherein judging current parabolic function ax2Whether the second condition is met,
Include:
Multiple independents variable are selected in the symmetric interval of the successive segmentation point, are respectively compared when using each independent variable
ax2With the difference between ln (cosh (x)).
Preferably, according to the method, wherein step 1-2) in the absolute value of the successive segmentation point chosen be greater than
1.5。
A kind of interpretation method for Polar code, comprising: in the iterative process for implementing BP decoding, using above-mentioned any
Iteration renewal function determined by one method is updated belief messages R and L.
A kind of computer readable storage medium, wherein being stored with computer program, the computer program is when executed
For realizing method described in above-mentioned any one.
Compared with the prior art, the advantages of the present invention are as follows:
Originally a kind of method of determining BP decoding iteration renewal function is provided, parabola approximation alternative, choosing are used
Select ax appropriate2Ln (cosh (x)) is replaced, multiplication twice can be directly carried out in successive segmentation point range you can get it and is close
Like numerical value, without directly being calculated using hyperbolic functions.Also, selected optimal parabola exists by means of the present invention
Curved portion is essentially coincided with hyperbolic functions lncoshx, can more be characterized iteration well compared to minimum and decoding and be updated letter
Number, this performance and the performance of traditional BP decoding algorithm that iteration renewal function obtained using this method is decoded
It is essentially identical.In addition, in the present invention, error big interval range in successive segmentation point section having been carried out parabola approximation and has been replaced
It changes, uses Min-Sum decoding algorithm in the minimum range of other errors, updated compared to iteration in traditional BP decoding algorithm public
The hyperbolic functions of formula, the iteration more new formula in improved BP decoding algorithm only have addition, subtraction, compare, multiplication and absolutely
Value and sgn function, greatly reduce the complexity of algorithm.
Detailed description of the invention
Embodiments of the present invention is further illustrated referring to the drawings, in which:
Fig. 1 a is the factor graph of traditional BP decoding in the prior art;
Fig. 1 b is a processing unit in the factor graph for Fig. 1 a;
Fig. 1 c is the general flow of traditional BP interpretation method, BP minimum and interpretation method, the improved BP interpretation method of the present invention
Cheng Tu;
Fig. 2 a is the dB figure of the error rate of traditional BP interpretation method and BP minimum and interpretation method under different signal-to-noise ratio;
Fig. 2 b be ln (cosh (x)) and | x | the comparison diagram of-ln2;
Fig. 3 be ln (cosh (x)), | x |-ln2 and parabola the ax preferably obtained using method of the invention2Comparison
Figure;
Fig. 4 is the method flow schematic diagram of determining BP decoding iteration renewal function according to an embodiment of the invention;
Fig. 5 is using traditional BP interpretation method, BP minimum and interpretation method and the improved BP interpretation method of the present invention
Performance Simulation Results.
Specific embodiment
Inventor after research by having found, there are non-compared to traditional BP decoding algorithm for the performance of Min-Sum decoding algorithm
Often big loss.Fig. 2 a, which is inventor, emulates drawn BP decoding algorithm and Min-Sum decoding algorithm not by MATLAB
The dB of error rate (BER) under same signal-to-noise ratio (Eb/No) schemes, it can be seen that the error rate of Min-Sum decoding algorithm is with signal-to-noise ratio
Fall be far below BP decoding algorithm, performance loss is about 0.5dB.
It has been recognised by the inventors that the major reason lost in this way is caused to be, the approximate calculation of Min-Sum decoding algorithm is only repeatedly
It is set up when being much larger than 1.5 for the independent variable in renewal function.For this purpose, inventor depicted with Fig. 2 b for ln (cosh (x)) and
| x | the comparison diagram of-ln2.It can be seen that the error of the two is larger in the section that x is equal to (- 1.5,1.5), and especially as | x |=0
When, ln (cosh (x)) and | x | the difference of-ln2 reaches ln2, this brings performance loss for Min-Sum decoding algorithm.
