CN101877591B - A kind of method and apparatus of binary symmetric source coding - Google Patents

Abstract

The method that the invention discloses a kind of binary symmetric source coding, constructs the generator matrix of polynary low-density generated matrix (LDGM) code according to code check and code length；After given source sequence, use enhancement mode belief propagation (RBP) encryption algorithm that source sequence is compressed according to the generator matrix of structure, it is thus achieved that compressed sequence, it is achieved binary symmetric source encodes；The present invention also discloses the device of a kind of binary symmetric source coding, pass through the solution of the present invention, it is possible to achieve there is uniform enconding complexity and the distortion performance binary symmetric source coding close to rate distortion capacity.

Description

A kind of method and apparatus of binary symmetric source coding

Technical field

The present invention relates to source coding technique, the method and apparatus particularly relating to a kind of binary symmetric source coding.

Background technology

Multi-antenna technology is a key technology of Long Term Evolution (LTE, LongTermEvolution) system.When downlink sending and receiving end configures many antennas, the signal how designing sending and receiving end just becomes an important topic with the channel capacity obtaining multi-input multi-output system downlink (MIMOdownlink).Theoretical research shows, uses dirty paper code (DPC, DirtyPaperCoding) technology at transmitting terminal (base station), it is possible to obtain the capacity of multi-input multi-output system broadcast channel (MIMOBC).Not being given due to theoretical research and how to design structurized DPC, the most structurized DPC designing technique just becomes a current academic and study hotspot of engineering field.

Supercomposed coding is that a kind of effective structuring DPC recently proposed realizes technology, and it requires to provide a good channel code and a good source code.In supercomposed coding structure, channel code typically can use the code of the up channel capacity such as the most ripe low-density checksum (LDPC, Low-DensityParityCheck) code；Source code can use Trellis coding quantization (TCQ, TrellisCodedQuantization) or low-density generated matrix (LDGM, Low-DensityGeneratorMatrix) code.In order to approach rate distortion capacity, when source code uses TCQ, need the biggest status number, such as: status number is with 2^tRepresenting, t is code storage length, and in order to approach rate distortion capacity, t typically requires more than 20.Accordingly, it would be desirable to research is based on LDGM code distortion quantizing of information source.Research show LDGM code be one can reach binary symmetric source (BSS, BinarySymmetricSource) rate distortion capacity have distortion message sink coding.But the complexity of the LDGM encryption algorithm that (SP, SurveyPropagation)/extraction (Decimation) is propagated in traditional employing investigation be code length square, complexity can be expressed as O (n²), n is code length.In view of in order to approach rate distortion capacity, the code length of LDGM code typically requires more than 10⁴, therefore its complexity is higher.

A kind of LDGM encryption algorithm with linear complexity is TAP (ThoulessAndersonPalmer) method, it is 2 that TAP method have linear complexity to be because the row degree of the generator matrix of binary LDGM code in TAP method, therefore enhancement mode belief propagation (RBP can be used, ReinforcedBeliefPropagation) algorithm encodes, and this is it can be avoided that necessary extraction step in other coded methods.But the poor-performing of TAP method, the circulation binary LDPC code that check matrix column degree is 2 of the binary LDGM code antithesis that the poor-performing of TAP method is primarily due to generator matrix row degree is 2 is not a good channel code, and this is the conclusion generally acknowledged.From coding theory, farther out, therefore, the performance of TAP method also is difficult to close to rate distortion capacity to be primarily due to the code redistribution of optimum channel code on the code redistribution deviation theory of the circulation binary LDPC code that row degree is 2.

Summary of the invention

In view of this, present invention is primarily targeted at the method and apparatus that a kind of binary symmetric source coding is provided, it is achieved there is uniform enconding complexity and the distortion performance BSS coding close to rate distortion capacity.

For reaching above-mentioned purpose, the technical scheme is that and be achieved in that:

The method of a kind of binary symmetric source coding that the present invention provides, the method includes:

The generator matrix of polynary LDGM code is constructed according to code check and code length；

After given source sequence, use RBP encryption algorithm that source sequence is compressed according to the generator matrix of structure, it is thus achieved that compressed sequence.

