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

Binary symmetric source coding method and device

Technical Field

The present invention relates to source coding technology, and in particular, to a method and apparatus for binary symmetric source coding.

Background

The multi-antenna technology is a key technology of a Long Term Evolution (LTE) system. When a plurality of antennas are configured at a downlink transceiver, how to design signals at the transceiver to obtain a channel capacity of a mimo downlink (mimo) system becomes an important issue. Theoretical research shows that the capacity of a multi-input multi-output system broadcast channel (MIMOBC) can be obtained by adopting a Dirty Paper Coding (DPC) technology at a transmitting end (base station). Since theoretical studies do not give how to design structured DPCs, the structured DPC design technique has become a research hotspot in the current academic and engineering fields.

Superposition coding is an efficient structured DPC implementation recently proposedThe technique requires the provision of a good channel code and a good source code. In the superposition coding structure, the channel code can generally adopt a code which can reach the channel capacity, such as a mature Low-density parity check (LDPC) code and the like; the source code may employ Trellis Coded Quantization (TCQ) or Low-density generator matrix (LDGM) code. In order to approach the rate-distortion capacity, when TCQ is used for the source code, a very large number of states is required, such as: number of states is 2^tTo show that t is the code storage length, t is generally required to be greater than 20 in order to approach the rate distortion capacity. Therefore, the LDGM code based quantization of distorted sources needs to be studied. Research shows that the LDGM code is a distorted source code which can reach rate-distortion capacity of a Binary Symmetric Source (BSS). However, the complexity of the conventional LDGM coding algorithm using Survey Propagation (SP)/Decimation (differentiation) is the square of the code length, and can be expressed as O (n)²) And n is the code length. Considering that the code length of the LDGM code is generally required to be more than 10 in order to approximate the rate distortion capacity⁴And therefore its complexity is high.

One LDGM coding algorithm with linear complexity is the TAP (thouless anderson palm) method, which has linear complexity because the generating matrix of binary LDGM codes in the TAP method has a row degree of 2, so that the coding can be performed by using the enhanced belief propagation (RBP) algorithm, which can avoid the decimation step necessary in other coding methods. However, it has been acknowledged that the performance of the TAP method is poor, mainly because the cyclic binary LDPC code with a check matrix column degree of 2, which is paired with the binary LDGM code with a generator matrix row degree of 2, is not a good channel code. In terms of coding theory, the code redistribution of the cyclic binary LDPC code with rank 2 is far from the code redistribution of the theoretically optimal channel code, and therefore, the performance of the TAP method is difficult to approach the rate-distortion capacity.

Disclosure of Invention

In view of the above, the main objective of the present invention is to provide a method and an apparatus for binary symmetric source coding, which implement BSS coding with linear coding complexity and rate-distortion performance close to rate-distortion capacity.

In order to achieve the purpose, the technical scheme of the invention is realized as follows:

the invention provides a binary symmetric source coding method, which comprises the following steps:

constructing a generating matrix of a multi-element LDGM code according to the code rate and the code length;

after an information source sequence is given, compressing the information source sequence by adopting an RBP coding algorithm according to the constructed generating matrix to obtain a compressed sequence.

In the foregoing scheme, the constructing a generator matrix of a multivariate LDGM code according to a code rate and a code length specifically includes: constructing a check matrix of the cyclic LDPC code with the size of m multiplied by n by adopting a progressive edge-growing (PEG) algorithm, wherein m is the product of a code rate and a code length, n is the code length, m is smaller than n, only elements on two positions on each column are 1, and elements on other positions are 0; randomly replacing each element with a value of 1 in the check matrix with any element in a set {1, 2.,. q-1} with a uniform probability, wherein q is a positive integer greater than 3; and finally, transposing the check matrix to obtain a generating matrix of the multi-element LDGM code with the size of n multiplied by m.

In the above scheme, the method further comprises: and when the RBP coding algorithm is adopted to calculate the message update of the check node, the fast Fourier transform is adopted to calculate the message update of the check node.

In the above scheme, the code rate and the code length are determined by a system control center responsible for information deployment according to a sequence to be compressed.

The invention provides a binary symmetric source coding device, which comprises: the device comprises a matrix generation module, a compressed sequence module and a reconstructed information source sequence module; wherein,

the generating matrix module is used for constructing a generating matrix of the multi-element LDGM code according to the code rate and the code length and informing the generating matrix to the compression sequence module;

and the compression sequence module is used for compressing the information source sequence by adopting an RBP coding algorithm according to the generating matrix constructed by the generating matrix module after the information source sequence is given to obtain a compression sequence.

