CN101877591A - Binary symmetric source coding method and device - Google Patents

Abstract

The invention discloses a binary symmetric source coding method, which comprises the following steps: according to code rate and code length, constructing a generator matrix of multivariate low-density generator matrix (LDGM) codes; and after a source sequence is given, and compressing the source sequence according to the constructed generator matrix by adopting a reinforced belief propagation (RBP) coding algorithm to obtain a compressed sequence, thus realizing the binary symmetric source coding. The invention also discloses a binary symmetric source coding device. By adopting the scheme, the binary symmetric source coding can be realized, which has linear coding complexity and rate-distortion performance close to rate-distortion volume.

Description

A kind of binary symmetric source Methods for Coding and device

Technical field

The present invention relates to source coding technique, relate in particular to a kind of binary symmetric source Methods for Coding and device.

Background technology

Multi-antenna technology is a key technology of Long Term Evolution (LTE, Long Term Evolution) system.When many antennas of down link sending and receiving end configuration, the signal that how to design the sending and receiving end just becomes an important topic with the channel capacity that obtains multi-input multi-output system down link (MIMO downlink).Theoretical research shows, adopts dirty paper code (DPC, Dirty Paper Coding) technology at transmitting terminal (base station), can obtain the capacity of multi-input multi-output system broadcast channel (MIMO BC).Because how theoretical research does not provide the DPC of project organizationization, therefore structurized DPC designing technique just becomes a research focus in current science and engineering field.

Supercomposed coding is a kind of effective structuring DPC realization technology that proposes recently, and it requires to provide a good channel code and a good source code.In the supercomposed coding structure, channel code generally can adopt very ripe low-density checksum (LDPC, Low-Density Parity Check) sign indicating number to wait the sign indicating number of up channel capacity; Source code can adopt grid coding to quantize (TCQ, Trellis Coded Quantization) or low-density generated matrix (LDGM, Low-Density Generator Matrix) sign indicating number.In order to approach the rate distortion capacity, when source code adopts TCQ, need very large status number, as: status number is with 2 ^tExpression, t is a code storage length, in order to approach the rate distortion capacity, t generally requires greater than 20.Therefore, need research to quantize based on the distortion information source that has of LDGM sign indicating number.Studies show that the LDGM sign indicating number be a kind of can reach binary symmetric source (BSS, Binary Symmetric Source) rate distortion capacity the distortion source encoding arranged.But traditional employing investigation propagate the complexity of (SP, Survey Propagation)/the extract LDGM encryption algorithm of (Decimation) be code length square, complexity can be expressed as O (n ²), n is a code length.Consider that the code length of LDGM sign indicating number generally requires greater than 10 in order to approach the rate distortion capacity ⁴, so its complexity is higher.

A kind of LDGM encryption algorithm with linear complexity is TAP (Thouless Anderson Palmer) method, it is because the capable degree of the generator matrix of binary LDGM sign indicating number is 2 in the TAP method that the TAP method has linear complexity, therefore can adopt enhancement mode belief propagation (RBP, Reinforced Belief Propagation) algorithm is encoded, and this can be avoided extraction step necessary in other coding methods.But the poor-performing of TAP method, the poor-performing of TAP method mainly be because with the capable degree of generator matrix be that the check matrix column degree of 2 binary LDGM sign indicating number antithesis is that 2 circulation binary LDPC sign indicating number is not a good channel code, this is existing conclusion of generally acknowledging.On coding theory, mainly be that therefore, the performance of TAP method also is difficult near the rate distortion capacity because the row degree is that the code weight of optimum channel sign indicating number distributes far on the code weight distribution deviation theory of 2 circulation binary LDPC sign indicating number.

Summary of the invention

In view of this, main purpose of the present invention is to provide a kind of binary symmetric source Methods for Coding and device, realizes having uniform enconding complexity and the distortion performance BSS coding near the rate distortion capacity.

For achieving the above object, technical scheme of the present invention is achieved in that

A kind of binary symmetric source Methods for Coding provided by the invention, this method comprises:

Construct the generator matrix of polynary LDGM sign indicating number according to code check and code length;

After given information source sequence, adopt the RBP encryption algorithm to the compression of information source sequence according to the generator matrix of constructing, obtain compressed sequence.

