CN110048814A - A kind of sparse superimposed code design scheme based on mixed iteration power distribution - Google Patents
A kind of sparse superimposed code design scheme based on mixed iteration power distribution Download PDFInfo
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- CN110048814A CN110048814A CN201910325061.8A CN201910325061A CN110048814A CN 110048814 A CN110048814 A CN 110048814A CN 201910325061 A CN201910325061 A CN 201910325061A CN 110048814 A CN110048814 A CN 110048814A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0045—Arrangements at the receiver end
- H04L1/0047—Decoding adapted to other signal detection operation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0045—Arrangements at the receiver end
- H04L1/0047—Decoding adapted to other signal detection operation
- H04L1/005—Iterative decoding, including iteration between signal detection and decoding operation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
- H04W52/04—TPC
- H04W52/30—TPC using constraints in the total amount of available transmission power
- H04W52/34—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
- H04W52/04—TPC
- H04W52/30—TPC using constraints in the total amount of available transmission power
- H04W52/34—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
- H04W52/346—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading distributing total power among users or channels
Abstract
The present invention proposes a kind of sparse superimposed code design scheme based on mixed iteration power distribution, specifically, first rarefaction representation is carried out using real-valued signal of the one-hot coding mode to input, so that only having a nonzero value in each grouping.Later using the mentioned mixed iteration power allocation scheme of the present invention, assignment is carried out to the nonzero value in each grouping of sparse message vector.Then the linear combination that corresponding grouping is carried out with random Hadamard design matrix, forms corresponding code word.Then, the code word of formation is inputted into awgn channel, it is 0 that code word, which adds mean value, variance σ2White Gaussian noise.The band of output is made an uproar into code word by AMP decoding algorithm, the iterative estimate operation for carrying out code word obtains the estimated value of message vector.Maximum value in each grouping of obtained estimated value is corresponded into position and is set as the preset value that power distribution obtains, remaining position is set as 0, and the reconstruction value of original signal can be obtained.It is tested using spyder3, the python third party for needing to use is surrounded by numpy, pyfht etc..
Description
Technical field
The invention belongs to signal processing technology field, specially a kind of sparse superimposed code based on mixed iteration power distribution
Design scheme.
Background technique
Communication is used as digital Age and the essential a part of information-intensive society, is always pair of researcher's extensive concern
As.1948, Shannon proposed that channel coding helps to realize effective reliable transmission of signal, and the big theorem of Shannon three proposed is
The design of channel coding specifies direction.As long as information is transmitted with the traffic rate lower than channel capacity, one kind is certainly existed
Channel coding method, so that the probability that transmission information goes wrong tends to be infinitely small with the increase of code length.Although channel
Coding can obtain good performance, but the presence of Shannon circle make the performance of transmission reach certain level after no longer increase
Add, or even sharply declines.Therefore, it is that one for a long time and again in information theory that development, which calculates effectively and can reach the code of Shannon circle,
The target wanted.Currently, some outstanding channel codings have been emerged, such as Turbo code, LDPC code and Polar code.No matter true
Under fixed channel theory model or in actual communication system, the performance close to Shannon capacity can be realized.Wherein,
LDPC code, which is proved to realize in binary system erasure channel, reaches the traffic rate of capacity, while having binary system defeated other
Enter, also show excellent properties on the channel of discrete input alphabet.However, many physical communication channels have successive value defeated
Enter, such as awgn channel.To by Turbo code, LDPC code etc. is applied to this kind of channel, then needs additional modulation scheme to letter
It number is modulated, common modulation scheme includes phase-shift keying (PSK), quadrature amplitude modulation etc..By binary error-correcting code and a standard
The process that combines of modulation scheme be known as coded modulation, and there is lot of documents to prove, coded modulation has excellent experience
Performance.But for awgn channel, the performance of capacity realization can achieve without theoretical proof encoding scheme so far.To study one kind
Effective channel coding schemes just may be directly applied to awgn channel without modulation, and can reach traffic rate and approach channel
The experts and scholars of the performance of capacity, information theory field conduct extensive research.Wherein, A.Joseph and A.Barron are in 2010
Year proposes sparse superimposed code (Sparse Superposition Code, sparse superimposed code), also referred to as sparse regression code
(Sparse regression code, SPARC), on awgn channel, which is decoded using efficient coding device can be achieved AWGN
Channel capacity.
