CN101075812A - Method for constructing system low-density code with parallel cascade - Google Patents

Abstract

The construction method of the system form low-density code of the parallel concatenation structure of the present invention is characterized in that an interleaver with minimum correlation is designed according to the column re-correlation between the exchange matrix H ₁ ' and the initial matrix H ₁ ; utilize this interleaver to The encoders of two systematic low-density codes are connected in parallel as an encoder; the designed interleaver and the corresponding deinterleaver are used to connect the decoders of two systematic low-density codes in series as a decoder; that is, the A low-density code in the form of a parallel cascaded structure with low coding complexity and good performance. The interleaver designed in the method of the present invention introduces more check relations for the coding sequence, so the performance is greatly improved compared with the low-density code in the system form; at the same time, the system form used for the concatenation will not be destroyed due to the parallel concatenation operation Due to the structural characteristics of the matrix, the system-form low-density code with a parallel cascade structure is constructed to the greatest extent retaining the advantages of the system-form low-density code with simple structure and low coding complexity.

Description

A Constructing Method of System Form Low Density Code with Parallel Cascade Structure

Technical field:

The invention belongs to the technical field of channel coding and decoding, and in particular relates to a method for constructing a systematic low-density code with a parallel cascade structure.

Background technique:

Low-density codes (LDPC Codes) technology is generally considered to be an important technology in the fourth generation mobile communication system.

The United States "Journal of the Institute of Radio Engineers (Information Theory Journal)" (IRE Transactions on Information Theory, vol.IT-8, NO.1, p21-28, January, 1962) first proposed the concept of LDPC codes. Item characteristics are analyzed, but a fixed construction method is not given. This is because the construction method of the LDPC code has great flexibility. The encoding complexity of ordinary LDPC codes is very high, mainly because the matrix multiplication operation and matrix storage involved in the encoding process of LDPC codes are difficult to simplify. The United States "International Institute of Electronics and Electrical Engineers Consumer Electronics Journal (International Symposium on Circuits and Systems)" (IEEE International Symposium on Circuits and Systems, vol.2, p26-29, May, 2002) proposed a LDPC with a system form structure code, its parity check matrix is a standard system form matrix, so the encoding process can be completed directly using the parity check matrix, and because the parity check matrix is a sparse matrix, the complexity of encoding is greatly reduced. However, because the check matrix contains a large number of columns with a column weight of 1, which affects the error correction performance of the LDPC code, the performance of the LDPC code constructed by this method is poor.

Invention content:

The present invention proposes a method for constructing a system-form low-density code with a parallel cascade structure to construct a class of low-density codes with lower complexity and better performance, which can maintain the system-form low-density code with simple structure and high coding complexity. The advantage of low error correction performance is greatly improved at the same time.

The method for constructing the systematic form low-density code of the parallel concatenated structure of the present invention comprises: constructing a systematic form low-density code and an interleaver, the size of the check matrix H of the systematic form low-density code is m×n, wherein m <n, the left side of the check matrix H is an initial matrix H ₁ with a size of m×(nm), and the right side is an identity matrix I with a size of m×m;

It is characterized by:

The following method is used to design an interleaver that minimizes the correlation between the two check sequences: first perform column exchange on the initial matrix H ₁ , and then calculate the column exchanged exchange matrix H ₁ ′ and the initial matrix H by the following formula Column-heavy correlation between ₁ :

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="h"\; filenames="A20071002359400112.png"\; state="\{\{state\}\}">h</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}$

$W=\underset{i}{\mathrm{\&Sigma;}}{C}_i,1\&le;i\&le;\mathrm{no}-m$ (1)

Among them, m and n respectively represent the number of rows and columns of the check matrix H, C _i represents the column re-correlation coefficient between the i-th column of the exchange matrix H ₁ ' and the i-th column of the initial matrix H ₁ , and W represents the exchange The column re-correlation coefficient of matrix H ₁ ' and initial matrix H ₁ ; Finally, the column exchange order corresponding to the case where W is the smallest is used as the interleaving order of the interleaver;