In the above scheme, the generating matrix module constructs a generating matrix of a multivariate LDGM code according to a code rate and a code length, specifically: the generation matrix module adopts a PEG algorithm to construct a check matrix of a cyclic LDPC code with the size of m multiplied by n, wherein m is the product of code rate and code length, n is the code length, m is smaller than n, only the elements on two positions on each column are 1, and the elements on other positions are 0; then randomly replacing each element with the value of 1 in the check matrix with any element in a set {1, 2.,. q-1} with uniform probability, wherein q is a positive integer greater than 3; and finally, transposing the check matrix to obtain a generating matrix of the multi-element LDGM code with the size of n multiplied by m, and informing the generating matrix to a reconstruction information source sequence module.

In the above scheme, the compressed sequence module is further configured to calculate the message update of the check node by using fast fourier transform when calculating the message update of the check node by using the RBP coding algorithm.

The invention provides a binary symmetric source coding method and a binary symmetric source coding device, wherein a generating matrix of a multi-element LDGM code is constructed according to a code rate and a code length; after an information source sequence is given, compressing the information source sequence by adopting an RBP coding algorithm according to a constructed generating matrix to obtain a compressed sequence; therefore, the BSS coding which has the linear coding complexity and rate distortion performance close to the rate distortion capacity can be realized, and the rate distortion performance of the BSS coding is improved.

Drawings

FIG. 1 is a schematic flow chart of a method for implementing binary symmetric source coding according to the present invention;

FIG. 2 is a factor graph for representing LDGM codes according to the present invention;

FIG. 3 is a schematic diagram of a simulation of rate-distortion performance of the TAP method and the method of the present invention for implementing binary symmetric source coding;

fig. 4 is a schematic structural diagram of an apparatus for implementing binary symmetric source coding according to the present invention.

Detailed Description

In the distorted source coding problem, the source sequence y to be compressed follows an independent equal distribution (i.i.d.) y for each element_iWherein y ∈ S, y_i∈P_SS denotes the character set to which the source belongs, P_SRepresenting a set of probabilities for each element in the character set S. The idea of source coding is to use a certain code word in the codebook CFor example, a binary symmetric Bernoulli source (be (1/2)) with a parameter p of 1/2, and a source encoder with a code rate R (i.e., compression ratio) of R of m/n, will use the source sequence y ∈ {0, 1} for quantization compression of the source sequence yⁿMapped as a binary vector x ∈ {0, 1} of length m < n^mThe source decoder maps x as a compressed sequence into a reconstructed source sequence

For a given binary sequence pairHamming distortion D is typically used as a measure of reconstruction fidelity. Wherein, denotes y andthe Hamming distance between, i.e. the sequences y andthe number of different element values at the middle corresponding position is as follows: d_H(001, 101) ═ 1. For the beer (1/2) source, there is the following equation (1) according to Shannon rate-distortion theory:

$R\left(D\right)=\left\{\begin{array}{cc}1-H\left(D\right),& D\&Element;\&lsqb;\mathrm{0,0.5}\&rsqb;\\ 0,& \mathrm{otherwise}\end{array}\right.---\left(1\right)$

where H (-) is a binary entropy function.

For a distorted source coding using binary LDGM code, given a code rate R < 1, let A ∈ {0, 1}^n×mIs a generator matrix for LDGM codes and assumes without loss of generality that its rank is mI.e., rank a ═ m. In addition, because the LDGM code has a low density characteristic, the number of elements 1 in each row and column of the generator matrix a is always limited, and therefore, the quantization codebook based on the LDGM code is defined as expression (2).

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

Where z denotes a codeword in the LDGM code quantization codebook, where the arithmetic operation is based on a galois field (GF (2)) of size 2.

The source encoder will give the source sequence y ∈ {0, 1}ⁿMapped as an information vector x ∈ {0, 1}^mSource decoding is performed by simpleThe realization is that, among others,which may be referred to as a reconstructed source sequence.

It can be seen that the main challenge of the distorted source coding using LDGM codes is how to determine the information bit vector x such that Hamming is distorted y-Ax₁The/n is minimum.