Initially, A.Joseph and A.Barron proposes a kind of effective decoding algorithm --- adaptive continuous decoding, it was demonstrated that
The decoding of sparse superimposed code can be made using the decoder with the increase of code length for any fixed communication rate R < C
Error probability is to approach the rate attenuation of index to 0.Then, adaptive soft-threshold decoder and approximate message transmission
(Approximate message passing, AMP) decoder is suggested, both decoders introduce soft-threshold, passes through iteration
Posterior probability is updated, original signal is estimated.Compared with the interpretation method for using hard -threshold, more excellent translate can be obtained
Code performance.Although above-mentioned three kinds of interpretation methods are in the case where code length increases, for arbitrary rate R < C, theory card
Decoding error probability, which is illustrated, can all decay to 0.But AMP decoding algorithm is because having lower computation complexity, and reconstruction property is excellent,
Sparse superimposed code decoding algorithm as current mainstream.
Although the decoding performance of sparse superimposed code is substantially improved in AMP decoder, when rate approaches Shannon circle
When, constrained by phase transformation, when reaching close to a certain transmission rate of channel capacity, decoder performance sharply declines, the phenomenon with
It is similar that LDPC code decodes process.To solve this problem, improve decoding performance of sparse superimposed code under the conditions of finite length, it can
Power distribution design is carried out to the code construction of sparse superimposed code.Different power allocation schemes is for Limited-Coding length condition
Under decoding performance it is significantly different, key is how to design effective power distribution mode so that sparse superimposed code decoding miss
Difference is minimum.To realize lower decoding error, it is currently suggested several effective power allocation schemes.But generally existing distribution is not
Reasonable problem causes decoding precision not high so that decoding process initiation is difficult or power distribution is unsatisfactory for decoding requirements.
For background above, the present invention proposes a kind of mixed iteration power allocation scheme.Based on this power allocation scheme, propose a kind of dilute
Superposition code constructing method is dredged, carries out uniform enconding using random hadamard matrix, realizes that sparse superimposed code exists using AMP decoder
Decoding on awgn channel.
Summary of the invention
Using power distribution to the positive effect of sparse superimposed code decoding performance, not for existing power allocation scheme
Foot, the present invention propose a kind of new power allocation scheme --- mixed iteration power distribution.It is that all groupings distribute most first
It is small to require power, unallocated complete power averaging is then assigned into each grouping.By this method, realize that each is grouped
It can obtain being higher than minimum desired power, avoid grouping initial in the design of iterative power allocation plan and be only capable of being assigned to minimum
It is required that power, may cause the situation that cascading failure causes decoding error high.Compared with iterative power allocation plan, guaranteeing often
One grouping can be realized under conditions of minimum requires power, still have extra power for resist interference, enhance the Shandong of decoding
Stick has the decoding performance more excellent compared with the iterative power method of salary distribution under Low SNR.
Technical solution of the present invention and process sequence are as follows:
(1) real-valued signal that will be transmitted is mapped as each grouping by way of one-hot coding only has a nonzero value
Sparse vector.Using the mentioned mixed iteration power allocation scheme of the present invention, the nonzero value designed in each grouping is
And meet
(2) the linear combination of corresponding grouping is carried out with the sparse vector using random Hadamard design matrix, being encoded to can
In the code word of awgn channel transmission；
(3) code word is transmitted via awgn channel, output band is made an uproar code word；
(4) decoding reconstruct is carried out by AMP decoder, obtains the estimated value of sparse vector；
(5) hard decision is carried out, original signal is restored.