In the such scheme, described generator matrix of constructing polynary LDGM sign indicating number according to code check and code length, be specially: adopt progressive edge to increase (PEG, Progressive Edge-Growth) size of algorithm construction check matrix that is the cyclic LDPC code of m * n, wherein, m is the product of code check and code length, n is a code length, m is less than n, and lists whenever that to have only two locational elements be 1, and element is 0 on other positions; Be 1 element with each value in the check matrix with uniform probability replace with at random set 1,2 ..., the arbitrary element among the q-1}, q are the positive integer greater than 3; At last the verification matrix transpose being obtained size is the generator matrix of the polynary LDGM sign indicating number of n * m.

In the such scheme, this method further comprises: when adopting the information updating of RBP encryption algorithm calculation check node, adopt the information updating of fast fourier transform calculation check node.

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

A kind of binary symmetric source apparatus for encoding provided by the invention, this device comprises: generator matrix module, compressed sequence module, reconstruct information source block; Wherein,

The generator matrix module is used for constructing according to code check and code length the generator matrix of polynary LDGM sign indicating number, and notifies the compressed sequence module with generator matrix;

The compressed sequence module is used for after given information source sequence, adopts the RBP encryption algorithm to the compression of information source sequence according to the generator matrix of generator matrix module structure, obtains compressed sequence.

In the such scheme, described generator matrix module is constructed the generator matrix of polynary LDGM sign indicating number according to code check and code length, be specially: the check matrix that it is the cyclic LDPC code of m * n that the generator matrix module adopts size of PEG algorithm construction, wherein, m is the product of code check and code length, and n is a code length, and m is less than n, and list whenever that to have only two locational elements be 1, element is 0 on other positions; Be 1 element then with each value in the check matrix with uniform probability replace with at random set 1,2 ..., the arbitrary element among the q-1}, q are the positive integer greater than 3; At last the verification matrix transpose being obtained size is the generator matrix of the polynary LDGM sign indicating number of n * m, and notifies reconstruct information source block with generator matrix.

In the such scheme, described compressed sequence module when being further used for adopting the information updating of RBP encryption algorithm calculation check node, adopts the information updating of fast fourier transform calculation check node.

A kind of binary symmetric source Methods for Coding provided by the invention and device are constructed the generator matrix of polynary LDGM sign indicating number according to code check and code length; After given information source sequence, adopt the RBP encryption algorithm to the compression of information source sequence according to the generator matrix of constructing, obtain compressed sequence; So, can realize having uniform enconding complexity and distortion performance, improve the distortion performance that BSS encodes near the BSS coding of rate distortion capacity.

Description of drawings

Fig. 1 realizes the schematic flow sheet of binary symmetric source Methods for Coding for the present invention;

Fig. 2 is used to represent the factor graph of LDGM sign indicating number for the present invention;

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

Fig. 4 realizes the structural representation of binary symmetric source apparatus for encoding for the present invention.

Embodiment

In the distortion information source coding problem was arranged, information source sequences y to be compressed was obeyed independent same distribution (i.i.d.) y for each element _iThe sampled value of random vector, wherein, y ∈ S, y _i∈ P _S, S represents the character set under the information source, P _SThe set that the probability of each element constitutes among the expression character set S.The thought of source encoding is exactly with certain code word among the code book C

Represent this information source sequences y, to realize the quantification compression of information source sequences y.As the binary system symmetry Bernoulli information source (Ber (1/2)) of: parameter p=1/2, code check R (being compression ratio) for the source encoder of R=m/n with information source sequences y ∈ 0,1} ⁿBe mapped as length and be m＜n binary system vector x ∈ 0,1} ^m, source decoder then is mapped as reconstruct information source sequence with x as compressed sequence

Right for given binary sequence

The general tolerance that adopts Hamming (Hamming) distortion D as the reconstruct fidelity.Wherein,

The expression y and Between Hamming distance from, promptly sequences y and

The different number of element value on the middle correspondence position, as: d _H(001,101)=1.For Ber (1/2) information source, following formula (1) is arranged according to the 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 the binary system entropy function.

For what adopt binary LDGM sign indicating number the distortion source encoding arranged, given code check R＜1, make A ∈ 0,1} ^{N * m}Be the generator matrix of LDGM sign indicating number, and its order of supposition that is without loss of generality is m, i.e. rank A=m.In addition, because the low-density characteristic of LDGM sign indicating number, the number of the element 1 in the each row and column of generator matrix A is bounded always, therefore, is defined as formula (2) based on the quantization code book of LDGM sign indicating number.

C(A)：＝{z∈{0，1} ⁿ|z＝Ax?for?some?x∈{0，1} ^m} (2)

Wherein, z represents the code word in the LDGM sign indicating number quantization code book, and arithmetical operation wherein is that 2 gal is patrolled magnificent territory (GF (2)) based on size.

