CN107612560A - Polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio - Google Patents
Polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio Download PDFInfo
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Abstract
The invention discloses a kind of polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio, comprise the following steps：S1 the maximum iteration of BP decodings) is preset；S2 row decoding) is entered to Polarization Coding information using BP decoding algorithms；S3) after the completion of an iteration, the adjacent output par, c of iterative decoding twice information bit likelihood ratio is compared；If wherein ratio of the identical information bit likelihood ratio in default relatively space reaches predetermined threshold value, stop iteration and export the decoding result obtained by current iteration, otherwise, continue iteration, until reaching default maximum iteration.The present invention is judged the partial information bit log likelihood ratio of front and rear iterative decoder twice output in iterative process each time；Stop if ratio of the identical information bit likelihood ratio in relatively space reaches predetermined threshold value, so as to substantially reduce the computation complexity of decoding and decoding delay, effectively reduce hardware resource consumption.
Description
Technical field
The present invention relates to a kind of polarization code processing method, more particularly to a kind of polarization based on partial information bit log likelihood ratio
Code earlier iterations method of shutting down.
Background technology
Based on channel-polarization phenomenon, Arikan proposes a kind of code word of capacity " reachable " in ISIT meetings within 2008,
Referred to as Polar codes, its in paper Strict Proof in binary system discrete memoryless channel(DMC) when code length tends to be infinite
Channel capacity can reach Shannon circle.At decoding end, Arikan proposes a kind of serial interpretation method simultaneously, claims serial offset to calculate
Method (Successive cancellation, SC).Because its serial decoding structure, SC algorithm decoding latencies are higher.In order to reduce
Decoding latency, confidence spread (Belief propagation, BP) algorithm of iteration are also used for the decoding of Polar codes.
BP algorithm is parallel, and its decoding latency is O (IlogN), and wherein I is iterations.It follows that reduce iteration time
Number is extremely important for reducing BP algorithm decoding latency.Traditional BP algorithm, which reaches default maximum iteration, can just stop, actual
Middle correct decoding result will obtain in iteration early stage, so correlative study person proposes a variety of earlier iterations method of shutting down to keep away
Exempt from unnecessary iteration, such as the methods of minLLR, G-Martix, LMA and CA.Earlier iterations method of shutting down is right during decoding
Decoding result is detected, and stops iteration output decoding if stopping criterion is met as a result, it is possible to effectively reduce Average Iteration
Number.The existing general complexity of earlier iterations method of shutting down is higher, proposes a kind of lower earlier iterations stopping side of complexity
Method is important research direction.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of polarization code early stage based on partial information bit log likelihood ratio
Iteration stopping method, can substantially reduce the computation complexity and decoding delay of decoding, while be easy to hardware to realize.
The present invention is to provide one kind for the technical scheme that solution above-mentioned technical problem uses and is based on partial information bit seemingly
The polarization code earlier iterations method of shutting down of right ratio, comprises the following steps：S1 the maximum iteration of BP decodings) is preset；S2) utilize
BP decoding algorithms enter row decoding to polarization code coding information；S3 it is defeated to the adjacent BP decoders of iteration twice) after the completion of an iteration
The partial information bit log likelihood ratio gone out is compared；If wherein identical information bit likelihood ratio is in default relatively space
Ratio reach predetermined threshold value, then stop iteration and export current iteration step obtained by decoding result, otherwise, continue to change
Generation, until reaching default maximum iteration.
The above-mentioned polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio, wherein, the polarization code
Code length be N, the polarization code includes K positions information bit, if set A be information bit set, setIt is referred to as more empty
Between, the setComprising the M positions information bit that error probability in A is minimum, M is referred to as comparing spatial content, K >=M>0, each
The error probability of polarisation channel emulates to obtain by Gaussian approximation method, the step S3) if meeting such as lower inequality, stop
Iteration：
Wherein, R is proportion threshold value, its span for R | 0<R≤1 },Represent the 1st row i-th in BP algorithm factor graph
The L information of row node.
The above-mentioned polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio, wherein, it is for parameter
The polarization code of (N, K), its corresponding factor graph is by n=log2N ranks computing unit and n+1 row node are formed, per rank by N/2 processing
Unit is formed, and (i, j) is represented from the i-th row from left to right, the node of jth row；Each node passes through node (i, j) from right to left
Soft Inform ation is designated as Li,j, the Soft Inform ation for from left to right passing through node (i, j) is designated as Ri,j, 1 row of factor graph high order end are saved
Soft Inform ation in point carries out the estimate that hard decision can obtain information bit sequence uThe step S2) renewal is first propagated to the left
L in nodei,j, start to propagate the R in more new node to the right after reaching the leftmost sidei,j；After iteration ends, if not information bit
Then the position is decoded as 0, otherwise according to the L in high order end nodei,1Symbol decision information bit be 0 or 1.