Utilize this interleaver to concatenate the encoders of two structured systematic low-density codes in parallel as encoders, and the two encoders used for parallel concatenation are respectively the first encoder and the second encoder, which The two encoders are exactly the same; the original coded sequence is interleaved to obtain the interleaved coded sequence, and then the original coded sequence and the interleaved coded sequence are encoded by the first encoder and the second encoder at the same time, respectively, to obtain the original check sequence and interleaved check sequence; finally, these three sequences are combined in the order of the original coded sequence, original check sequence and interleaved check sequence as a complete coded frame;

Utilizing the interleaver and the corresponding deinterleaver to connect the decoders of the two systematic low-density codes in series as a decoder, the two decoders used in series are respectively the first decoder and the second decoder, These two decoders use the same or different conventional low-density code decoding algorithms, including sum product decoding algorithm, minimum sum decoding algorithm or posterior probability decoding algorithm; The confidence degree of the test sequence is decoded, and then the confidence degree of the original coded sequence output by the first decoder is processed by the interleaver to obtain the confidence degree of the interleaved coded sequence, and then the confidence degree of the interleaved coded sequence and the interleaved coded sequence are obtained by the second decoder. The confidence degree of the check sequence is decoded, and then the confidence degree of the interleaved coded sequence output by the second decoder is processed by the deinterleaver to obtain the confidence degree of the updated original coded sequence, and then according to this process between the two decoders Iterate until the decoding termination condition is satisfied, that is, construct a system form low-density code with a parallel cascaded structure with low coding complexity and good performance.

The advantage of the systematic form low-density code is that the systematic form structure of its parity check matrix is helpful to reduce coding complexity very much, and the shortcoming is that error correction performance is relatively poor; The construction method of the present invention is to pass two systematic form low-density codes through Specially designed interleavers are concatenated in parallel to construct a systematic form low-density code with a parallel concatenated structure. Since the parallel concatenated operation will not affect the systematic form structure of the parity check matrix used for concatenation, the present invention constructs Low-density codes have a simple structure and low coding complexity comparable to systematic low-density codes. At the same time, because the interleaver in the parallel cascaded structure introduces more constraint relations to the coding sequence, the performance of the low-density code constructed by the present invention is greatly improved compared with that of the existing system form low-density code.

The system form low-density code of the parallel cascade structure constructed by the method of the present invention has low coding complexity equivalent to the existing general system form low-density code, and has more excellent error correction performance, so it is better than the existing general system form Low-density codes have greater practical application value.

Description of drawings:

Figure 1 is a schematic diagram of the structure of a system form matrix H with a size of 675×1800.

Fig. 2 is a schematic structural diagram of an encoder of a systematic low-density code with a parallel cascaded structure.

Fig. 3 is a schematic diagram of the decoder structure of the system form low-density code of the parallel cascade structure.

Fig. 4 is a performance simulation comparison curve of a system form low-density code using a parallel cascaded structure of a correlated interleaver and an uncorrelated interleaver respectively.

Fig. 5 is a performance simulation comparison curve of the system-form low-density code and the system-form low-density code of the parallel cascade structure.

Detailed ways:

Example 1:

1. Construct a systematic form matrix H with a size of 675×1800 as the check matrix of the low-density code:

Construct a system form matrix H with a size of 675×1800. The left side of the matrix is an initial matrix H ₁ with a size of 675×1125, and the right side is an identity matrix I with a size of 675×675; the system form matrix H is used as a low-density The check matrix of the code can construct a set of low-density codes in systematic form. The matrix shown in Figure 1 is the system form matrix H with a size of 675×1800 constructed in this embodiment; the oblique lines in the figure are actually composed of a series of continuous points, and these points represent the system form matrix H The element at the corresponding position is 1, and blank means that the element at the corresponding position is 0; the short oblique line in the left half of the figure represents element 1 in the initial matrix H ₁ , and the random distribution of element 1 leads to different short oblique lines The difference in length between the lines, the long slash in the right half represents element 1 on the diagonal in the identity matrix I.

