CN106877883A - A kind of LDPC interpretation methods and device based on limited Boltzmann machine - Google Patents
A kind of LDPC interpretation methods and device based on limited Boltzmann machine Download PDFInfo
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- 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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Abstract
The present invention discloses a kind of LDPC interpretation methods and device based on limited Boltzmann machine, be combined for limited Boltzmann machine in traditional LDPC decoding algorithms and neutral net by the method, LDPC decodings process is modeled using mathematical description more ripe in limited Boltzmann machine, determine energy function, again by training minimum energy function, the code word after finally being decoded.The method and device can describe the limited Boltzmann machine that high dimensional nonlinear maps by introducing, and more subtly be iterated decoding, obtain than the more preferable effect of standard BP decoding algorithm optimal before.
Description
Technical field
The present invention relates to technical field of electronic communication, particularly a kind of LDPC interpretation methods based on limited Boltzmann machine
And device.
Background technology
Loe-density parity-check code (LDPC, Low Density Parity Check codes) is a kind of to approach shannon limit
Modern coding techniques, due to its superior performance and the characteristics of be easy to Parallel Implementation, LDPC is by various modern communication standard
Adopt.But at present in the practical applications such as mobile communication, SSD error correction, bit error rate of the LDPC based on traditional BP decoding technique etc.
Performance is preferable not enough, it is necessary to new method and apparatus further reduce the bit error rate, to adapt to the demand of application.
LDPC interpretation methods and device based on limited Boltzmann machine are built upon the limited glass in neutral net category
The graceful machine of Wurz is theoretic.Limited Boltzmann machine can cause that the value of aobvious layer neuron reaches Bohr of stabilization maximum likelihood
Zi Man is distributed.The advantage of limited Boltzmann machine is that it is a kind of structure that can accurately describe high dimensional nonlinear mapping,
And the value of aobvious layer neuron can be more subtly changed when being trained by gradient descent method, therefore, it is possible to than traditional BP
Interpretation method has the lower bit error rate.
The content of the invention：
The present invention shows more excellent method to find than BP decoding algorithms best before, it is proposed that one kind is based on receiving
The new LDPC interpretation methods and device of Boltzmann machine are limited, so as to further reduce the bit error rate.The present invention is by being limited Bohr
Hereby the thought of graceful machine goes back original sender data as far as possible from the receiving sequence containing noise and interference, can be used for the communications field
The correcting data error of receiver and SSD.
Technical scheme：A kind of LDPC interpretation methods based on limited Boltzmann machine, comprise the following steps：
(1) check matrix H is determined according to application demand, size is m × n, row weight is L, and row weight is K.
(2) Tanner figures are set up according to check matrix, determines the annexation of variable node and check-node.
(3) limited Boltzmann machine model is set up according to Tanner figures, the variable node in Tanner figures is used as aobvious layer god
Through unit, check-node is used as hidden neuron.
(4) Boolean expression of XOR is input into according to KConstruct the output of hidden neuron
Function.The Boolean expression of K input XORs is rewritten into the form of minterm sum, for the change of Boolean type in Boolean expression
Amount Xi, with real-valued variable expression 1+xiReplace, for the variable of Boolean typeWith real-valued variable expression 1-xiReplace, wherein
xiIt is the value of information bit.
(5) energy function of limited Boltzmann machine is constructed, energy function is：
E in formulajIt is j-th output of hidden neuron in (4), E is the energy of whole model.
(6) value of the information bit after the BPSK modulation that will be received is assigned to aobvious layer neuron.
(7) feedforward is calculated, and the value of aobvious layer neuron passes to hidden neuron, and the output function determined by (4) is calculated
Hidden neuron ejValue and energy function E value.
(8) feedback is calculated, the energy function value according to obtained by current iteration, and aobvious layer neuron is changed by gradient descent method
Value, specific method is as follows：
X in formulaiI-th value of information bit is represented, α represents learning rate, for regulating and controlling the step-length that each iteration declines, asked
With the gradient summation for being the L hidden neuron offer participated in each information bit.
(9) value of aobvious layer neuron is updated, hard decision is carried out, it is small even the value of the aobvious layer neuron more than or equal to 0 is 1
In 0 aobvious layer neuron value be -1, the energy function brought into (5).It is successfully decoded if E=0；Otherwise repeat step (7)
(8)。
(10) when maximum iteration of the iterations more than setting, no longer enter row decoding, directly export.
Based on the code translator of limited Boltzmann machine, including following part：
(1) control module, the execution sequence for controlling code translator.
(2) feedover computing module, for calculating (7) in the above method, including with hidden neuron number identical simultaneously
Row output function computing module and energy function computing module.
