CN107241106A - Polarization code decoding algorithm based on deep learning - Google Patents
Polarization code decoding algorithm based on deep learning Download PDFInfo
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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
- H03M13/11—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 using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1191—Codes on graphs other than LDPC 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
- H03M13/13—Linear codes
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Abstract
The invention discloses a kind of polarization code decoding algorithm based on deep learning, it is proposed that various dimensions scale Min sum confidence spreads (Beliefpropagation) decoding algorithm, to accelerate decoding algorithm convergence rate；Then according to the factor graph of BP algorithm and the similitude of deep neural network, realize the polarization code decoder based on deep neural network, deep neural network decoder is trained using depth learning technology, compared to the decoding iteration number of times that original BP decoding algorithms reduce nearly 90%, while achieving more preferable decoding performance；It is last The present invention gives the hardware realization of deep neural network polarization code decoder basic operation module, and reduce using hardware folding 50% hardware consumption.
Description
Technical field
The invention belongs to deep neural network and polarization code decoding field, more particularly to a kind of polarization based on deep learning
Code decoding algorithm.
Background technology
Polarization code (Polar code) is in paper " Channel in 2009 by ErdalArikan
polarization：A method for constructing capacity-achieving codes for symmetric
The a kind of of proposition can tend to the coded system of shannon limit in binary-input memoryless channels ".Channel
Polarization phenomena refer to that when channel quantity tends to infinity a part of channel tends to be perfect, and a part of channel tends to pure noise
Channel.Based on this channel-polarization phenomenon, channel relatively good in aggregate channel is chosen, polarization code is constructed.Polarization code was the 5th generation
One of highly important technology in (5G) GSM.
Most common two kinds of polarization code decoding algorithms are successive elimination (SC) algorithm and confidence spread (BP) algorithm.Its
In, SC decoding computation complexities are low, and have good error-correcting performance, but are due to the serial arithmetic structure of SC algorithms, and it is deposited
In longer decoding latency.
Compared with SC decodings, BP decodings, due to its parallel organization, decoding latency is decoded much smaller than SC in the case of long code；
But be due to BP decoding need carry out successive ignition processing, therefore BP decoding computation complexity it is very high, and decoding performance with
SC has certain gap.In order to reduce computation complexity, early stopping algorithm and Min-sum algorithms are introduced into BP decodings, but not
There is the convergence for accelerating BP decodings.People also introduce deep learning (Deeplearning) technology and deep neural network
(DNN) more preferable decoding performance is obtained, but neutral net complexity exponentially increases with code length.Therefore how multiple
It is one of emphasis of BP decoding algorithms research based on deep learning that good trade-off is obtained on miscellaneous degree and decoding performance.
The content of the invention
Goal of the invention：For problem above, the present invention proposes a kind of polarization code decoding algorithm based on deep learning, overcome
Existing polarization code BP decoding algorithms are reached with less using deep learning technology the problem of convergence rate is slow under low signal-to-noise ratio
Iterations obtains the target of more excellent decoding performance, reduction decoding complexity and decoding delay.
Technical scheme：To realize the purpose of the present invention, the technical solution adopted in the present invention is：One kind is based on deep learning
Polarization code decoding algorithm, specifically include following steps：
(1) BP algorithm based on scaling Min-sum, proposes that improved multidimensional scales Min-sum BP algorithm；
(2) similitude of factor graph and neural network structure, the expansion polarization code BP decoding factors are decoded according to polarization code BP
Figure constitutes deep neural network decoder；
(3) generate all-zero code word, after awgn channel is transmitted, using the back-propagating in deep learning technology and
Mini-batch stochastic gradient descent algorithms train deep neural network decoder；
(4) hardware structure of improved B P decoders is provided based on original BP decoders, is reduced using hardware folding
Hardware consumption.
In step (1), multidimensional scaling Min-sum BP algorithm is：
Wherein,WithRepresent to be located at BP factor graphs the i-th row jth row log-likelihood ratio characteristic in the t times iteration respectively
Information,WithThe zoom factor propagated and propagated to the right to the left for correspondence, g (x, y)=sign (x) sign (y)
min(|x|,|y|)。
In step (2), using deep neural network and the similitude of BP factor graphs, deploy polarization code factor graph, selection is solid
Determine iterations, finally output uses Sigmoid activation primitives, constitute deep neural network polarization code decoder.