The above-mentioned polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio, wherein, the step S3)
Realize that earlier iterations stop mechanism by the way that comparator, adder and threshold comparator is applied in combination；M ratio is used after each iteration
Obtained by comparing current iteration compared with deviceObtained by last iterationT-1 iterationFrom BP
Read in the memory of decoder, t iterationDirectly obtained from decoder processing unit；The comparative result of comparator
For { q1,q2,...,qM, ifThen qi=1, otherwise qi=0；Adder is used to calculateKnot
Fruit isThreshold comparator judges whether Q is more than or equal to M*R, if exporting D=1 more than or equal to if, otherwise exports 0；D
=1 BP decoder stops iteration output decoding result, and then BP decoders continuation iteration changes D=0 until reaching default maximum
Generation number.
The above-mentioned polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio, wherein, the maximum changes
Generation number is preset as 15~80.
Present invention contrast prior art has following beneficial effect：It is provided by the invention to be based on partial information bit log likelihood ratio
Polarization code earlier iterations method of shutting down, after the completion of an iteration, the letter in space is compared to belonging to for adjacent iteration twice output
Breath bit log likelihood ratio is compared；If wherein ratio of the identical information bit likelihood ratio in relatively space reaches default threshold
Value, then stop iteration and export the decoding result obtained by current iteration step.When maximum iteration is 40 times and Eb/N0=
During 3.5dB, compared with the original BP decoders of fixed iteration 40 times, the present invention can make mean iterative number of time reduce 83.16%, have
Effect reduces computation complexity and decoding latency.The add operation complexity of minLLR standards is N, and comparison operation complexity is N；
The add operation complexity of LMA standards is 2N, and comparison operation complexity is N.Add operation complexity of the invention by comparison
Only N/32, the complexity of comparison operation is N/32+1, can effectively reduce the hardware complexity of earlier iterations stopping criterion.
Brief description of the drawings
Fig. 1 is the polarization code factor graph that parameter of the present invention is (8,4)；
Fig. 2 is the elementary cell schematic diagram of polarization code factor graph of the present invention；
Fig. 3 is that earlier iterations of the present invention stop schematic flow sheet；
Fig. 4 is earlier iterations stopping modular hardware configuration of the present invention；
Fig. 5 is the polarization code that parameter of the present invention is (1024,512), the BP interpretation methods that maximum iteration is 40 and original
Mean iterative number of time comparison schematic diagram of the beginning BP decoder under different signal to noise ratio channels；
Fig. 6 parameters of the present invention be (1024,512) polarization code, maximum iteration be 40 BP interpretation methods with it is original
The decoding performance comparison schematic diagram of BP decoders.
Embodiment
The invention will be further described with reference to the accompanying drawings and examples.
In order to reduce the decoding complexity of BP decoding algorithms, it is particularly significant that earlier iterations stop algorithm.Earlier iterations stop
Algorithm refers to adaptively detect whether to have obtained reliable decoding output in decoding iteration process, if condition satisfaction can
To terminate to decode at once.Earlier iterations, which stop algorithm, can linearly reduce decoding complexity and decoding delay.The present invention provides
The polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio, comprise the following steps：
S1 the maximum iteration of BP decodings) is preset；
S2 row decoding) is entered to Polarization Coding information using BP decoding algorithms；
S3) after the completion of an iteration, belonging to for adjacent iteration twice output is compared by the information bit likelihood ratio in space entered
Row compares；If wherein ratio of the identical information bit likelihood ratio in relatively space reaches predetermined threshold value, stop iteration
And the decoding result obtained by current iteration step is exported, otherwise, continue iteration, until reaching default greatest iteration time
Number.
The present invention's has the polarization code BP interpretation methods that earlier iterations stop mechanism, and channel is connect using BP decoding algorithms
Receipts are worth as follows into row decoding, information updating formula：
f(x,y)≈α*sign(x)sign(y)min(|x|,|y|) (2)
Code length is that N Polar codes include K positions information bit, if set A is the set of information bit.SetIt is referred to as comparing
Space, include M (K >=M that error probability in A is minimum>0) position information bit, M are referred to as comparing spatial content, each polarisation channel
Error probability can emulate to obtain by Gaussian approximation method.Entering the iteration each time of row decoding to polarization code using BP decoders
During, stop iteration, output decoding result if inequality (3) is met.
Wherein 0≤R≤1,Represent the L information of the 1st row the i-th row node in BP algorithm factor graph.If it is unsatisfactory for inequality
(3) iteration, is then continued, until reaching default maximum iteration.