In such scheme, the described generator matrix constructing polynary LDGM code according to code check and code length, particularly as follows: use progressive edge to increase (PEG, ProgressiveEdge-Growth) one size of algorithm construction is the check matrix of cyclic LDPC code of m × n, and wherein, m is the product of code check and code length, n is code length, m is 1 less than the element on only two positions on n, and each column, and on other positions, element is 0；By element that value each in check matrix is 1 with uniform probability random replacement for set 1,2 ..., the arbitrary element in q-1}, q is the positive integer more than 3；Finally verification matrix transpose is obtained the generator matrix of the polynary LDGM code that size is n × m.

In such scheme, the method farther includes: when the information updating using RBP encryption algorithm to calculate check-node, uses fast fourier transform to calculate the information updating of check-node.

In such scheme, described code check and code length are determined according to sequence to be compressed by the System Control Center being responsible for information allotment.

The device of a kind of binary symmetric source coding that the present invention provides, this device includes: generator matrix module, compressed sequence module, reconstruct source sequence module；Wherein,

Generator matrix module, for constructing the generator matrix of polynary LDGM code according to code check and code length, and notifies compressed sequence module by generator matrix；

Compressed sequence module, for after given source sequence, uses RBP encryption algorithm to compress source sequence according to the generator matrix of generator matrix module structure, it is thus achieved that compressed sequence.

In such scheme, described generator matrix module constructs the generator matrix of polynary LDGM code according to code check and code length, particularly as follows: the check matrix of the cyclic LDPC code that generator matrix module employing one size of PEG algorithm construction is m × n, wherein, m is the product of code check and code length, and n is code length, and m is less than n, and the element on only two positions is 1 in each column, on other positions, element is 0；Then by element that value each in check matrix is 1 with uniform probability random replacement for set 1,2 ..., the arbitrary element in q-1}, q is the positive integer more than 3；Finally verification matrix transpose is obtained the generator matrix of the polynary LDGM code that size is n × m, and by generator matrix notice reconstruct source sequence module.

In such scheme, described compressed sequence module, when being further used for the information updating using RBP encryption algorithm calculating check-node, use fast fourier transform to calculate the information updating of check-node.

The method and apparatus of a kind of binary symmetric source coding that the present invention provides, constructs the generator matrix of polynary LDGM code according to code check and code length；After given source sequence, use RBP encryption algorithm that source sequence is compressed according to the generator matrix of structure, it is thus achieved that compressed sequence；So, it is possible to achieve there is uniform enconding complexity and the distortion performance BSS coding close to rate distortion capacity, improve the distortion performance of BSS coding.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet that the present invention realizes the method for binary symmetric source coding；

Fig. 2 is that the present invention is for representing the factor graph of LDGM code；

Fig. 3 is the emulation schematic diagram that TAP method and the inventive method realize the distortion performance that binary symmetric source encodes；

Fig. 4 is the structural representation that the present invention realizes the device of binary symmetric source coding.

Detailed description of the invention

In having distortion information source coding problem, source sequence y to be compressed is that each element obeys independent same distribution (i.i.d.) y_iThe sampled value of random vector, wherein, y ∈ S, y_i∈P_S, S represents the character set belonging to information source, P_SRepresent the set that in character set S, the probability of each element is constituted.The thought of message sink coding is exactly by certain code word in code book CRepresent this source sequence y, to realize the quantization compression of source sequence y.As: the Binary Symmetric Bernoulli information source (Ber (1/2)) of parameter p=1/2, code check R (i.e. compression ratio) is that the source encoder of R=m/n is by source sequence y ∈ { 0,1}ⁿIt is mapped as the binary vector x ∈ { 0,1} of a length of m ＜ n^m, x then is mapped as reconstructing source sequence by source decoder as compressed sequence

For given binary sequence pairTypically use Hamming (Hamming) distortion D as the tolerance of reconstruction fidelity.Wherein, Represent y andBetween Hamming distance from, i.e. sequences y andThe number that on middle correspondence position, element value is different, such as: d_H(001,101)=1.For Ber (1/2) information source, there is a following formula (1) according to Shannon rate distortion theory:

$R\left(D\right)=\left\{\begin{array}{cc}1-H\left(D\right),& D\∈\[\mathrm{0,0.5}\]\\ 0,& \mathrm{otherwise}\end{array}\right.---\left(1\right)$

Wherein H () is binary system entropy function.