In step (3), nerve is trained using back-propagating in deep learning and Mini-batch stochastic gradient descent algorithms
Network, obtains the combination of the optimal zooming parameter of multidimensional scaling Min-sum algorithms, by complete the zero of additive white Gaussian noise channel
Code word, introduces the Adam algorithms that learning rate is 0.001, and automatic adjusument learning rate accelerates deep neural network polarization code
The training convergence of decoder.
In step (4), using hardware folding, selection is suitable to fold set, and be time-multiplexed same module, folds it
Basic calculating module afterwards includes 1 adder, 1 g function module and 1 multiplier.
Beneficial effect：It is of the invention compared with original polarization code BP decoders, its remarkable advantage is：Greatly speed up decoding algorithm
Convergence rate, reduces the iterations reached needed for convergence effect, the deep neural network polarization code decoder of 5 iteration
Performance has exceeded the performance of original polarization code BP decoders 50 times, about 10 times of convergence rate；In addition, by hardware folding
Hardware consumption after processing saves about 50% compared to original deep neural network decoder.
Brief description of the drawings
Fig. 1 is 8 bit polarization code BP decoding factor graphs；
Fig. 2 is 8 bit polarization code neural network decoders once complete BP decoding iteration process figures；
Fig. 3 is the deep neural network polarization code decoder architecture figure of T iteration of 64 bit；
Fig. 4 is the basic operation module with various dimensions zoom function in polarization code decoder；
Fig. 5 is the polarization code decoder basic operation module after hardware is folded；
Fig. 6 is various dimensions scaling Min-sum computing modules；
Fig. 7 is the performance comparison figure of deep neural network polarization code decoder and conventional polar code BP decoders.
Embodiment
Technical scheme is further described with reference to the accompanying drawings and examples.
Be as shown in Figure 1 polarization code BP decoding iteration factor figure, polarization code BP decoding be on factor graph iteration to
The log-likelihood ratio information that from left to right is propagated.By taking code length N=8 polarization code as an example, high order end corresponding bit is believed in the factor graph
Cease for u, the code word that low order end correspondence receives is x.
Wherein, (i, j) represents the node of jth row in the i-th row, and each node includes log-likelihood ratio letter to the left and to the right
The information propagated to the left in breath, the t times iteration is designated asThe information propagated to the right is designated asThe starting stage is decoded to most
The information progress of left end and low order end initializes as follows：
Wherein, A represents information bit set, n=log2N。
It is iterated after conventional polar code BP decoding initializations according to below equation：
Wherein, g (x, y)=sign (x) sign (y) min (| x |, | y |), sign is sign function.
After iteration is finished, to a certain bit word if not information bit is then decoded as 0, if information bit is then sentenced according to the following formula
Certainly：
Based on the BP algorithm of existing scaling Min-sum (Scaled min-sum), improved multidimensional scaling Min- is proposed
Sum (Multiple scaled min-sum) BP algorithm, each iteration uses different zoom factors to function g, can improve
Decode effect.
Wherein,WithThe zoom factor propagated and propagated to the right to the left is corresponded to respectively.
The similitude of factor graph and neutral net is decoded using polarization code BP, expansion polarization code BP decoding factor graphs constitute deep
Spend neural network decoder.It is polarization code neural network decoder once complete BP decoding iteration process as shown in Figure 2, once
Complete 8 bit polarizations code BP iteration correspondence neutral nets, it, which is exported, passes through Sigmoid activation primitives.For 64 bit T times
The deep neural network polarization code BP decoders of iteration, its structure can be represented intactly by Fig. 3.
A number of plus noise all-zero code word is generated, loss function (Loss function) uses following cross entropy
(Crossentropy) function is fine or not to measure decoding effect：
Utilize back-propagating in deep learning (Back propagation) and Mini-batch stochastic gradient descents
(Mini-batch stochastic gradient descent) Algorithm for Training neutral net, obtains multidimensional scaling Min-sum
The optimal zooming parameter of algorithmWithCombination θ={ α, β }.Only need to by additive white Gaussian noise (AWGN) channel
All-zero code word, considerably reduces training complexity., can be adaptive by introducing the Adam algorithms that learning rate is 0.001
Learning rate is adjusted, accelerates the training convergence of deep neural network polarization code decoder.