Inventor's discovery can take other approximate functions to replace ln (cosh (x)), and parabolic function is exactly wherein
One of.Fig. 3 is the parabola ax that inventor draws2, ln (cosh (x)) and | x | the comparison figure of-ln2, wherein a is optional ginseng
Number.As can be seen that there are a certain parabola ax2It is very approximate with the value of ln (cosh (x)) in suitable one section of section.Separately
Outside, inventor is in view of calculating ax2Multiplying three times is needed to be implemented, and ln2 is constant, is calculated | x |-ln2 is only needed simply
Subtraction, thus ln (cosh (x)) can also be indicated with the formal approximation of piecewise function, to be further reduced calculation amount,
I.e. only in ln (cosh (x)) and | x |-ln2 error it is larger when, ln (cosh (x)) is regarded as a parabola, in x
Remaining within the scope of ln (cosh (x)) is regarded as | x |-ln2.
For the considerations of indicating ln (cosh (x)) using piecewise function, can according to need determination and be directed to | x |-ln2
And ax2Successive segmentation point, the section of piecewise function is determined with successive segmentation point:
It can be seen that the selection of successive segmentation point and parabola parameter a will affect to ln's (cosh (x)) in (1)
Whether expression is accurate and reality executes calculation amount when decoding.In this regard, the present invention proposes that one kind can determine BP decoding iteration
The method of renewal function determines the successive segmentation point for the piecewise interval of x by iterative calculation and indicates the parabola
Parameter a, so that it is determined that used iteration renewal function g (x when decoding1,x2)。
It elaborates with reference to the accompanying drawings and detailed description to the present invention.
Fig. 4 is the method flow schematic diagram of determining BP decoding iteration renewal function according to an embodiment of the invention.
With reference to Fig. 4, which comprises
Step 1. is by comparing hyperbolic function ln (cosh (x)) and function | x |-ln2, and near smaller error amount point
Choose successive segmentation point.
Successive segmentation point is determined by the way of directly selecting specific value in the present embodiment, thus convenient for directly control
Make iteration renewal function g (x obtained1,x2) calculation amount.The absolute value of successive segmentation point is smaller, then in iteration renewal function
What is needed to be implemented is fewer for parabolical multiplication computation amount.If otherwise the absolute value for the successive segmentation point chosen is relatively
Greatly, then it will increase the calculation amount of iteration renewal function.By choosing suitable successive segmentation point, iteration renewal function can be taken into account
Accurate expression and the iteration renewal function calculation amount.
As discussed above in institute analytically, x be equal to (- 1.5,1.5) section in ln (cosh (x)) and | x | the difference of-ln2
It is different larger, thus preferably ± 1.5 are set by the selection lower limit of the absolute value of successive segmentation point.
Step 2. determines the parabolic function ax of a variety of candidates with different parameters a2。
It is appreciated that being not any one parabolic function ax2May ensure that its i.e. with | x | the segmentation of-ln2 in selection
Point is nearby the value that ln (cosh (x)) can continuously and be again expressed well in corresponding section.Thus at this
In embodiment, the parabolic function of various candidates is preset by step 2, it is most reasonable with the step determination that will pass through subsequent
Parabola.
According to the experience of inventor, the selection section of parameter a can be preferably arranged are as follows:
The parameter granularity that wherein variable k' ∈ [1,1.5] and k' choose is 0.1.Wherein, k ' is for x
The cut-point absolute value.
Step 3. is directed to current parabolic function ax2, judge that can it effectively characterize ln (cosh (x)).
It, can be only in successive segmentation point in order to reduce the search calculation amount when determining BP decoding iteration renewal function
Symmetric interval in ax2Ln (cosh (x)) can be characterized well to be judged.
It, can be in comparable one section of area for some preferred parabolic functions as being hereinbefore directed to Fig. 3 institute analytically
It is interior very well to characterize ln (cosh (x)).Thus, it is complete for certain some application for only needing to be calculated in the section
Parabolic function ax can be directly used entirely2To replace ln (cosh (x)).
However, then needing to indicate ln using piecewise function for the application that needs are calculated other than the section
(cosh(x)).For example, with parabolic function ax in the symmetric interval of successive segmentation point2Ln (cosh (x)) is replaced, even
Then use other than the symmetric interval of continuous cut-point | x |-ln2 replaces ln (cosh (x)).It not only needs to judge ax at this time2It can
Effectively characterize ln (cosh (x)), it is also necessary to judge the ax near the successive segmentation point2With | x | whether-ln2 is continuous.