(3) computing module is fed back, for calculating (8) in the above method, including parallel gradient computing module and corresponding
Correction value computing module, the intermediate result of the shared output function computing module of gradient calculation module.
(4) show layer neuron assignment module, the correction value of computing module output and the aobvious layer god of last iteration will be fed back
It is added through the value of unit, feeding feedforward computing module.
Advantage of the invention：
The present invention has used for reference powerful neural network algorithm generally acknowledged at present, using the thought of limited Boltzmann machine
LDPC decodings process is modeled, information bit is solved indirectly using the mode for minimizing energy function.Due to being limited glass
The boolean's table for mapping high dimensional nonlinear powerful expression ability and the utilization XOR for using here that the graceful machine of Wurz has in itself
The method that hidden neuron output function is constructed up to formula, interpretation method proposed by the present invention is under nearly all state of signal-to-noise
All show the performance more excellent than BP algorithm.The present invention can be used for the receiver of various communication systems and solid state hard disc data
The application scenarios such as error correction.
Brief description of the drawings
Fig. 1 is the structure chart of the limited Boltzmann machine code translator that the present invention builds；
Fig. 2 is the flow chart of interpretation method proposed by the present invention；
Fig. 3 is that the bit error rate of method proposed by the present invention and BP algorithm in embodiment compares.
Specific embodiment
With reference to embodiment and accompanying drawing, the present invention is further described, but embodiments of the present invention are not limited to
This.
The present invention with LDPC code that (100,200,3,6) code check is 1/2 as embodiment, to proposed by the present invention based on glass
The LDPC interpretation methods of the graceful machine of Wurz and being described in detail for device.
The check matrix H of the LDPC code of (100,200,3,6) in embodiment is the matrix of the dimensions of 100x 200, and row are again 3,
Row is again 6.The information bit for receiving is yi.Fig. 1 gives the structure chart of limited Boltzmann machine code translator.
The flow of decoding algorithm as shown in Fig. 2 enter row decoding the step of according to flow chart successively.
(1) check matrix H is determined, 100x200 dimensions, row weight is 3, row weight is 6.
(2) Tanner figures are drawn according to check matrix, determines the annexation of variable node and check-node.
(3) limited Boltzmann machine model is built according to tanner graph, the variable node in Tanner figures is used as aobvious layer nerve
Unit, check-node is used as hidden neuron.
(4) according to the Boolean expression of 6 input XORsConstruction hidden layer god
Through the output function of unit.The Boolean expression of 6 input XORs is rewritten into the form of minterm sum, 32 minterms are had.
For the variable X of Boolean type in Boolean expression each mintermi, with real-valued variable expression 1+xiReplace, for Boolean type
VariableWith real-valued variable expression 1-xiReplace, wherein xiIt is the value of information bit.
(5) energy function of limited Boltzmann machine is constructed, energy function is：
E in formulaiIt is j-th output of hidden neuron in (4), E is the energy of whole model.
(6) value of the information bit after the BPSK modulation that will be received is assigned to aobvious layer neuron, xi=yi。
(7) feedforward is calculated, and the value of aobvious layer neuron passes to hidden neuron, and the output function determined by (4) is calculated
Hidden neuron ejValue and energy function E value.
(8) feedback is calculated, the energy function value according to obtained by current iteration, and aobvious layer neuron is changed by gradient descent method
Value, specific method is as follows：
X in formulaiI-th value of information bit is represented, α represents learning rate, 0.01 is taken here, for regulating and controlling under each iteration
The step-length of drop, summation is the gradient summation provided 3 hidden neurons that each information bit is participated in.
(9) the value x of aobvious layer neuron is updatedi=xi+Δxi, hard decision is carried out, even the aobvious layer neuron more than or equal to 0
Value be 1, the value of the aobvious layer neuron less than 0 is -1, is brought into (5).It is successfully decoded if E=0；Otherwise repeat step (7)
(8)。
(10) when maximum iteration of the iterations more than setting, no longer enter row decoding, directly export, it is maximum here
Iterations takes 400.