Source encoder with given information source sequences y ∈ 0,1} ⁿBe mapped as dope vector x ∈ 0,1} ^m, source decoding is then by simple

Realize, wherein,

The information source sequence that can be called reconstruct.

As can be seen, adopting the main challenge that the distortion source encoding is arranged of LDGM sign indicating number is how to determine that information bit vector x makes the Hamming distortion || y-Ax|| ₁/ n minimum.

The present invention notices when parameter q is bigger among the GF (q), most row degree of the best LDPC sign indicating number on the GF (q) are 2, proposition is the generator matrix of the check matrix of 2 polynary cyclic LDPC code as the LDGM sign indicating number with the row degree, and adopt the RBP algorithm to encode, realization has uniform enconding complexity (O (n)) and performance has distortion to quantize described GF (q)={ 0,1 near the BSS based on polynary LDGM sign indicating number of rate distortion capacity, ..., q-1}.

Basic thought of the present invention is: the generator matrix of constructing polynary LDGM sign indicating number according to code check and code length; After given information source sequence, adopt the RBP encryption algorithm to the compression of information source sequence according to the generator matrix of constructing, obtain compressed sequence.

The present invention is described in further detail below by drawings and the specific embodiments.

The present invention realizes a kind of binary symmetric source Methods for Coding, and as shown in Figure 1, this method comprises following step:

Step 101: the generator matrix of constructing polynary LDGM sign indicating number according to code check and code length;

Concrete, the check matrix B of the cyclic LDPC code that at first to adopt size of PEG algorithm construction be m * n, wherein, m is the product of code check and code length, and n is a code length, and m is less than n, and lists whenever that to have only two locational elements be 1, and element is 0 on other positions; Be 1 element then with each value in the verification matrix B with uniform probability replace with at random set 1,2 ..., the arbitrary element among the q-1}, q are the positive integer greater than 3; At last verification matrix B transposition being obtained size is the generator matrix A of the polynary LDGM sign indicating number of n * m; Described code check and code length can be definite according to the sequence that will compress by the System Control Center of being responsible for the information allotment, and System Control Center can be the control centre of image data samples, perhaps the control centre of audio data samples etc.

Step 102: given information source sequence;

Concrete, the LDGM sign indicating number can be used factor graph G=(V, C as shown in Figure 2, E) expression, V={1 wherein, 2, ..., m} represents the set of information node x, i.e. " zero " on the left side among Fig. 2, C={1,2 ..., n} represents the set of check-node z, be " " among Fig. 2, E represents to connect the set on the limit of check-node and information node.As can be seen from Figure 2, each check-node z _i(i=1 2...n) has an exclusive information source node y _i(i=1,2...n) neighbours and two information node neighbours, described information source node y _i(i=1,2...n) neighbours are " zero " on the right among Fig. 2.In factor graph, define g on the limit of link information node j and check-node i _{I, j}∈ GF (q)/{ 0}, described g _{I, j}The value of the nonzero element of the capable j row of i among the corresponding generator matrix A;

The information node neighbours' of verification node i set is designated as V (i), the check node neighbours' of information node i set is designated as C (i).Obviously, the LDGM sign indicating number of structure has | V (i) | and=2, i=1,2 ..., n.Given all bits satisfy the information source sequences y of verification relational expression (3), and the code length of information source sequences 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 the formula (3) is based on GF (q).

Step 103: after given information source sequence, adopt the RBP encryption algorithm to the compression of information source sequence, obtain compressed sequence according to the generator matrix of constructing;

Concrete, order

Message vector from information node x to check-node z when representing the l time iteration, to symbol a ∈ GF (q) arbitrarily,

The probability of a representation in components information node symbol x=a, be designated as

Similar,

Message vector from check-node z to information node x when representing the l time iteration,

For

A component; μ _{Y → z}The message vector of expression from information source node y to check-node z, μ _{Y → z}(a) be μ _{Y → z}A component; λ ^lThe reliability vector of representing information node x after the l time iteration, λ ^l(a) be λ ^lA component;

The initialization of information source node message is suc as formula shown in the RBP-1;

μ _y→z(a)∝exp(-2βd _H(y，a)) (RBP-1)

Among the formula RBP-1, parameter beta be chosen as satisfy following formula on the occasion of separating:

lncoshβ-βtanhβ+Rln?2＝0

The initialization of information node message is suc as formula shown in the RBP-2;

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

Wherein, dither be (0,1/q ²) between equally distributed random number;

The check-node information updating is suc as formula shown in the RBP-3;