For using binary LDGM code to have distortion message sink coding, given code check R ＜ 1, make A ∈ { 0,1}^n×mFor the generator matrix of LDGM code, and suppose that its order is m, i.e. rankA=m without loss of generality.Further, since the low-density characteristic of LDGM code, the number always bounded of the element 1 in each row and column of generator matrix A, therefore, quantization code book based on LDGM code is defined as formula (2).

C (A) :={ z ∈ { 0,1}ⁿ| z=Axforsomex ∈ { 0,1}^m}(2)

Wherein, z represents the code word in LDGM code quantization code book, and arithmetical operation therein patrols China territory (GF (2)) based on the gal that size is 2.

Source encoder is by given source sequence y ∈ { 0,1}ⁿIt is mapped as dope vector x ∈ { 0,1}^m, source decoding is then by simpleRealize, wherein,It is properly termed as the source sequence of reconstruct.

It can be seen that the significant challenge having distortion message sink coding using LDGM code is how to determine that information bit vector x makes Hamming distortion | | y-Ax | |₁/ n is minimum.

Present invention contemplates that when in GF (q), parameter q is bigger, most row degree of the optimal LDPC code on GF (q) are 2, propose the check matrix of polynary cyclic LDPC code that row degree is 2 as the generator matrix of LDGM code, and use RBP algorithm to encode, realization has uniform enconding complexity (O (n)) and performance has distortion to quantify close to the BSS based on polynary LDGM code of rate distortion capacity, described GF (q)={ 0,1, ..., q-1}.

The basic thought of the present invention is: construct the generator matrix of polynary LDGM code according to code check and code length；After given source sequence, use RBP encryption algorithm that source sequence is compressed according to the generator matrix of structure, it is thus achieved that compressed sequence.

Below by drawings and the specific embodiments, the present invention is described in further detail.

The present invention realizes the method for a kind of binary symmetric source coding, as it is shown in figure 1, the method includes following step:

Step 101: construct the generator matrix of polynary LDGM code according to code check and code length；

Concrete, initially with the check matrix B of the cyclic LDPC code that one size of PEG algorithm construction is m × n, wherein, m is the product of code check and code length, and n is code length, and m is 1 less than the element on only two positions on n, and each column, and on other positions, element is 0；Then by verification matrix B in each value be 1 element with uniform probability random replacement for set 1,2 ..., the arbitrary element in q-1}, q is the positive integer more than 3；Finally verification matrix B transposition is obtained the generator matrix A of the polynary LDGM code that size is n × m；The System Control Center that described code check and code length can be allocated by responsible information determines according to sequence to be compressed, and System Control Center can be the control centre of image data samples, or the control centre etc. of audio data samples.

Step 102: given source sequence；

Concrete, LDGM code can be with factor graph G=(V, C as shown in Figure 2, E) represent, wherein V={1,2, ..., m} represents the "○" on the left side in the set of information node x, i.e. Fig. 2, C={1,2 ..., n} represents the set of check-node z, " " in i.e. Fig. 2, E represent the set on the limit connecting check-node and information node.From figure 2 it can be seen that each check-node z_i(i=1,2...n) has exclusive information source node y_i(i=1,2...n) neighbours, and two information node neighbours, described information source node y_iThe "○" on the right in (i=1,2...n) neighbours i.e. Fig. 2.G is defined on the limit of link information node j and check-node i in factor graph_{I, j}∈ GF (q)/{ 0}, described g_{I, j}The value of the nonzero element of the i-th row jth row in corresponding generator matrix A；

The set of the information node neighbours of verification node i is designated as V (i), the set of the inspection nodes neighbors of information node i is designated as C (i).Obviously, the LDGM code of structure has | V (i) |=2, i=1,2 ..., n.Given all bits meet the source sequence y of verification relational expression (3), and the code length of source sequence y is n.

