CN104104393A - Quasi-cycle LDPC code design method with simple iterative code structure - Google Patents

Abstract

The invention discloses a quasi-cycle LDPC code design method with a simple iterative code structure; the method comprises the following steps: A, optimization construction of a biradical matrix; B, optimization construction of an index matrix. A QC-LDPC code is formed and capable of keeping an H matrix structure used for carrying out simple iterative coding in an optimization process, and is provided with an optimization biradical matrix threshold value and a short length ring distribution of a corresponding index matrix, so a mis-bit rate performance of the QC-LDPC can be improved, and hardware realization is easy.

Description

A kind of quasi-cyclic LDPC code method for designing with simple iterative code structure

Technical field

The present invention relates to channel coding technology, be specifically related to a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure.

Background technology

LDPC (Low Density Parity Check) code deep space communication, the 4th Generation Mobile Communication System, at a high speed with the even various aspects such as power line communication of very high speediness rate Digital Subscriber Line, magnetic recording system, cause the great attention of countries in the world academia and IT industry circle, become the study hotspot that current field of channel coding is attracted attention most.The encoder complexity that LDPC code is higher is a Main Bottleneck of LDPC code application, QC-LDPC is an important subclass of LDPC code, in IEEE 802.16e international standard, the encoder complexity of QC-LDPC is higher, first traditional method generally need to be converted to generator matrix by parity matrix, then initial data utilizes generator matrix to encode, and this kind of cataloged procedure is relatively complicated, is not easy to the realization of hardware.

Summary of the invention

For solving the problems of the technologies described above, the present invention proposes a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure, reach hard-wired object.

For achieving the above object, technical scheme of the present invention is as follows:

A quasi-cyclic LDPC code method for designing with simple iterative code structure, comprises the steps:

A. the Optimal Construction of biradical matrix;

B. the Optimal Construction of exponential matrix;

The Optimal Construction concrete steps of described biradical matrix are as follows:

A (1). be provided with S the molecular population of grain, each particle is a J n dimensional vector n, and that particle is corresponding here is exactly the message part H of biradical matrix H ₁, produce at random the binary vector that S J ties up;

A (2). obtain after S J dimension binary vector of A (1) generation, set up accordingly the message part B (H of the biradical matrix B 1 (H) that S size is M × K ₁), with the check part B (H of H matrix _p) combine, structure biradical matrix B 1 (H), adopts prototype external information branching algorithm to calculate the threshold value that each basic matrix is corresponding, can obtain altogether S threshold value, upgrade the optimal value pbest of each particle, and then more all pbest, global optimum gbest obtained;

A (3). the movement law that following formula is each particle:

$v_{\mathrm{ij}}^t=w{v}_{\mathrm{ij}}^{t-1}+c_1{\mathrm{\η}}_1({\mathrm{pbest}}_{\mathrm{ij}}^{t-1}-x_{b,\mathrm{ij}}^{t-1})+c_2{\mathrm{\η}}_2({\mathrm{gbest}}_{\mathrm{ij}}^{t-1}-x_{b,\mathrm{ij}}^{t-1})$

Wherein, w=1.0, c ₁=c ₂=2.0, coefficient η ₁and η ₂for equally distributed random number between (0,1), can obtain accordingly intermediate variable sig (v ^t _ij);

$\mathrm{sig}\left(v_{\mathrm{ij}}^t\right)=\frac{1}{1+e^{-v_{\mathrm{ij}}^t}}$

On this basis, can obtain the j position of i particle, upgrade according to the following formula

$x_{b,\mathrm{ij}}^t=\left\{\begin{array}{cc}1,& r_{\mathrm{ij}}^t<\mathrm{sig}\left(v_{\mathrm{ij}}^t\right)\\ 0,& r_{\mathrm{ij}}^t\&GreaterEqual;\mathrm{sig}\left(v_{\mathrm{ij}}^t\right)\end{array}\right.$

Wherein, r ^t _ijfor equally distributed random number between (0,1);

A (4). iterations adds 1, returns to steps A (2), upgrades pbest and gbest, until iterations reaches maximum;

The Optimal Construction concrete steps of described exponential matrix are as follows:

B (1). establishing nonzero integer element to be optimized in exponential matrix is Je, and each integer correspondence log ₂ls binary bits string, therefore binary vector length to be optimized is Je × log ₂ls, generates S Je × log at random ₂the binary vector of Ls dimension;

B (2). in the random each binary vector generating, with log ₂ls bit is one group, a corresponding scope is [0, Ls-1] integer, can construct accordingly Je dimension integer vector, Je is tieed up to integer vector and is converted to the exponential matrix E (H) of big or small M × N, therefore the S constructing in a first step two-dimensional vector, can relative configurations go out S exponential matrix E (H), detect the number of the short length ring that in each exponential matrix E (H), length is 6, the number assignment of the short length ring that is 6 by length is to pbest, therefore S exponential matrix correspondence S pbest, the relatively value of S pbest, by the value assignment of minimum pbest to gbest, and the now E (H) of correspondence of record,

B (3). the update rule of the position of each particle is identical with A (3) step;

B (4). stopping criterion is identical with A (4) step stopping criterion.