${\mathrm{\&mu;}}_{z\&RightArrow;x}^l\left(a\right)=\underset{g_{x\&prime;z}{a}_1+{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HSA00000161538100012.png"\; state="\{\{state\}\}">a</figure-callout>}}_2=-g_{\mathrm{xz}}a}{\mathrm{\&Sigma;}}{\mathrm{\&mu;}}_{x\&prime;\&Element;V\left(z\right)\backslash \left\{x\right\}\&RightArrow;z}^l\left(a_1\right)\&CenterDot;{\mathrm{\&mu;}}_{y\&RightArrow;z}\left(a_2\right)---(\mathrm{RBP}-3)$

Wherein, g <sub>X`z</sub>The nonzero element value of the capable x` row of z among the expression generator matrix A, g _XzThe nonzero element value of the capable x row of z among the expression generator matrix A;

The information node reliability is upgraded suc as formula shown in the RBP-4;

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

The information node information updating is suc as formula shown in the 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 as

r ₀, r ₁∈ [0,1].

Above-mentioned, the iteration stopping condition of RBP algorithm is: iterations l reaches a predetermined maximum L _MaxPerhaps there is formula (4) to set up for all information nodes 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 the RBP algorithm computation,, get the symbol a formation compressed sequence x of probability maximum in each information node according to the probability that formula RBP-4 obtains all symbol a in each information node, then the code length of x is m, because m, has realized the compression to the information source sequences y less than n, promptly BSS encodes.

Further, in the RBP algorithm, because degree is d _xThe computation complexity of information node be O (d _xQ), degree is that the computation complexity of 3 check-node (promptly comprising 2 information node neighbours and 1 information source node neighbour) is O (3 ²Q ²).In order to reduce complexity, the information updating of check-node can adopt 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 ^-1Fast fourier transform and invert fast fourier transformation are adopted in expression respectively.Adopt fast fourier transform, the complexity of the Fourier transform of the message vector of each check-node is O (pq), wherein p=log ₂Q.Therefore the computation complexity of each check-node is O (3 ²Pq), code length (symbol lengths) is O (3 for the encoder complexity of the LDGM sign indicating number of n ²Pqn), complexity O (3 as can be seen ²Pqn) be linear complexity.

Among the present invention, can be by reconstruct information source Sequence Detection distortion performance, can establish reconstruct information source sequence and be

According to the compressed sequence x that obtains in generator matrix A in the step 101 and the step 103, according to

Reconstruct information source sequence.

For example, according to above-mentioned method, when q=8, when promptly GF (q) is GF (8), suppose that code length is n=4000 GF (a 8) symbol, corresponding bit length is 12000, γ ₁=0.9995, γ ₀=0.95, L _Max=300, the value of parameter beta is as shown in table 1, code check R value be R=0.1,0.2 ..., 0.9; GF (8) under the then different code checks goes up the LDGM sign indicating number and adopts the distortion performance of RBP encryption algorithm shown in " " among Fig. 3, the distortion performance of TAP method is represented with " zero " in Fig. 3, as can be seen from the figure, the distortion performance that the distortion performance of present embodiment is compared the TAP method has great improvement, and the distortion performance of present embodiment and rate distortion Capacity Ratio are more approaching.

Table 1

When q=16, when promptly GF (q) is GF (16), suppose that code length is n=3000 GF (a 16) symbol, corresponding bit length is 12000, γ ₁=0.9995, γ ₀=0.95, L _Max=300, the value of parameter beta is as shown in table 1, code check R value be R=0.1,0.2 ..., 0.9; GF (16) under the then different code checks goes up the LDGM sign indicating number and adopts the distortion performance of RBP encryption algorithm shown in " △ " among Fig. 3, as can be seen from the figure, the last LDGM sign indicating number of GF (8) that the distortion performance of this embodiment is compared with code length adopts the distortion performance of RBP encryption algorithm to improve, and very approaching with the rate distortion capacity.Wherein, in code check≤0.5 o'clock, the distortion performance of present embodiment is no more than 0.005 apart from the rate distortion capacity; In code check＞0.5 o'clock, the distortion performance of present embodiment is no more than 0.01 apart from the rate distortion capacity.

When q=256, when promptly GF (q) is GF (256), suppose that code length is n=1500 GF (a 256) symbol, corresponding bit length is 12000, γ ₁=0.9995, L _Max=300, γ ₀Be chosen as the experiment optimal value, the value of parameter beta is as shown in table 1, code check R value be R=0.1,0.2 ..., 0.9; GF (256) under the then different code checks goes up the LDGM sign indicating number and adopts the distortion performance of RBP encryption algorithm shown in " ◇ " among Fig. 3, as can be seen from the figure, the distortion performance of present embodiment is compared GF (16) with code length and is gone up distortion performance that the LDGM sign indicating number adopts the RBP encryption algorithm more by a small margin raising is only arranged.