Detailed description of the invention
Working principle diagram of the sparse superimposed code of Fig. 1 on awgn channel
Fig. 2 mixed iteration power allocation scheme schematic diagram
Fig. 3 design matrix A and the sparse linear combination schematic diagram of message vector β
Sparse superimposed code system diagram of the Fig. 4 based on mixed iteration power distribution
Decoding error comparison under the conditions of Fig. 5 difference B
The corresponding decoding error comparison of Fig. 6 difference R under the conditions of B=L=1024, M=512, snr=7
The corresponding decoding error comparison of Fig. 7 difference R under the conditions of B=L=1024, M=512, snr=3
The corresponding decoding error comparison of Fig. 8 difference R under the conditions of B=L=256, M=256, snr=7
Specific embodiment
The present invention is described in more detail with reference to the accompanying drawing
Fig. 1 is working principle diagram of the sparse superimposed code in awgn channel in Figure of description, referring to attached drawing, and combines this hair
Bright mentioned mixed iteration power allocation scheme is described in detail the coding and decoding process of sparse superimposed code as follows:
Step 1: input real-valued signalThe signal contains L element, and
Each element value size is no more than M.Using one-hot coding mode, a sparse message vector is converted by the input real-valued signal
β, so that the sparse message vector β that conversion obtains has L grouping, each grouping has in M element and each grouping only
One nonzero value, remaining M-1 element is all 0.To have a clear understanding of original signalIt is how to be converted into β, passes through a letter
Single example is illustrated.IfIt is clear that the real-valued signal has 6 elements, and each element is not
More than d, i.e. alphabet only includes four symbols { a, b, c, d }.Therefore, L=6, M=4, then β=[[1000], [0010],
[0100], [1000], [0001], [0010]], wherein [] indicates cascade.
Step 2: the nonzero value being arranged in each grouping isWherein P1,P2,...,PLTo refer in advance
Fixed normal number meets following relationships:
Wherein, P is general power, is claimedBe assigned a value of power distribution.The present invention translates sparse superimposed code using power distribution
The positive effect of code performance has made intensive studies existing power allocation scheme.
Currently, iterative power distributes more existing other power allocation schemes, lower decoding error can be obtained.But its is right
When front grouping carries out power distribution, only considers that distribution decoding minimum requires power, make an uproar so that the grouping of foremost may be because
Acoustic jamming is excessive, can not correct decoding, lead to cascading failure.The present invention is directed to this problem, distributes iterative power and carries out
It improves, proposes a kind of mixed iteration power allocation scheme.Purpose is to reduce noise jamming, enhancing decoding robustness, to make
It obtains sparse superimposed code and combines mentioned mixed iteration power allocation scheme, preferably decoding property can be obtained under Low SNR
Energy.
For convenience of the explanation of variable in subsequent power scheme, first such as to the AMP decoding algorithm description based on power distribution
Under:
Assuming that the output of awgn channel is y=x+ ω=A β+ω, wherein x is the code word that coding generates.A is for generating
The design matrix of code word, also referred to as " dictionary ".ω is that mean value is 0, variance σ2White Gaussian noise.AMP decoder iteration is more
Newly, the continuous estimation { β of message vector β is generatedt, wherein
Initialize β0=0, it calculates
Wherein, the aleatory variable for being designated as negative value up and down is all set as 0.Constant { τtAnd estimation functionDefinition is such as
Under:
Wherein, σ2For Gaussian noise variance, P is code word general power, these values are all preset given value, signal-to-noise ratio
Snr=P/ σ2.Assuming that noise variance σ in awgn channel2=1, then general power P is equal with signal-to-noise ratio snr.For formula (4), in (5)
Variable xt-1, have
xt-1:=x (τt-1) (6)
In formula (7), j ∈ [M], It indicates to obey independent same distributionStochastic variable.
ForDefine estimation functionSuch as following formula:
Obviously, it can be noted thatAll elements depending on s in sec (i).
It enablesFor sufficiently large M, and for arbitrary constant δ ∈ (0,1), have
Wherein κ1, κ2For general normal number.