$\underset{j\∈V\left(i\right)}{\mathrm{\Σ}}{g}_{j,i}{x}_j+y_i=0,(i=\mathrm{1,2},...,n)---\left(3\right)$

Wherein, the arithmetical operation in formula (3) is based on GF (q).

Step 103: after given source sequence, uses RBP encryption algorithm to compress source sequence according to the generator matrix of structure, it is thus achieved that compressed sequence；

Concrete, orderFrom information node x to the message vector of check-node z when representing the l time iteration, to arbitrary symbol a ∈ GF (q),The probability of a representation in components information node symbol x=a, be designated asSimilar,From check-node z to the message vector of information node x when representing the l time iteration,ForThe a component；μ_y→zRepresent from information source node y to the message vector of check-node z, μ_y→zA () is μ_y→zThe a component；λ^lRepresent the reliability vector of information node x, λ after the l time iteration^lA () is λ^lThe a component；

Information source node message initialization is as shown in formula RBP-1；

μ_y→z(a)∝exp(-2βd_H(y, a)) (RBP-1)

In formula RBP-1, parameter beta be chosen as meeting following formula on the occasion of solution:

Lncosh β-β tanh β+Rln2=0

Information node message initialization is as shown in formula RBP-2；

${\mathrm{\μ}}_{x\→z}^1\left(a\right)=1/q\±\mathrm{dither}---(\mathrm{RBP}-2)$

Wherein, dither is (0,1/q²Equally distributed random number between)；

Check-node information updating is as shown in formula RBP-3；

${\mathrm{\μ}}_{z\→x}^l\left(a\right)=\underset{g_{x\′z}{a}_1+a_2=-g_{\mathrm{xz}}a}{\mathrm{\Σ}}{\mathrm{\μ}}_{x\′\∈V\left(z\right)\backslash \left\{x\right\}\→z}^l\left(a_1\right)\·{\mathrm{\μ}}_{y\→z}\left(a_2\right)---(\mathrm{RBP}-3)$

Wherein, g<sub>x`z</sub>Represent the nonzero element value of z row xth ` row, g in generator matrix A_xzRepresent the nonzero element value of z row xth row in generator matrix A；

Information node reliability updates as shown in formula RBP-4；

${\mathrm{\&lambda;}}^l\left(a\right)=\mathrm{\&alpha;}\underset{z\&Element;C\left(x\right)}{\mathrm{\&Pi;}}{\mathrm{\&mu;}}_{z\&RightArrow;x}^l\left(a\right)---(\mathrm{RBP}-4)$

Information node information updating is as shown in formula RBP-5；

${\mathrm{\&mu;}}_{x\&RightArrow;z}^{l+1}\left(a\right)\&Proportional;{\left({\mathrm{\&lambda;}}^1\left(a\right)\right)}^{\mathrm{\&gamma;}\left(l\right)}\underset{z\&prime;\&Element;C\left(x\right)\backslash \left\{z\right\}}{\mathrm{\&Pi;}}{\mathrm{\&mu;}}_{z\&prime;\&RightArrow;x}^l\left(a\right)---(\mathrm{RBP}-5)$

Wherein, γ (l) is defined asr₀, r₁∈ [0,1].

Above-mentioned, the iteration stopping condition of RBP algorithm is: iterations l reaches a predetermined maximum L_max；Or there is formula (4) to set up for all of information node and check-node；

${\mathrm{\&mu;}}_{z\&RightArrow;x}^{l+1}\left(a\right)={\mathrm{\&mu;}}_{z\&RightArrow;x}^l\left(a\right)---\left(4\right)$

After RBP algorithm calculates, obtaining the probability of all symbol a in each information node according to formula RBP-4, the symbol a taking maximum probability in each information node constitutes compressed sequence x, then the code length of x is m, because m is less than n, it is achieved that the compression to source sequence y, i.e. BSS encodes.