The invention is noticed that when the parameter q in GF (q) is relatively large, the most part of the column degree of the optimal LDPC code on GF (q) is 2, a check matrix of a multi-element cyclic LDPC code with the column degree of 2 is proposed as a generation matrix of the LDGM code, and an RBP algorithm is adopted for coding, so that the BSS distortion quantization based on the multi-element LDGM code with linear coding complexity (O (n)) and performance approaching rate distortion capacity is realized, wherein the GF (q) is {0, 1., q-1 }.

The basic idea of the invention is: constructing a generating matrix of a multi-element LDGM code according to the code rate and the code length; after an information source sequence is given, compressing the information source sequence by adopting an RBP coding algorithm according to the constructed generating matrix to obtain a compressed sequence.

The invention is further described in detail below with reference to the figures and the specific embodiments.

The invention realizes a binary symmetric source coding method, as shown in fig. 1, the method comprises the following steps:

step 101: constructing a generating matrix of a multi-element LDGM code according to the code rate and the code length;

specifically, a check matrix B of a cyclic LDPC code with the size of m multiplied by n is constructed by a PEG algorithm, wherein m is the product of a code rate and a code length, n is the code length, m is smaller than n, only two elements on each column are 1, and the elements on other positions are 0; then randomly replacing each element with the value of 1 in the check matrix B with any element in a set {1, 2.,. q-1} with uniform probability, wherein q is a positive integer greater than 3; finally, transposing the check matrix B to obtain a generating matrix A of the multivariate LDGM code with the size of n multiplied by m; the code rate and the code length can be determined by a system control center in charge of information allocation according to a sequence to be compressed, and the system control center can be a control center for image data sampling, a control center for audio data sampling and the like.

Step 102: giving a source sequence;

specifically, the LDGM code may be represented by a factor graph G ═ (V, C, E) as shown in fig. 2, where V ═ 1, 2.. multidata, m } represents a set of information nodes x, i.e., "○" on the left in fig. 2, C ═ 1, 2.. multidata, n } represents a set of check nodes z, i.e., "□" in fig. 2, and E represents a set of edges connecting the check nodes and the information nodes, as can be seen from fig. 2_i(i 1, 2.. n) has a unique source node y_iN, and two information node neighbors, the source node y_iN (i-1, 2.. n) neighbors, "○", on the right in fig. 2, g is defined on the edge connecting the information node j and the check node i in the factor graph_i，j∈ GF (q)/{0}, the g_i，jCorresponding to the value of the non-zero element in the ith row and the jth column in the generated matrix A;

the set of information node neighbors of check node i is denoted as V (i), and the set of check node neighbors of information node i is denoted as C (i). Obviously, LDGM codes are constructed with | v (i) | 2, i ═ 1, 2. A source sequence y is given, all bits of which satisfy the check relation (3), and the code length of the source sequence y is n.

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

Wherein the arithmetic operation in formula (3) is based on gf (q).

Step 103: after an information source sequence is given, compressing the information source sequence by adopting an RBP coding algorithm according to a constructed generating matrix to obtain a compressed sequence;

specifically, orderThe message vector representing the flow from the information node x to the check node z at the l-th iteration is, for an arbitrary symbol a ∈ gf (q),the a-th component of (a) represents the probability that the information node symbol x is aIs composed ofIn a similar manner to that described above,representing the message vector from check node z to information node x at the ith iteration,is composed ofThe a-th component of (a); mu.s_y→zRepresenting a message vector, μ, from source node y to check node z_y→z(a) Is mu_y→zThe a-th component of (a); lambda [ alpha ]^lRepresenting the reliability vector, λ, of the information node x after the ith iteration^l(a) Is λ^lThe a-th component of (a);

initializing the information source node message as shown in a formula RBP-1;

μ_y→z(a)∝exp(-2βd_H(y，a))(RBP-1)

in the formula RBP-1, the parameter β is chosen to satisfy a positive solution of:

lncoshβ-βtanhβ+Rln2＝0

initializing the information node message as shown in a formula RBP-2;

${\mathrm{\&mu;}}_{x\&RightArrow;z}^1\left(a\right)=1/q\&PlusMinus;\mathrm{dither}---(\mathrm{RBP}-2)$

wherein dither is in (0, 1/q)²) Random numbers uniformly distributed among them;

updating check node information as shown in a formula RBP-3;