LDPC code translators based on limited Boltzmann machine, including control module, feedforward computing module, feedback calculate mould
Block, aobvious layer neuron assignment module, device under the regulation and control of control module, when each iteration starts by aobvious layer neuron assignment
Information bit feeding feedforward computing module in module, the value and energy function value of the hidden neuron that feedforward is calculated are sent
Enter to feed back the correction value that computing module calculates Grad and aobvious layer neuron, finally show layer neuron by current iteration information bit
Initial value be added with correction value, obtain the information bit of next iteration；
Control module, the execution sequence for controlling code translator；
Feedforward computing module is used to for the value of aobvious layer neuron to pass to hidden neuron, by the hidden neuron for constructing
Output function calculate hidden neuron ejValue and energy function E value, it is including parallel with hidden neuron number identical
Output function computing module and energy function computing module；Aobvious layer neuron x of the output function computing module according to inputiValue
Calculate hidden neuron ejValue, and export and give energy function computing module；Energy function computing module is according to output function meter
The calculating of the output computation energy function E of module is calculated, if E=0, stops iteration signal to control module output, otherwise to anti-
The value of feedback computing module output energy function E；
Energy function value of the feedback computing module according to obtained by current iteration, aobvious layer neuron is changed by gradient descent method
Value, specific method is as follows：
X in formulaiI-th value of information bit is represented, α represents learning rate, for regulating and controlling the step-length that each iteration declines, asked
With the gradient summation for being the L hidden neuron offer participated in each information bit；Including parallel gradient computing module and
Corresponding correction value computing module.It is right that the value of the hidden neuron that gradient calculation module is exported according to feedforward computing module calculates its
Should be in the gradient of each aobvious layer neuron, i.e.,Because Grad is identical with the intermediate result of output function computing module, because
The intermediate result of the shared output function computing module of this gradient calculation module；It is defeated that correction value computing module receives gradient calculation module
The Grad for going out, is weighted summation, multiplies the computings such as learning rate, to aobvious layer neuron assignment according to above-mentioned specific method packet
Module output Δ xi；
Aobvious layer neuron assignment module, will feed back the correction value of computing module output and the aobvious layer god of last iteration
It is added through the value of unit, feeding feedforward computing module.
When entering row decoding using this code translator, follow the steps below.
(1) initialize, the initial value of the information bit that will be received is input to aobvious layer neuron assignment module.
(2) by the value x of aobvious layer neuroniFeedforward computing module is input to, by the output function meter in feedforward computing module
Calculate modular concurrent ground and calculate value e because of once neuronj, the e that energy function computing module is exported by output function computing modulejMeter
Energy function E is calculated, if E=0, stopping iteration signal being sent to control module, now just the value of aobvious layer neuron is decoding
Successfully it is worth；Otherwise, to feedback computing module output E and ej。
(3) the gradient calculation module in feedback computing module passes through ejCalculated with the intermediate result in feedforward computing module
Corresponding GradIncoming correction value computing module；Correction value computing module is calculated by Grad and hidden neuron value
Go out the correction value Δ x of aobvious layer neuroni, it is input to aobvious layer neuron assignment module.
(4) layer neuron assignment module is shown by the initial value x of current iterationiWith correction value Δ xiIt is added, is changed next time
The initial value in generation.
(5) when the iteration count in control module reaches 400, decoding is stopped, output now shows the value of layer neuron.
Interpretation method proposed by the present invention is mainly by powerful neural network algorithm and LDPC decoding generally acknowledged at present
Be combined, using limited Boltzmann machine thought to LDPC decoding process be modeled, using the Boolean expression of XOR come
Construct hidden neuron output function and solve information bit indirectly using the mode for minimizing energy function.Additionally, this hair
It is bright also appropriate to have selected learning rate and end condition to improve the decoding efficiency of decoding algorithm.Fig. 3 gives proposition of the present invention
Method and BP algorithm be that the bit error rate in 1/2 LDPC code compares in (100,200,3,6) code check, it can be seen that the present invention is carried
The interpretation method for going out all shows the performance more excellent than BP algorithm under nearly all state of signal-to-noise.
Code translator proposed by the present invention is based on foregoing interpretation method and builds, including control module, feedforward computing module,
Feedback computing module, aobvious layer neuron assignment module.Because the gradient calculation in feedback procedure is needed using big in calculating process
Intermediate result in amount feedforward calculating, therefore the present apparatus have effectively achieved the shared of intermediate result, greatly reduce redundancy meter
Calculate, reduce computational complexity.Additionally, the present apparatus has also carried out streamlined and parallelization treatment to handling process, greatly improve
Calculating speed, reduces decoding latency.
Above-described embodiment is one embodiment of the present invention, but method proposed by the present invention should not be limited by the examples,
Other it is any without departing from the modification done under essence of the invention and principle, replacement, combination, simplification should be equivalent displacement side
Formula, is included in protection scope of the present invention.