Scheme compared with prior art, the present invention can be substantially reduced decoding in the case where not causing decoding performance to lose and change
Generation number.For (1024,512) polarization code, when maximum iteration is 40 times and Eb/E0=3.5dB, the present invention can make to put down
Equal iterations reduces by 83.16%, effectively reduces computation complexity and decoding latency.The present invention add operation complexity be
N/32, comparison operation complexity are N/32+1.
The present embodiment uses parameter to be tested for the Polar codes of (1024,512), code length N=1024, K=512, code
Rate is 0.5.Using Gaussian approximation method, in the case where signal to noise ratio is 1.5dB, emulation obtains the error probability of 1024 sub-channels, mistake
512 minimum sub-channels positions of probability form set A, for transmitting information, referred to as information bit；Remaining 512 channels are used
In transmission fix information, it is referred to as freezing position.Modulation system be binary phase shift keying (Binary Phase Shift Keying,
BPSK), channel is additive white Gaussian noise channel (Additive White Gaussian Noise, AWGN).Code wordBy
Length is 1024It is multiplied to obtain with generator matrix G.Generator matrix Representing matrix's
log21024=10 Kronecker product.Channel reception value Y1 NUse log-likelihood ratio (Log-likelihood ratio, LLR)
Form represents.1 bit sign position is used in the present embodiment, 4 integer-bits, 7 quantization schemes of 2 decimal places, is easy to hardware real
It is existing.
Parameter is the factor graph of the polarization code of (1024,512) by log2(code length is 8 factor graph to 1024=10 ranks composition
As shown in Figure 1), wherein being made up of (Fig. 2 is single processing unit schematic diagram) N/2=512 processing unit per rank.Factor graph is most
One row corresponding informance bit u of left end.(i, j) is represented from the i-th row from left to right, the node of jth row.Each node has two kinds of letters
The information for passing through node (i, j) from right to left is designated as L by breath, the present inventioni,j, will from left to right pass through node (i, j)
Information be designated as Ri,j, these information mutually transmit renewal in the form of LLR.
During decoding, it is 40 times to preset iteration maximum iteration, first to Ri,1And Li,n+1Initialized.Li,n+1
It is initialized as channel acceptance value Yi, Ri,1It is initialized as the maximum that 0 and 7 quantization scheme can represent respectively according to positional information
15.75.Specific formula is as follows：
Li,n+1=Yi (5)
α=0.9 is set in the present embodiment, according to formula (1), (2) first propagate the L in more new node to the lefti,j, reach the leftmost side
After start to propagate to the right start update Ri,j。
The basic procedure of the inventive method is as shown in Figure 3.Parameter M is set to 32 in the present embodiment, and β value is set to 1/4.In order to drop
The computation complexity and decoding delay of low decoding, if Li,1, keep in i ∈ S constant ratio to be more than 1/ in front and rear iteration twice
4, decoding output can now is considered reliable decoding output.Specific formula is as follows：
If being unsatisfactory for formula (6), judge to decode whether number reaches 40 times, terminated repeatedly if maximum iteration is reached
Generation；If it is not, continuing fresh information, next iteration is carried out.
After iteration ends, if freezing position, then the position is decoded as 0, otherwise according to the L in high order end nodei,1Symbol
It is 0 or 1 to judge information bit, obtains decoding result.The formula of BP decoder hard decision foundations is as follows：
Fig. 4 is the earlier iterations stopping modular hardware structure of the present embodiment, is compared after each iteration using M comparator and worked as
Obtained by preceding iterationObtained by last iterationT-1 iterationFrom depositing for BP decoders
Read in reservoir, t iterationDirectly obtained from decoder processing unit.The comparative result of comparator is { q1,
q2,...,qM, ifThen qi=1, otherwise qi=0.Adder is used to calculateAs a result it isThreshold value R is set to 1/4 in the present embodiment, and threshold comparator judges whether Q is more than or equal to M*R, if defeated more than or equal to if
Go out D=1, otherwise export 0.BP decoders judge whether to stop iteration, i.e. D=according to the output result of earlier iterations stopping modular
Decoder stops iteration output decoding result when 1, continues iteration during D=0 until reaching maximum iteration.