It at this time can be for the parabolic function ax currently selected2Judge that can it meet first condition and Article 2 simultaneously
Part;Wherein, the first condition are as follows: the ax in the symmetric interval of the successive segmentation point2It is whether similar to ln (cosh (x)),
The second condition are as follows: the ax near the successive segmentation point2With | x | whether-ln2 is continuous.Such judgement can be with preparatory
The mode of one small threshold is set to realize, for example, by comparing in the symmetric interval of the successive segmentation point, ax2With
Whether the difference between ln (cosh (x)) is less than the threshold value of setting, to judge current parabolic function ax2Whether meet described
First condition;When by comparing using the successive segmentation point as independent variable, ax2(| x |-ln2) whether it is less than the threshold value of setting,
To judge current parabolic function ax2Whether the second condition is met.
Step 4. continues subsequent step according to the judging result in step 3, if current parabolic function ax2It can
Meet the Rule of judgment in step 3 and then continue subsequent step 5, otherwise from the candidate parabolic function determined by step 2
ax2Set in select a new parabolic function ax2And repeat the above steps 3.
Step 5. is according to current parabolic function ax2Determine the ln (cosh in the iteration renewal function for BP decoding
(x))。
As described in the text, it can be selected here according to the demand of application directly with ax2Replace ln (cosh (x)),
Ln (cosh (x)) can be indicated in the form of piecewise function.It can be joined in a manner of indicating ln (cosh (x)) by piecewise function
Examine formula (1) hereinbefore.
At this point, the iteration renewal function g (x for BP decoding1,x2) can be represented as:
Wherein, k is the absolute value of the point of successive segmentation described in step in front.
The iteration renewal function for BP decoding has then been determined as a result,.
A kind of interpretation method for Polar code is additionally provided in the present invention, comprising: in the iteration for implementing BP decoding
In the process, iteration renewal function determined by use according to the method for the present invention is updated belief messages R and L.I.e. such as
Shown in Fig. 1 c, when updating belief messages L and R, no longer using traditional
But use the iteration renewal function generated by the above method.
It is appreciated that traditional BP decoding algorithm iteration update calculate need to be implemented logarithm operation, hyperbolic functions operation,
Multiplying, add operation, complexity is relatively high, and there is no realize to calculate hyperbolic letter in actual communication system
Several and logarithmic function specialized hardware.In contrast, the iteration of method proposed by the invention updates to calculate and at most only needs to hold
2 comparison operations of row, 2 sub-addition operations, 2 signed magnitude arithmetic(al)s, 2 sub-symbol operations and 2 multiplyings, complexity obtain
It reduces significantly, and above-mentioned operation is very beneficial for the realization of hardware.Also, 2 are used compared to minimum and decoding
Sub-symbol operation takes absolute value for 2 times and 1 comparison operation, although it is in terms of considerably less invention increases multiplication calculating
Calculation complexity is cost, exchanges the larger promotion to error-correcting performance for.
In order to verify method and the difference of the prior art in effect of the invention, traditional BP has been respectively adopted in inventor
Decoding, minimum and decoding and according to the present invention provided by iteration renewal function implement the decoding for Polar code.Imitative
When true test, the code length used is 1024, code rate 0.5, total the number of iterations 60 times, and the modulation system used communicates for BPSK
The channel used is AWGN channel.Specific simulation result is as shown in Figure 5.
From figure 5 it can be seen that error-correcting performance and traditional BP interpretation method base by the improved interpretation method of the present invention
This is suitable, this method almost free of losses in performance.Also, in Eb/N0When less than 2dB, in the case where the identical bit error rate,
The error-correcting performance of present invention improvement interpretation method good 0.6dB or so than minimum and interpretation method.