${\mathrm{\&mu;}}_{z\&RightArrow;x}^l\left(a\right)=\underset{g_{x\&prime;z}{a}_1+a_2=-g_{\mathrm{xz}}a}{\mathrm{\&Sigma;}}{\mathrm{\&mu;}}_{x\&prime;\&Element;V\left(z\right)\backslash \left\{x\right\}\&RightArrow;z}^l\left(a_1\right)\&CenterDot;{\mathrm{\&mu;}}_{y\&RightArrow;z}\left(a_2\right)---(\mathrm{RBP}-3)$

wherein, g_x`zRepresents the value of the non-zero element, g, of the z-th row and x' column in the generator matrix A_xzRepresenting the value of a nonzero element of the xth row and the xth column in the generator matrix A;

updating the reliability of the information node as shown in a formula RBP-4;

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

the information node message is updated as shown in a 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]。

The iteration stop condition of the RBP algorithm is as follows: the number of iterations L reaches a predetermined maximum value L_max(ii) a Or the formula (4) holds for all the information nodes and the check nodes;

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

after calculation by the RBP algorithm, the probability of all symbols a in each information node is obtained according to the formula RBP-4, the symbol a with the highest probability in each information node is taken to form a compression sequence x, the code length of x is m, and the compression of the information source sequence y, namely BSS (base station system) coding, is realized because m is smaller than n.

Further, in the RBP algorithm, the degree is d_xThe computational complexity of the information node of (2) is O (d)_xQ) with a computation complexity of O (3) for a check node of degree 3 (i.e. comprising 2 information node neighbors and 1 source node neighbor)²·q²). In order to reduce complexity, the message update of the check node can be realized by adopting the fast fourier transform of the formula (5);

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

wherein, F and F^-1Respectively, indicating the use of a fast fourier transform and an inverse fast fourier transform. The complexity of the Fourier transform of the message vector of each check node is O (p.q) by using the fast Fourier transform, wherein p is log₂q is calculated. The computational complexity of each check node is therefore O (3)²P.q) code length (symbol length) n, and the code complexity of the LDGM code is O (3)²P.q.n), the complexity O (3) can be seen²P.q.n) is the linear complexity.

In the invention, the rate distortion performance can be detected by reconstructing the information source sequence, and the reconstructed information source sequence can be set asAccording to the generation matrix A in step 101 and the compressed sequence x obtained in step 103The source sequence is reconstructed.

For example, according to the above method, when q is 8, that is, when GF (q) is GF (8), the code length is assumed to be n 4000 GF (8) symbols, the corresponding bit length is 12000, and γ is₁＝0.9995，γ₀＝0.95，L_max300, the value of the parameter β is shown in table 1, and the code rate R is 0.1, 0.2, 0.9, then the rate-distortion performance of the LDGM code using the RBP coding algorithm over GF (8) at different code rates is shown as "□" in fig. 3, and the rate-distortion performance of the TAP method is shown as "○" in fig. 3, which shows that the rate-distortion performance of the present embodiment is greatly improved compared with the rate-distortion performance of the TAP method, and the rate-distortion performance of the present embodiment is closer to the rate-distortion capacity.

TABLE 1

When q is 16, that is, GF (16) is GF (q), the code length is assumed to be n is 3000 GF (16) symbols, the corresponding bit length is 12000, γ₁＝0.9995，γ₀＝0.95，L_max300, the value of the parameter β is shown in table 1, and the code rate R is 0.1, 0.2, 0.9, then the rate-distortion performance of the LDGM code using the RBP coding algorithm over GF (16) at different code rates is shown as "△" in fig. 3, which shows that the rate-distortion performance of the present embodiment is improved to a certain extent compared with the rate-distortion performance of the LDGM code using the RBP coding algorithm over GF (8) at the same code length, and is very close to the rate-distortion capacity, wherein the rate-distortion performance of the present embodiment is not more than 0.005 from the rate-distortion capacity when the code rate is less than or equal to 0.5, and the rate-distortion performance of the present embodiment is not more than 0.01 from the rate-distortion capacity when the code rate is greater than 0.5.

When q is 256, that is, GF (256) is GF (q), the code length is 1500 GF (256) symbols, the corresponding bit length is 12000, γ₁＝0.9995，L_max＝300，γ₀The optimal value is selected as the experimental optimal value, the value of the parameter β is shown in table 1, the value of the code rate R is 0.1, 0.2, 0.9, the rate distortion performance of the LDGM code on GF (256) at different code rates by using the RBP coding algorithm is shown as "◇" in fig. 3, and it can be seen from the figure that the rate distortion performance of the embodiment is compared with the rate distortion performance of the LD on GF (16) at the same code lengthThe rate distortion performance of the GM code adopting the RBP coding algorithm is only improved by a small margin.