Following table contrasts for the method for the present invention and the computation complexity of other two kinds of earlier iterations stopping criterions.The present embodiment
Middle M=N/32, then add operation complexity of the invention is N/32, and the complexity of comparison operation is N/32+1, is effectively reduced
The computation complexity of earlier iterations stopping criterion.
| Early stage stopping criterion | minLLR | LMA | The present invention |
| Add operation | N | 2N | N/32 |
| Comparison operation | N | N | N/32+1 |
Fig. 5 shows Average Iteration of this implementation from conventional polar code BP interpretation methods in different signal to noise ratio channels
Number.Eb/N0 is signal to noise ratio in figure, and Average number of iterations represent mean iterative number of time.Work as greatest iteration
When number is 40 times and Eb/N0=3.5dB, compared with iterations is fixed as the original BP decoders of 40 times, the present invention can make
Mean iterative number of time reduces 83.16%, and compared with minLLR (β=9.5) and LMA, iteration reduces performance and rises 6.48% respectively
With 8.14%.
Fig. 6 shows the test result of this implementation and conventional polar code BP decoders in Gauss additive white noise channel.
Abscissa Eb/N0 is signal to noise ratio in figure, and fer is FER in legend, and ber is bit error rate, and 40Fixed Iteration are represented
Iterations is fixed as 40 times.It can be seen that the present invention can be in situation of the iterations considerably less than traditional BP decoder according to Fig. 6
Under, reach the decoding performance as traditional BP decoder, do not cause decoding performance to lose.
Although the present invention is disclosed as above with preferred embodiment, so it is not limited to the present invention, any this area skill
Art personnel, without departing from the spirit and scope of the present invention, when a little modification and perfect, therefore the protection model of the present invention can be made
Enclose to work as and be defined by what claims were defined.
Claims (5)
1. a kind of polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio, it is characterised in that including as follows
Step：
S1 the maximum iteration of BP decodings) is preset；
S2 row decoding) is entered to polarization code coding information using BP decoding algorithms；
S3) after the completion of an iteration, the partial information bit log likelihood ratio of the adjacent BP of iteration twice decoders output is compared；
If wherein ratio of the identical information bit likelihood ratio in default relatively space reaches predetermined threshold value, stop iteration simultaneously
The decoding result obtained by current iteration is exported, otherwise, continues iteration, until reaching default maximum iteration.
2. the polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio as claimed in claim 1, its feature
It is, the code length of the polarization code is N, and the polarization code includes K positions information bit, if set A is the set of information bit, setIt is referred to as comparing space, the setComprising the M positions information bit that error probability in A is minimum, M is referred to as comparing space
Capacity, K >=M>0, the error probability of each polarisation channel emulates to obtain by Gaussian approximation method, the step S3) if meeting
Such as lower inequality, then stop iteration：
Wherein, R is proportion threshold value, its span for R | 0<R≤1 },Represent the 1st row the i-th row section in BP algorithm factor graph
The L information of point.
3. the polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio as claimed in claim 2, its feature
It is, for the polarization code that parameter is (N, K), its corresponding factor graph is by n=log2N ranks computing unit and n+1 row node are formed,
It is made up of per rank N/2 processing unit, (i, j) is represented from the i-th row from left to right, the node of jth row；Each node transmits from right to left
L is designated as by the Soft Inform ation of node (i, j)i,j, the Soft Inform ation for from left to right passing through node (i, j) is designated as Ri,j, to the factor
Soft Inform ation in 1 row node of figure high order end carries out the estimate that hard decision can obtain information bit sequence uThe step S2)
The L in more new node is first propagated to the lefti,j, start to propagate the R in more new node to the right after reaching the leftmost sidei,j；After iteration ends,
If not information bit, then the position is decoded as 0, otherwise according to the L in high order end nodei,1Symbol decision information bit be 0 or
1。
4. the polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio as claimed in claim 3, its feature
It is, the step S3) realize that earlier iterations stop mechanism by the way that comparator, adder and threshold comparator is applied in combination；Often
Obtained by comparing current iteration using M comparator after secondary iterationObtained by last iteration
T-1 iterationRead from the memory of BP decoders, t iterationDirectly obtained from decoder processing unit
；The comparative result of comparator is { q1,q2,...,qM, ifThen qi=1, otherwise qi=0；Adder is used to calculateAs a result it isThreshold comparator judges whether Q is more than or equal to M*R, if more than or equal to if
D=1 is exported, otherwise exports 0；Then BP decoders stop iteration output decoding result to D=1, and then BP decoders continue iteration to D=0
Until reaching default maximum iteration.
5. the polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio as claimed in claim 4, its feature
It is, the maximum iteration is preset as 15~80.
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| CN111726202A (en) * | 2020-06-16 | 2020-09-29 | 杭州电子科技大学 | Early termination iteration method for polarization code belief propagation decoding |
| CN113938227A (en) * | 2021-10-08 | 2022-01-14 | 天津津航计算技术研究所 | Signal-to-noise ratio dynamic judgment method based on iterative decoding |
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