By technique scheme, the QC-LDPC code of the method construct that the present invention proposes, adopts the H matrix with simple iteration coding structure to encode, and reaches and is convenient to hard-wired object.

Brief description of the drawings

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, will the accompanying drawing of required use in embodiment or description of the Prior Art be briefly described below.

Fig. 1 is the structural representation of the disclosed a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure of the embodiment of the present invention;

Fig. 2 is the associated code parameter adopting in the emulation of the disclosed a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure of the embodiment of the present invention;

Fig. 3 is the group moment system of battle formations of the disclosed a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure of the embodiment of the present invention;

Fig. 4 is the exponential matrix figure of the disclosed a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure of the embodiment of the present invention;

Fig. 5 is the optimization group moment system of battle formations of the disclosed a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure of the embodiment of the present invention;

Fig. 6 is the Optimization Index matrix diagram of the disclosed a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure of the embodiment of the present invention;

Fig. 7 is the disclosed a kind of quasi-cyclic LDPC code method for designing relatively schematic diagram of performance of BER under awgn channel with simple iterative code structure of the embodiment of the present invention;

Fig. 8 is the disclosed a kind of quasi-cyclic LDPC code method for designing relatively schematic diagram of performance of BER under Rayleigh channel with simple iterative code structure of the embodiment of the present invention.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described.

The invention provides a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure, its operation principle is by construct a kind of H matrix structure that can carry out simple iteration coding that both retained in optimizing process, there is again the QC-LDPC code that the threshold value of optimization biradical matrix and the short length ring of corresponding exponential matrix distribute, reach and improve the performance of BER of QC-LDPC and be easy to hard-wired object.

Below in conjunction with embodiment and embodiment, the present invention is further detailed explanation.

Be illustrated in figure 1 QC-LDPC code based on the low encoder complexity application block diagram in wireless communication system, as seen from Figure 1, the present invention successively Optimal Construction goes out biradical matrix, exponential matrix, and then construct corresponding H matrix, then source data directly utilizes H matrix to carry out iteration coding, obtains coding codeword, send in channel and transmit by modulator, at receiving terminal, pass through successively demodulator, decoder, last data reconstruction.

For the ease of with 802.16e standard in QC-LDPC code compare, the embodiment providing has all adopted the identical code parameters with this, specifically as shown in Figure 2.

Embodiment 1:

The exponential matrix E (H) shown in upper and Fig. 4 at the basic matrix B (H) shown in Fig. 3, adopt the Optimization Steps of TS-PSO algorithm second stage of the present invention, " 0 " in Fig. 3 in basic matrix B (H) is in exponential matrix E (H), replace with " 1 ", nonzero element in B (H) is the integer element in corresponding E (H), and wherein the representative of " 0 " in E (H) is that size is 96 × 96 unit matrix.

Embodiment 2:

Adopt the first stage Optimizing Search of TS-PSO algorithm of the present invention to there is the biradical matrix B 1 (H) of optimum gate limit value, as shown in Figure 5; Free variable when optimization is B (H _i), i.e. the message part of basic matrix, size is 12 × 12, figure below is the iteration through 100 times, the biradical matrix with optimum gate limit value that search obtains, the threshold value of this biradical matrix is 0.71.

On the optimization basic matrix basis obtaining, adopt the second stage of TS-PSO algorithm, search has the exponential matrix E1 (H) that optimum short length ring distributes, as shown in Figure 6; The message part of B (H) in Fig. 5 is 70 nonzero elements, and in the check part of B (H) in order to keep simple code structure, the number of free variable is wherein 9, and, in the Optimizing Search of second stage, integer variable size to be optimized is 79.

Figure below is the embodiment 1 of method construct that provides of the present invention and the threshold value of the QC-LDPC code of embodiment 2 and 802.16e code, the comparison of short length ring:

Can be found out by upper figure, the threshold value that the length of the shortest cycles of three kinds of QC-LDPC codes is 6, embodiment 1 is 0.86dB, and the threshold value of the basic matrix of embodiment 2 is 0.71dB; The number of the exponential matrix shortest cycles of embodiment and embodiment 2 is 2.

Fig. 7 and Fig. 8 are respectively under wireless communication system, embodiment 1, embodiment 2 and the 802.16e code performance of BER under awgn channel and Rayleigh channel.Can find out the performance of BER of embodiment 1 and embodiment 2, under awgn channel and Rayleigh channel, all be better than 802.16e code.