In order to implement the above method, the present invention further provides a binary symmetric source coding apparatus, as shown in fig. 4, the apparatus comprising: a matrix generation module 41, a compressed sequence module 42,

a generating matrix module 41, configured to construct a generating matrix of the multi-element LDGM code according to the code rate and the code length, and notify the generating matrix to the compression sequence module 42;

specifically, the matrix generation module 41 constructs a check matrix of a cyclic LDPC code with a size of mxn by using a PEG algorithm, where m is a product of a code rate and a code length, n is the code length, m is smaller than n, and only two elements on each column are 1, and elements on other positions are 0; then randomly replacing each element with the value of 1 in the check matrix with any element in a set {1, 2.,. q-1} with uniform probability, wherein q is a positive integer greater than 3; finally, transposing the check matrix to obtain a generating matrix of the multivariate LDGM code with the size of nxm, and informing the generating matrix to a reconstruction information source sequence module 43;

a compressed sequence module 42, configured to, after a source sequence is given, compress the source sequence by using an RBP coding algorithm according to the generator matrix constructed by the generator matrix module 41 to obtain a compressed sequence;

further, when the compressed sequence module 42 calculates the message update of the check node by using the RBP coding algorithm, the message update of the check node is calculated by using fast fourier transform, which may be specifically referred to as formula (5), and is not described herein again.

The above description is only exemplary of the present invention and should not be taken as limiting the scope of the present invention, and any modifications, equivalents, improvements, etc. that are within the spirit and principle of the present invention should be included in the present invention.

Claims (5)

1. A method of binary symmetric source coding, the method comprising:

constructing a generating matrix of a multi-element low-density generating matrix LDGM code according to the code rate and the code length;

after an information source sequence is given, compressing the information source sequence by adopting an enhanced belief propagation (RBP) coding algorithm according to a constructed generating matrix to obtain a compressed sequence;

the constructing of the generating matrix of the multiple low-density generating matrix LDGM code according to the code rate and the code length specifically comprises the following steps: constructing a check matrix of the LDPC code with the size of m multiplied by n by adopting a progressive edge-added PEG algorithm, wherein m is the product of a code rate and a code length, n is the code length, m is smaller than n, only elements on two positions on each column are 1, and elements on other positions are 0; randomly replacing each element with a value of 1 in the check matrix with any element in a set {1, 2.,. q-1} with a uniform probability, wherein q is a positive integer greater than 3; and finally, transposing the check matrix to obtain a generating matrix of the multi-element low-density generating matrix LDGM code with the size of n multiplied by m.

2. The method of claim 1, further comprising: and when the message update of the check node is calculated by adopting an enhanced belief propagation (RBP) coding algorithm, the message update of the check node is calculated by adopting fast Fourier transform.

3. The method of claim 1, wherein the code rate and the code length are determined by a system control center responsible for information deployment according to a sequence to be compressed.

4. An apparatus for binary symmetric source coding, the apparatus comprising: the device comprises a matrix generation module, a compressed sequence module and a reconstructed information source sequence module; wherein,

the generating matrix module is used for constructing a generating matrix of a multi-element low-density generating matrix LDGM code according to the code rate and the code length and informing the generating matrix to the compression sequence module;

the compression sequence module is used for compressing the information source sequence by adopting an enhanced belief propagation (RBP) coding algorithm according to the generation matrix constructed by the generation matrix module after the information source sequence is given to obtain a compression sequence;

the generation matrix module constructs a generation matrix of a multi-element low-density generation matrix LDGM code according to the code rate and the code length, and specifically comprises the following steps: the matrix generation module adopts a progressive edge PEG (polyethylene glycol) increasing algorithm to construct a check matrix of the LDPC code with the size of mxn, wherein m is the product of a code rate and a code length, n is the code length, m is smaller than n, only elements on two positions on each column are 1, and elements on other positions are 0; then randomly replacing each element with the value of 1 in the check matrix with any element in a set {1, 2.,. q-1} with uniform probability, wherein q is a positive integer greater than 3; and finally, transposing the check matrix to obtain a generating matrix of the multi-element low-density generating matrix LDGM code with the size of n multiplied by m, and informing the reconstructing information source sequence module of the generating matrix.

5. The apparatus of claim 4, wherein the compressed sequence module is further configured to compute the message update of the check node using fast fourier transform when the message update of the check node is computed using an enhanced belief propagation (RBP) coding algorithm.