Claims (3)
1. a kind of LDPC interpretation methods based on limited Boltzmann machine, it is characterised in that comprise the following steps：
(1) check matrix H is determined according to application demand, size is m × n, and row weight is L, and row weight is K；
(2) Tanner figures are set up in the position according to " 1 " in check matrix, determine the annexation of variable node and check-node；
(3) limited Boltzmann machine model is set up according to Tanner figures, the variable node in Tanner figures as aobvious layer neuron,
Check-node is used as hidden neuron；
(4) the Boolean expression e=X of XOR is input into according to K1⊕X2⊕…⊕Xk, construct the output function of hidden neuron；By K
The Boolean expression for being input into XOR is rewritten into the form of minterm sum, for the variable X of Boolean type in Boolean expressioni, use
Real-valued variable expression 1+xiReplace, for the variable of Boolean typeWith real-valued variable expression 1-xiReplace, wherein xiIt is letter
Cease the value of bit；
(5) energy function of limited Boltzmann machine is constructed, energy function is：E in formulajFor j-th in (4)
The output of hidden neuron, E is the energy of whole model；
(6) value of the information bit after the BPSK modulation that will be received is assigned to aobvious layer neuron；
(7) feedforward is calculated, and the value of aobvious layer neuron passes to hidden neuron, and the output function determined by (4) calculates hidden layer
Neuron ejValue and energy function E value；
(8) feedback is calculated, the energy function value according to obtained by current iteration, and aobvious layer neuron is changed by gradient descent method
Value, specific method is as follows：
X in formulaiI-th value of information bit is represented, α represents learning rate, for regulating and controlling the step-length that each iteration declines, summation is
The gradient summation provided the L hidden neuron that each information bit is participated in.
(9) value of aobvious layer neuron is updated, hard decision is carried out, even the value of the aobvious layer neuron more than or equal to 0 is 1, less than 0
The value of aobvious layer neuron is -1, the energy function brought into (5).It is successfully decoded if E=0；Otherwise repeat step (7) (8)；
(10) when maximum iteration of the iterations more than setting, no longer enter row decoding, directly export.
2. LDPC interpretation methods based on limited Boltzmann machine according to claim 1, it is characterised in that：Using limited
Boltzmann machine is modeled to LDPC decodings process, and continuously differentiable hidden neuron is constructed by the Boolean expression of XOR
Output function, optimal information bit distribution is obtained by way of minimizing energy function；Minimizing energy function
During use gradient descent method, can adaptively according to the far and near adjusting step apart from optimization aim.
3. a kind of LDPC code translators based on limited Boltzmann machine, it is characterised in that calculate mould including control module, feedforward
Block, feedback computing module, aobvious layer neuron assignment module, device, will when each iteration starts under the regulation and control of control module
Information bit feeding feedforward computing module in aobvious layer neuron assignment module, the value of the hidden neuron that feedforward is calculated
Correction value with energy function value feeding feedback computing module calculates Grad and aobvious layer neuron, finally shows layer neuron and incite somebody to action this
The initial value of secondary iterative information bit is added with correction value, obtains the information bit of next iteration；
The control module, the execution sequence for controlling code translator；
The feedforward computing module is used to for the value of aobvious layer neuron to pass to hidden neuron, by the hidden neuron for constructing
Output function calculate hidden neuron ejValue and energy function E value, it is including parallel with hidden neuron number identical
Output function computing module and energy function computing module；Aobvious layer neuron x of the output function computing module according to inputiValue
Calculate hidden neuron ejValue, and export and give energy function computing module；Energy function computing module is according to output function meter
The calculating of the output computation energy function E of module is calculated, if E=0, stops iteration signal to control module output, otherwise to anti-
The value of feedback computing module output energy function E；
Energy function value of the feedback computing module according to obtained by current iteration, aobvious layer neuron is changed by gradient descent method
Value, specific method is as follows：
X in formulaiI-th value of information bit is represented, α represents learning rate, for regulating and controlling the step-length that each iteration declines, summation is
The gradient summation provided the L hidden neuron that each information bit is participated in；Including parallel gradient computing module and correspondence
Correction value computing module.The value of the hidden neuron that gradient calculation module is exported according to feedforward computing module calculates it and corresponds to
The gradient of each aobvious layer neuron, i.e.,Because Grad is identical with the intermediate result of output function computing module, therefore ladder
The intermediate result of the shared output function computing module of degree computing module；Correction value computing module receives the output of gradient calculation module
Grad, is weighted summation, multiplies the computings such as learning rate, to aobvious layer neuron assignment module according to above-mentioned specific method packet
Output Δ xi；
Aobvious layer neuron assignment module, will feed back the value of the correction value of computing module output and the aobvious layer neuron of last iteration
It is added, feeding feedforward computing module.
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Application publication date: 20170620 |