Further, in RBP algorithm, owing to degree is d_xThe computation complexity of information node be O (d_xQ), degree be the computation complexity of check-node (i.e. including 2 information node neighbours and 1 information source node neighbour) of 3 be O (3²·q²).In order to reduce complexity, the information updating of check-node can use the fast fourier transform of formula (5) to realize；

${\mathrm{\&mu;}}_{z\&RightArrow;x}^l\left(a\right)=F^{-1}(F\left({\mathrm{\&mu;}}_{C\left(z\right)\backslash \left\{x\right\}\&RightArrow;z}^l\left(a\right)\right)\&CenterDot;F\left({\mathrm{\&mu;}}_{y\&RightArrow;z}\left(a\right)\right))---\left(5\right)$

Wherein, F and F^-1Represent respectively and use fast fourier transform and fast Flourier inverse transformation.Using fast fourier transform, the complexity of the Fourier transform of the message vector of each check-node is O (p q), wherein p=log₂q.The computation complexity of the most each check-node is O (3²P q), code length (symbol lengths) be the encoder complexity of the LDGM code of n be O (3²P q n), it can be seen that complexity O (3²P q n) it is linear complexity.

In the present invention, can by reconstruct source sequence verification and measurement ratio distortion performance, can set reconstruct source sequence asAccording to the compressed sequence x obtained in the generator matrix A in step 101 and step 103, according toReconstruct source sequence.

Such as, according to above-mentioned method, when q=8, i.e. when GF (q) is GF (8), it is assumed that code length is n=4000 GF (8) symbol, corresponding bit length is 12000, γ₁=0.9995, γ₀=0.95, L_max=300, the value of parameter beta is as shown in table 1, code check R value is R=0.1,0.2 ..., 0.9；Then in the distortion performance such as Fig. 3 of GF (8) the upper LDGM code employing RBP encryption algorithm under different code checks shown in " ", the distortion performance of TAP method represents with "○" in figure 3, as can be seen from the figure, the distortion performance of the present embodiment compares the distortion performance of TAP method improvement greatly, and the distortion performance of the present embodiment is closer to rate distortion Capacity Ratio.

Table 1

When q=16, i.e. when GF (q) is GF (16), it is assumed that code length is n=3000 GF (16) symbol, corresponding bit length is 12000, γ₁=0.9995, γ₀=0.95, L_max=300, the value of parameter beta is as shown in table 1, code check R value is R=0.1,0.2 ..., 0.9；Then in the distortion performance such as Fig. 3 of GF (16) the upper LDGM code employing RBP encryption algorithm under different code checks shown in " △ ", as can be seen from the figure, the distortion performance of this embodiment is compared the upper LDGM code of GF (8) of same code length and is used the distortion performance of RBP encryption algorithm to improve, and with rate distortion capacity closely.Wherein, when code check≤0.5, the distortion performance distance rate distortion capacity of the present embodiment is less than 0.005；When code check ＞ 0.5, the distortion performance distance rate distortion capacity of the present embodiment is less than 0.01.

When q=256, i.e. when GF (q) is GF (256), it is assumed that code length is n=1500 GF (256) symbol, corresponding bit length is 12000, γ₁=0.9995, L_max=300, γ₀Being chosen as testing optimal value, the value of parameter beta is as shown in table 1, code check R value is R=0.1,0.2 ..., 0.9；Then in the distortion performance such as Fig. 3 of GF (256) the upper LDGM code employing RBP encryption algorithm under different code checks shown in " ◇ ", it can be seen that the upper LDGM code of GF (16) that the distortion performance of the present embodiment compares same code length uses the distortion performance of RBP encryption algorithm to only have raising more by a small margin.