The size of the system form matrix can be designed according to actual needs, as long as its system form is guaranteed. Setting its size to 675×1800 in this embodiment is just an example of random selection. If the size of the systematic form matrix constructed is m×n, wherein m＜n, then the code length of the systematic form low-density code of the parallel concatenated structure constructed by the method of the present invention is n+m, and the coding rate is (n-m) /(n+m).

2. Design the interleaver with the least correlation

In order to introduce as many constraint relationships as possible, an interleaver with the least correlation must be designed according to the column redistribution of the initial matrix H ₁ .

The operation of the interleaver is actually the column exchange of the initial matrix H ₁ , and the column re-correlation between the exchange matrix H ₁ ′ obtained through column exchange and the initial matrix H ₁ can be calculated by using formula (1), where the smaller W indicates that this The smaller the column re-correlation between two matrices is, the smaller the correlation of the corresponding interleavers is, and the interleaver satisfying W=0 is an uncorrelated interleaver. The smaller the correlation of the interleaver, the smaller the correlation between the two check sequences, and the more obvious the performance improvement.

In order to illustrate this problem more vividly, in this embodiment, a correlated interleaver with W=3375 and an uncorrelated interleaver with W=0 are deliberately selected for comparison. Fig. 4 has provided the performance emulation comparison curve of the system form low-density code of the parallel concatenated structure adopting correlative interleaver and non-correlative interleaver respectively: Correlation interleaver performance curve b has adopted the parallel interleaver of W=3375 Performance of systematic low-density codes with concatenated structure; uncorrelated interleaver performance curve c represents the performance of systematic low-density codes with parallel concatenated structure of non-correlated interleavers with W=0. From the simulation comparison results, it can be seen that the performance of the low-density code using the uncorrelated interleaver is about 0.4dB higher than that of the low-density code using the correlated interleaver.

It should be noted that for initial matrices H ₁ with different structural characteristics, the interleavers designed according to formula (1) will be very different, for some initial matrices H ₁ it may not be possible to design an uncorrelated interleaver, and for some Then it is possible to design multiple different uncorrelated interleavers, so it is only necessary to select the interleaver with the smallest W during actual design. Multiple irrelevant interleavers can be designed for the initial matrix _H1 constructed in this embodiment, and only one of them is selected arbitrarily here.

3. Construct a system-form low-density code encoder with a parallel cascaded structure

By using the interleaver designed above to connect two identical encoders of systematic low-density codes in parallel, the encoder of systematic low-density codes with parallel cascaded structure constructed by the method of the present invention is obtained.

Figure 2 shows the structure diagram of the encoder. As shown in Figure 2, the working steps of encoder among the present invention are:

(1), the original coded sequence 1 is interleaved by the interleaving module A to obtain the interleaved coded sequence 2;

(2), the first encoding module B encodes the original encoding sequence 1 to obtain the original check sequence 3, and the second encoding module C encodes the interleaved encoding sequence 2 to obtain the interleaved check sequence 4;

(3) The original coding sequence 1, the original check sequence 3 and the interleaved check sequence 4 are combined in order to form the final coding sequence.

4. Constructing a system-form low-density code decoder with a parallel cascaded structure

Using the interleaver designed above and the corresponding de-interleaver to connect two decoders of systematic low-density codes in series, a decoder of systematic low-density codes with a parallel concatenated structure constructed by the method of the present invention is obtained.