As a result, the present invention provides a kind of method of determining BP decoding iteration renewal function, replaced using parabola approximation
Scheme is changed, appropriate ax is selected2Ln (cosh (x)) is replaced, can directly carry out multiplication twice in successive segmentation point range
Numerical approximation that you can get it, without directly being calculated using hyperbolic functions.Also, selected by by means of the present invention most
Excellent parabola is essentially coincided in curved portion and hyperbolic functions lncoshx, can more be characterized well compared to minimum and decoding
Iteration renewal function, this performance that iteration renewal function obtained using this method is decoded are decoded with traditional BP
The performance of algorithm is essentially identical.In addition, in the present invention, error big interval range in successive segmentation point section has been carried out parabolic
The replacement of line approximation uses Min-Sum decoding algorithm in the minimum range of other errors, changes compared in traditional BP decoding algorithm
For the hyperbolic functions of more new formula, the iteration more new formula in improved BP decoding algorithm only has addition, subtraction, compares, multiplication
And absolute value and sgn function, greatly reduce the complexity of algorithm.
It should be noted that each step introduced in above-described embodiment is all not necessary, those skilled in the art
Can carry out according to actual needs it is appropriate accept or reject, replacement, modification etc..
It should be noted last that the above examples are only used to illustrate the technical scheme of the present invention and are not limiting.On although
The invention is described in detail with reference to an embodiment for text, those skilled in the art should understand that, to skill of the invention
Art scheme is modified or replaced equivalently, and without departure from the spirit and scope of technical solution of the present invention, should all be covered at this
In the scope of the claims of invention.
Claims (12)
1. a kind of method of determining BP decoding iteration renewal function, comprising:
1) a parabolic function ax is found in the range intervals of specified x2, so that the ax in the range intervals2Function
It is worth close with the functional value of ln (cosh (x));
2) according to the parabolic function ax2Determine the ln (cosh (x)) in the iteration renewal function for BP decoding.
2. according to the method described in claim 1, wherein step 1) further include:
1-1) determine the parabolic function ax of a variety of candidates with different parameters a2;
1-2) it is directed to current parabolic function ax2, judge whether it meets following Rule of judgment, comprising: first condition: in institute
State ax in the symmetric interval of successive segmentation point2It is whether similar to ln (cosh (x));
If 1-3) current parabolic function ax2Can satisfy step 1-2) in Rule of judgment then continue step 2), otherwise adjust
Current parabolic function ax2And continue step 1-2).
3. according to the method described in claim 2, wherein step 1) further include:
1-0) choose a successive segmentation point so that when using the successive segmentation point as independent variable ln (cosh (x)) function
Value and | x | the functional value of-ln2 is close, and the successive segmentation point is for determining the range intervals of the specified x.
4. according to the method described in claim 3, step 1-2) in the Rule of judgment, further includes: second condition: described
Ax near successive segmentation point2With | x | whether-ln2 is continuous.
5. according to the method described in claim 1, wherein step 2) includes:
Using the parabolic function ax2Instead of the ln (cosh (x)) in the iteration renewal function that is decoded for BP.
6. according to the method described in claim 4, wherein step 2) includes:
According to the parabolic function ax2With | x |-ln2 determines that the iteration for BP decoding updates letter in the form of piecewise function
Number, the piecewise interval of the piecewise function are determined by the successive segmentation point.
7. according to the method described in claim 6, the iteration renewal function g (x1,x2) it is represented as:
Wherein, k is the absolute value of the successive segmentation point.
8. according to the method described in claim 4, wherein step 1-2) include:
By comparing in the symmetric interval of the successive segmentation point, ax2Whether the difference between ln (cosh (x)), which is less than, sets
Fixed threshold value, to judge current parabolic function ax2Whether the first condition is met;
When by comparing using the successive segmentation point as independent variable, ax2(| x |-ln2) whether it is less than the threshold value of setting, with judgement
Current parabolic function ax2Whether the second condition is met.
9. according to the method described in claim 6, wherein judging current parabolic function ax2Whether the second condition is met,
Include:
Multiple independents variable are selected in the symmetric interval of the successive segmentation point, are respectively compared ax when using each independent variable2With
Difference between ln (cosh (x)).
10. according to the method described in claim 4, wherein step 1-2) in the absolute value of the successive segmentation point chosen be greater than
1.5。
11. a kind of interpretation method for Polar code, comprising: in the iterative process for implementing BP decoding, using such as claim
Iteration renewal function determined by any one of 1-10 method is updated belief messages R and L.
12. a kind of computer readable storage medium, wherein being stored with computer program, the computer program is used when executed
In method of the realization as described in any one of claim 1-11.
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