The H matrix that the method that the present invention proposes is constructed, in optimizing process, retain the H matrix structure that can carry out simple iteration coding, be distributed as target with the threshold value of optimization biradical matrix and the short length ring of corresponding exponential matrix, obtained the QC-LDPC code of performance optimization.The QC-LDPC code that Optimal Construction goes out, the short length ring number that in the threshold value of its biradical matrix, corresponding exponential matrix, length is 6 is all better than the QC-LDPC code in 802.16e international standard; Bit error rate (BER:bit error rates) Performance Ratio emulation experiment shows, is 10 in bit error rate ^-5time, under additive white Gaussian noise (AWGN) channel, the QC-LDPC code of the present invention's structure will obtain the performance gain of 0.35dB left and right than the QC-LDPC code in 802.16e; And be 10 in bit error rate ^-4time, under Rayleigh (Rayleigh) channel, the QC-LDPC code of the present invention's structure is compared than the QC-LDPC code in 802.16e, obtain the performance gain of 0.25dB left and right.

By above mode a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure provided by the present invention, by construct a kind of H matrix structure that can carry out simple iteration coding that both retained in optimizing process, there is again the QC-LDPC code that the threshold value of optimization biradical matrix and the short length ring of corresponding exponential matrix distribute, reach and improve the performance of BER of QC-LDPC and be easy to hard-wired object.

Above-described is only the preferred implementation of a kind of quasi-cyclic LDPC code method for designing with simple iterative code structure disclosed in this invention; should be understood that; for the person of ordinary skill of the art; without departing from the concept of the premise of the invention; can also make some distortion and improvement, these all belong to protection scope of the present invention.

Claims (1)

1. a quasi-cyclic LDPC code method for designing with simple iterative code structure, is characterized in that, comprises the steps:

A. the Optimal Construction of biradical matrix;

B. the Optimal Construction of exponential matrix;

The Optimal Construction concrete steps of described biradical matrix are as follows:

A (1). be provided with S the molecular population of grain, each particle is a J n dimensional vector n, and that particle is corresponding here is exactly the message part H of biradical matrix H _i, produce at random the binary vector that S J ties up;

A (2). obtain after S J dimension binary vector of first step generation, set up accordingly the message part B (H of the biradical matrix B 1 (H) that S size is M × K _i), with the check part B (H of H matrix _p) combine, structure biradical matrix B 1 (H), adopts prototype external information branching algorithm to calculate the threshold value that each basic matrix is corresponding, can obtain altogether S threshold value, upgrade the optimal value pbest of each particle, and then more all pbest, global optimum gbest obtained;

A (3). the movement law that following formula is each particle:

$v_{\mathrm{ij}}^t=w{v}_{\mathrm{ij}}^{t-1}+c_1{\mathrm{\&eta;}}_1({\mathrm{pbest}}_{\mathrm{ij}}^{t-1}-x_{b,\mathrm{ij}}^{t-1})+c_2{\mathrm{\&eta;}}_2({\mathrm{gbest}}_{\mathrm{ij}}^{t-1}-x_{b,\mathrm{ij}}^{t-1})$

Wherein, w=1.0, c ₁=c ₂=2.0, coefficient η ₁and η ₂for equally distributed random number between (0,1), can obtain accordingly intermediate variable sig (v ^t _ij);

$\mathrm{sig}\left(v_{\mathrm{ij}}^t\right)=\frac{1}{1+e^{-v_{\mathrm{ij}}^t}}$

On this basis, can obtain the j position of i particle, upgrade according to the following formula

$x_{b,\mathrm{ij}}^t=\left\{\begin{array}{cc}1,& r_{\mathrm{ij}}^t<\mathrm{sig}\left(v_{\mathrm{ij}}^t\right)\\ 0,& r_{\mathrm{ij}}^t\&GreaterEqual;\mathrm{sig}\left(v_{\mathrm{ij}}^t\right)\end{array}\right.$

Wherein, r ^t _ijfor equally distributed random number between (0,1);

A (4). iterations adds 1, returns to steps A (2), upgrades pbest and gbest, until iterations reaches maximum;

The Optimal Construction concrete steps of described exponential matrix are as follows:

B (1). establishing nonzero integer element to be optimized in exponential matrix is Je, and each integer correspondence log ₂ls binary bits string, therefore binary vector length to be optimized is Je × log ₂ls, generates S Je × log at random ₂the binary vector of Ls dimension;

B (2). in the random each binary vector generating, with log ₂ls bit is one group, a corresponding scope is [0, Ls-1] integer, can construct accordingly Je dimension integer vector, Je is tieed up to integer vector and is converted to the exponential matrix E (H) of big or small M × N, therefore the S constructing in a first step two-dimensional vector, can relative configurations go out S exponential matrix E (H), detect the number of the short length ring that in each exponential matrix E (H), length is 6, the number assignment of the short length ring that is 6 by length is to pbest, therefore S exponential matrix correspondence S pbest, the relatively value of S pbest, by the value assignment of minimum pbest to gbest, and the now E (H) of correspondence of record,

B (3). position A (3) step of each particle is identical;

B (4). stopping criterion is identical with A (4) step stopping criterion.