In order to realize said method, present invention also offers a kind of binary symmetric source coding device, as shown in Figure 4, this device includes: generator matrix module 41, compressed sequence module 42 wherein,

Generator matrix module 41, for constructing the generator matrix of polynary LDGM code according to code check and code length, and notifies compressed sequence module 42 by generator matrix；

Concrete, the check matrix of the cyclic LDPC code that generator matrix module 41 uses one size of PEG algorithm construction to be m × n, wherein, m is the product of code check and code length, and n is code length, and m is less than n, and the element on only two positions is 1 in each column, on other positions, element is 0；Then by element that value each in check matrix is 1 with uniform probability random replacement for set 1,2 ..., the arbitrary element in q-1}, q is the positive integer more than 3；Finally verification matrix transpose is obtained the generator matrix of the polynary LDGM code that size is n × m, and by generator matrix notice reconstruct source sequence module 43；

Compressed sequence module 42, for after given source sequence, uses RBP encryption algorithm to compress source sequence according to the generator matrix of generator matrix module 41 structure, it is thus achieved that compressed sequence；

Further, when described compressed sequence module 42 uses the information updating that RBP encryption algorithm calculates check-node, use fast fourier transform to calculate the information updating of check-node, specifically may refer to formula (5), repeat no more here.

The above, only presently preferred embodiments of the present invention, it is not intended to limit protection scope of the present invention, all any amendment, equivalent and improvement etc. made within the spirit and principles in the present invention, should be included within the scope of the present invention.

Claims (5)

1. the method for a binary symmetric source coding, it is characterised in that the method includes:

The generator matrix of polynary low-density generated matrix LDGM code is constructed according to code check and code length；

After given source sequence, use enhancement mode belief propagation RBP encryption algorithm that source sequence is compressed according to the generator matrix of structure, it is thus achieved that compressed sequence；

The described generator matrix constructing polynary low-density generated matrix LDGM code according to code check and code length, particularly as follows: the check matrix of the cyclic low-density parity check LDPC code using progressive edge increasing one size of PEG algorithm construction to be m × n, wherein, m is the product of code check and code length, n is code length, m is 1 less than the element on only two positions on n, and each column, and on other positions, element is 0；By element that value each in check matrix is 1 with uniform probability random replacement for set 1,2 ..., the arbitrary element in q-1}, q is the positive integer more than 3；Finally verification matrix transpose is obtained the generator matrix of the polynary low-density generated matrix LDGM code that size is n × m.

Method the most according to claim 1, it is characterised in that the method farther includes: when the information updating using enhancement mode belief propagation RBP encryption algorithm to calculate check-node, uses fast fourier transform to calculate the information updating of check-node.

Method the most according to claim 1, it is characterised in that described code check and code length are determined according to sequence to be compressed by the System Control Center being responsible for information allotment.

4. the device of a binary symmetric source coding, it is characterised in that this device includes: generator matrix module, compressed sequence module, reconstruct source sequence module；Wherein,

Generator matrix module, for constructing the generator matrix of polynary low-density generated matrix LDGM code according to code check and code length, and notifies compressed sequence module by generator matrix；

Compressed sequence module, for after given source sequence, uses enhancement mode belief propagation RBP encryption algorithm to compress source sequence according to the generator matrix of generator matrix module structure, it is thus achieved that compressed sequence；

Described generator matrix module constructs the generator matrix of polynary low-density generated matrix LDGM code according to code check and code length, the check matrix of the cyclic low-density parity check LDPC code that one size of PEG algorithm construction is m × n particularly as follows: generator matrix module uses progressive edge to increase, wherein, m is the product of code check and code length, n is code length, m is 1 less than the element on only two positions on n, and each column, and on other positions, element is 0；Then by element that value each in check matrix is 1 with uniform probability random replacement for set 1,2 ..., the arbitrary element in q-1}, q is the positive integer more than 3；Finally verification matrix transpose is obtained the generator matrix of the polynary low-density generated matrix LDGM code that size is n × m, and by generator matrix notice reconstruct source sequence module.

Device the most according to claim 4, it is characterised in that described compressed sequence module, when being further used for the information updating using enhancement mode belief propagation RBP encryption algorithm calculating check-node, uses fast fourier transform to calculate the information updating of check-node.