The base in the hardware structure of improved B P decoders, deep neural network decoder is provided based on original BP decoders
This computing module can be expressed as Fig. 4, wherein, s modules are the g functions with zoom function as shown in Figure 6.Basic calculating module
It is made up of 2 adders and 2 g function modules and 2 multipliers.
Using hardware folding, selection is suitable to fold set, and be time-multiplexed same module, it is only necessary to 1 adder and 1
Individual g function modules and 1 multiplier, the basic calculating module after folding can be expressed as Fig. 5, reduce polarization code BP decodings
In device in basic calculating module nearly 50% hardware consumption.
, can be with as shown in fig. 7, the performance comparison of deep neural network polarization code decoder and conventional polar code BP decoders
Find out and greatly speed up decoding algorithm convergence rate, reduce the iterations reached needed for convergence effect, the depth god of 5 iteration
The performances of original polarization code BP decoders 50 times, about 10 times of convergence rate are exceeded through the polarize performance of code decoder of network.
Claims (5)
1. a kind of polarization code decoding algorithm based on deep learning, it is characterised in that：Specifically include following steps：
(1) BP algorithm based on scaling Min-sum, proposes that improved multidimensional scales Min-sum BP algorithm；
(2) similitude of factor graph and neural network structure, expansion polarization code BP decoding factor graph structures are decoded according to polarization code BP
Into deep neural network decoder；
(3) all-zero code word is generated, after awgn channel is transmitted, the back-propagating in deep learning technology and Mini- is utilized
Batch stochastic gradient descent algorithms train deep neural network decoder；
(4) hardware structure of improved B P decoders is provided based on original BP decoders, hardware is reduced using hardware folding
Consumption.
2. the polarization code decoding algorithm according to claim 1 based on deep learning, it is characterised in that：The step (1)
In, multidimensional scaling Min-sum BP algorithm is：
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Wherein,WithRepresent to be located at BP factor graphs the i-th row jth row log-likelihood ratio characteristic information in the t times iteration respectively,WithThe zoom factor propagated and propagated to the right to the left for correspondence, g (x, y)=sign (x) sign (y) min (| x |,
|y|)。
3. the polarization code decoding algorithm according to claim 1 based on deep learning, it is characterised in that：The step (2)
In, using deep neural network and the similitude of BP factor graphs, deploy polarization code factor graph, select fixed number of iterations, finally
Output uses Sigmoid activation primitives, constitutes deep neural network polarization code decoder.
4. the polarization code decoding algorithm according to claim 1 based on deep learning, it is characterised in that：The step (3)
In, neutral net is trained using back-propagating in deep learning and Mini-batch stochastic gradient descent algorithms, multidimensional contracting is obtained
The combination of the optimal zooming parameter of Min-sum algorithms is put, by the all-zero code word of additive white Gaussian noise channel, study speed is introduced
Rate is 0.001 Adam algorithms, and automatic adjusument learning rate, the training for accelerating deep neural network polarization code decoder is received
Hold back.
5. the polarization code decoding algorithm according to claim 1 based on deep learning, it is characterised in that：The step (4)
In, using hardware folding, selection is suitable to fold set, and be time-multiplexed same module, the basic calculating mould after folding
Block includes 1 adder, 1 g function module and 1 multiplier.
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| CN107659318A (en) * | 2017-11-07 | 2018-02-02 | 东南大学 | A kind of adaptive polarization code coding method |
| CN108023679A (en) * | 2017-12-07 | 2018-05-11 | 中国电子科技集团公司第五十四研究所 | Iterative decoding zoom factor optimization method based on parallel cascade system polarization code |
| CN108092672A (en) * | 2018-01-15 | 2018-05-29 | 中国传媒大学 | A kind of BP interpretation methods based on folding scheduling |
| CN108199807A (en) * | 2018-01-19 | 2018-06-22 | 电子科技大学 | A kind of polarization code reliability estimation methods |
| CN108418588A (en) * | 2018-01-17 | 2018-08-17 | 中国计量大学 | Low latency polarization code SMS design of encoder |
| CN108449091A (en) * | 2018-03-26 | 2018-08-24 | 东南大学 | A kind of polarization code belief propagation interpretation method and decoder based on approximate calculation |
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