In order to realize said method, the present invention also provides a kind of binary symmetric source apparatus for encoding, and as shown in Figure 4, this device comprises: generator matrix module 41, compressed sequence module 42 wherein,

Generator matrix module 41 is used for constructing according to code check and code length the generator matrix of polynary LDGM sign indicating number, and notifies compressed sequence module 42 with generator matrix;

Concrete, the check matrix that it is the cyclic LDPC code of m * n that generator matrix module 41 adopts size of PEG algorithm construction, wherein, m is the product of code check and code length, and n is a code length, and m is less than n, and list whenever that to have only two locational elements be 1, element is 0 on other positions; Be 1 element then with each value in the check matrix with uniform probability replace with at random set 1,2 ..., the arbitrary element among the q-1}, q are the positive integer greater than 3; At last the verification matrix transpose being obtained size is the generator matrix of the polynary LDGM sign indicating number of n * m, and notifies reconstruct information source block 43 with generator matrix;

Compressed sequence module 42 is used for after given information source sequence, and the generator matrix of constructing according to generator matrix module 41 adopts the RBP encryption algorithm to the compression of information source sequence, obtains compressed sequence;

Further, when described compressed sequence module 42 adopts the information updating of RBP encryption algorithm calculation check node, adopt the information updating of fast fourier transform calculation check node, specifically can repeat no more here referring to formula (5).

The above is preferred embodiment of the present invention only, is not to be used to limit protection scope of the present invention, all any modifications of being done within the spirit and principles in the present invention, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. a binary symmetric source Methods for Coding is characterized in that, this method comprises:

Construct the generator matrix of polynary low-density generated matrix (LDGM) sign indicating number according to code check and code length;

After given information source sequence, adopt enhancement mode belief propagation (RBP) encryption algorithm to the compression of information source sequence according to the generator matrix of constructing, obtain compressed sequence.

2. method according to claim 1, it is characterized in that, described generator matrix of constructing polynary LDGM sign indicating number according to code check and code length, be specially: the check matrix of cyclic low-density parity check (LDPC) sign indicating number that it is m * n that the employing progressive edge increases size of (PEG) algorithm construction, wherein, m is the product of code check and code length, n is a code length, m is less than n, and lists whenever that to have only two locational elements be 1, and element is 0 on other positions; Be 1 element with each value in the check matrix with uniform probability replace with at random set 1,2 ..., the arbitrary element among the q-1}, q are the positive integer greater than 3; At last the verification matrix transpose being obtained size is the generator matrix of the polynary LDGM sign indicating number of n * m.

3. method according to claim 1 is characterized in that, this method further comprises: when adopting the information updating of RBP encryption algorithm calculation check node, adopt the information updating of fast fourier transform calculation check node.

4. method according to claim 1 is characterized in that, described code check and code length are determined according to the sequence that will compress by the System Control Center of the information of being responsible for allotment.

5. a binary symmetric source apparatus for encoding is characterized in that, this device comprises: generator matrix module, compressed sequence module, reconstruct information source block; Wherein,

The generator matrix module is used for constructing according to code check and code length the generator matrix of polynary LDGM sign indicating number, and notifies the compressed sequence module with generator matrix;

The compressed sequence module is used for after given information source sequence, adopts the RBP encryption algorithm to the compression of information source sequence according to the generator matrix of generator matrix module structure, obtains compressed sequence.

6. device according to claim 5, it is characterized in that, described generator matrix module is constructed the generator matrix of polynary LDGM sign indicating number according to code check and code length, be specially: the check matrix that it is the cyclic LDPC code of m * n that the generator matrix module adopts size of PEG algorithm construction, wherein, m is the product of code check and code length, n is a code length, m is less than n, and lists whenever that to have only two locational elements be 1, and element is 0 on other positions; Be 1 element then with each value in the check matrix with uniform probability replace with at random set 1,2 ..., the arbitrary element among the q-1}, q are the positive integer greater than 3; At last the verification matrix transpose being obtained size is the generator matrix of the polynary LDGM sign indicating number of n * m, and notifies reconstruct information source block with generator matrix.

7. device according to claim 5 is characterized in that, described compressed sequence module when being further used for adopting the information updating of RBP encryption algorithm calculation check node, adopts the information updating of fast fourier transform calculation check node.

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