If the constant κ in formula (9), (10)1, κ2When cannot be specified exactly, for design power allocation plan, under
The approximation of face x (τ):
Approximate expression shown in formula (11), as L, M increase, accuracy increases, for designing suitable power distribution
With preferable directive function.For the effective noise variance after t iteration of progressIf any groupingNormalized powerGreater than threshold value 2R τ2Ln2, then the sparse superimposed code of (t+1) secondary iteration can be with correct decoding.For given power point
Match, the lower bound pair parameter in formula (11) can be passed throughIt is iterated estimation, use can be examined to give rapidly
Whether power distribution can reliably be decoded under big system limits.In conjunction with Fig. 2 in Figure of description, illustrate to mention in the present invention
Mixed iteration power distribution design out is as follows:
(1) L grouping of sparse superimposed code is divided into B block, each piece has L/B grouping, and all distribute equal-wattage.
(2) minimum power needed for being sequentially allocated decoding to each piece.Minimum power is distributed to the grouping in first piece first,
So that being grouped in the condition of satisfaction in first pieceWhen, it can translate in the first iteration.According to formula (11), first piece
In each grouping can be set to
Then, it using formula (11) and formula (5), can obtain
Using the value of formula (13), second piece of all groupings can distribution power It can successively be calculated according to such methodUntil all groupings all distribute least work
Rate.
(3) after distribution terminates along these lines, in R < C, allocated power is centainly less than general power P, this
When by remaining power PremainIt is evenly distributed in all groupings.
It is described according to above-mentioned steps, it is as follows to summarize algorithm:
Step 3: the design matrix A that one dimension of design is n × LM, wherein n is the line number of A, and columns N=LM, n can be by
L, M and R are acquired.Design matrix A has L grouping, and the columns of each grouping is M.Because sparse message vector β has L grouping,
And each group is all made of M column, therefore code word number in total is ML, in order to obtain the traffic rate of Rbits, need
ML=2nR (14)
Both sides take logarithm that can obtain
Llog2M=nR (15)
Therefore, the line number n=Llog of design matrix A can be obtained2M/R。
Design matrix A uses random hadamard matrix, relative to traditional Gauss matrix, hence it is evident that has lower coding and translates
Code complexity, the occupancy of memory also reduce many.The building method of random hadamard matrix is from one 2m×2mHadamard
N row is randomly selected in square matrix and is ranked up, and avoids selection the first row and first row (in Hadamard square matrix during randomly selecting
The first row and the first column element are all+1).Therefore, the size of m must satisfySo that
Under conditions of excluding the first row and first row is chosen, there are enough row and columns for choosing.Randomly select the design square to be formed
Battle array need all column means be 0, and need by each of matrix element divided bySo that each column norm is all 1.
Fig. 3 is the linear combination schematic diagram of design matrix Yu sparse message vector in Figure of description, indicates the life of code word
At process.The construction of code word is exactly that the column of design matrix A are linearly combined in fact, is expressed as
X=A β (16)
Step 4: the code word x that uniform enconding is formed being transmitted through awgn channel, so that the output of receiving end is y, is met
Y=x+ ω (17)
Step 5: using iterative equation shown in AMP decoder algorithms Chinese style (2) in step 2, (3), to sparse message to
Amount is iterated estimation, the estimate vector β after obtaining T iterationT。
Step 6: the estimate vector β that iteration is obtainedTHard decision is carried out, in the corresponding each grouping of setting corresponding to maximum value
Position isAnd remaining M-1 is 0, then can obtain reconstruct sparse vectorIfIllustrate that original signal inputs
By success reconstructed error free.
In order to evaluate reconstruction property, packet error rate (Section Error Rate, SER) is introduced to assess reconfiguring false
Ratio shared by packet count
Fig. 4 is the coding and decoding flow chart that sparse superimposed code works in awgn channel in Figure of description, is clearly shown
Detailed system workflow of sparse superimposed code under the conditions of based on mixed iteration power distribution proposed by the present invention, is conducive to
Solve the work step of entire coding/decoding system.
The mixed iteration power allocation scheme proposed to illustrate the invention has performance compared with iterative power is distributed really
It is promoted, it is verified by experiment simulation.It is 1 that all experiments, which are respectively provided with noise variance, and maximum number of iterations is 64 times, with
Machine generates 200 different message sequences, and is tested respectively, and the average SER of 200 experiments is counted.Because proposing mixing
Iterative power distribution utilizes the approximation relation of formula (11) with iterative power distribution, therefore under actual conditions, can be calculated most
It is small to require power for approximation.Optimal value is obtained to make finally to decode result, the R in formula does not choose present communications rate directly,
But use RPA, enable RPA=aR.For the mixed iteration power distribution mentioned, general a < 1, as R increases, corresponding a
It will increase.A is adjusted, optimal decoding result is chosen.
The simulation comparison of Fig. 5 illustrates L=1024 in Figure of description, 200 groups of different messages sequences of M=512 size,
Decoding performance under the conditions of two kinds of different signal-to-noise ratio under a certain rate conditions.It can be found that as B increases, decoding performance variation
It less can even obtain lower decoding error.Therefore, it chooses B=L and carries out further verification test.
Fig. 6 in Figure of description, Fig. 7 and Fig. 8 have carried out exponential damping, iteration distribution and mixed iteration power distribution respectively
Under the conditions of three kinds of different schemes, sparse superimposed code is under the conditions of different signal-to-noise ratio, using the decoding under different R and different size
Error.It can be seen that mixed iteration power allocation scheme can help sparse superimposed code under Low SNR, letter is being approached
More preferably decoding performance is realized under the conditions of the high speed rate of road capacity.
Mixed iteration power distribution proposed by the present invention and coding/decoding system implementation process are carried out above detailed
It introduces and illustrates, help to understand core of the invention thought.The present invention is based on power distributions to decode precision to sparse superimposed code
Critical impact effect, devise a kind of mixed iteration power allocation scheme.It is required most to each grouping distribution decoding first
Then dump power is averagely assigned to each grouping by small-power, so that each grouping has sufficient power to be decoded, resistance is made an uproar
Acoustic jamming.Experimental verification, with exponential damping power distribution, iterative power distribution is compared, and suggesting plans, it is superior to obtain
Reconstruction property.
Claims (2)
1. a kind of sparse superimposed code design scheme based on mixed iteration power distribution, it is characterised in that: believe the real value of input
Number one-hot coding is converted into each grouping only with the sparse vector of a nonzero value；Utilize the mentioned mixed iteration power of the present invention
Allocation plan is to the nonzero value assignment in each grouping of sparse vector；According to the size of the grouping of message vector β, by random hada
Ma design matrix A carries out the linear combination of corresponding grouping, formation can be on awgn channel to specifications in attached drawing shown in Fig. 2
The code word of transmission；By awgn channel, in addition mean value is 0, variance σ2White Gaussian noise, obtain output codons；Finally, through
It crosses AMP decoder and is iterated estimation, the estimated value of message vector is obtained, and use hard-decision method, by each real value element
Element corresponds to maximum position and is set as in corresponding vectorRemaining is set as 0 method, recovers original sparse vector.
2. scheme according to claim 1, which is characterized in that using a kind of such as power point shown in Fig. 3 in Figure of description
It is the nonzero value assignment in the sparse each grouping of message vector β with scheme.It is characterized in that distributing first each grouping minimum
It is required that power, then divides dump power in each grouping equally, specific assigning process includes the following steps:
(1) the L packeting average of message vector β is divided into B block, is then grouped containing L/B for every piece；
(2) distribute identical power to each grouping after piecemeal, based on formula it is as follows:
Then for L/B grouping in first piece, distribution powerL/B in second piece is grouped,
Distribution powerWhereinContinue as in the same fashion each piece into
Row power distribution is all assigned to minimum power until all pieces.
(3) remaining power P after distributingremainDivide each grouping equally.
According to such power distribution mode, more excellent decoding performance can be obtained.
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