Figure 3 shows the schematic diagram of the structure of the decoder, P _1f in the figure represents the channel posterior probability of the original coding sequence 1; P _3f represents the channel posterior probability of the original check sequence 3; P _4f represents the interleaved check sequence 4 The channel posterior probability of ; P _1e and P _2e represent the decoding input prior probabilities of the original coded sequence 1 and the interleaved coded sequence 2 respectively; P ₁ and P ₂ represent the decoding output posteriors of the original coded sequence 1 and the interleaved coded sequence 2 probability. As shown in Figure 3, the working steps of the decoder among the present invention are:

(1), decode P _1f and P _3f by the first decoding module D;

(2), whether the decoding result of the first decoding module D is judged by the first judging module C is correct, if correct, then the decoding output posterior probability _P1 of the original coded sequence 1 is sent to the hard decision module H, and by this module Output the final decoding result, otherwise send it to the interleaving module E for interleaving processing;

(3), the interleaving results P _2e and P _4f of the interleaving module E are decoded by the second decoding module F;

(4), whether the decoding result of the second decoding module F is checked by the second judging module 1 is correct, if correct, then the decoding output posterior probability P ₂ of the interleaved coding sequence 2 is sent to the hard decision module H, and by this module Output the final decoding result, otherwise send it to the deinterleaving module G for deinterleaving processing;

(5), the deinterleaving result P _1e of the deinterleaving module G and the decoding a posteriori probability of the original check sequence that the first decoding module D decodes in step (1) is decoded by the first decoding module D;

(6) Steps (2)-(5) are repeated until the decoding ends.

Both the first decoding module D and the second decoding module F in this embodiment have adopted the sum-product decoding algorithm, and the decoding process is as follows:

Suppose the system adopts binary phase-shift keying (BPSK) modulation mode, and the channel is an additive Gaussian white noise channel (AWGN). If the coded sequence to be sent is x=(x ₁ , x ₂ ,...x _N ), where N is the length of the coded sequence, then the data received by the receiver can be written as: y=(y ₁ , y ₂ ,... y _N ), where:

y _i =s _i +n _i i=1, 2,...N

s _i =2x _i -1 i=1, 2, ... N(1)

where n _i is Gaussian white noise with zero mean and N ₀ /2 variance.

For the sake of illustration, the following concepts are first defined:

N(m): {n: H _mn ′=1}, which means all columns with a value of 1 in the mth row of the parity check matrix H’, and N(m)\n means that except the nth column in N(m) All other columns of .

M(n): {m: H _mn ′=1}, indicating all rows with a value of 1 in the nth column of the parity check matrix H′. M(n)\m means all lines in M(n) except line m.

L _mn : represents the probability information transmitted from the check node m to the bit node n.

q _mn : Indicates the probability information transmitted from bit node n to check node m.

q _n : Indicates the posterior probability information of the nth bit, which is also the basis for decoding the hard decision output.

It should be noted that the probability information involved here is the probability of the logarithmic domain (Log-Likelihood Ratio, LLR). According to the above definition, the sum-product decoding algorithm can be simply summarized as follows:

Initialization, that is, calculate the initial posterior probability according to the received signal and channel information:

${\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Horizontal iteration, that is, calculate L _mn according to q _mn :

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\underset{{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \backslash </span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; (</span>\underset{{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \backslash </span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

where α _mn =sign(q _mn )

β _mn = |q _mn |

$Q\left(x\right)=\log \frac{e^x+1}{e^x-1}$ (3)

Vertical iteration, that is, calculate q _mn according to L _mn :

${\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="N"\; filenames="A20071002359400101.png"\; state="\{\{state\}\}">N</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>\underset{{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \backslash </span>\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Judgment output and termination conditions:

${\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="N"\; filenames="A20071002359400101.png"\; state="\{\{state\}\}">N</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; mn</span>}}$

${x^{\&prime;}}_{\mathrm{no}}=\left\{\begin{array}{cc}1,& q_{\mathrm{no}}>0\\ 0,& q_{\mathrm{no}}<0\end{array}\right.$ (5)

When H'x'=0 is satisfied or the number of iterations reaches the upper limit, the decoding process is terminated and the decoding result x'=(x' ₁ , x' ₂ , . . . x' _N ) is output, otherwise the iterative process continues.

The detailed introduction of the above algorithm can be found in the American "International Institute of Electronics and Electrical Engineers Consumer Electronics Journal (Information Theory Journal)" (IEEE Transactions on Information Theory, vol.45, NO.2, p399-431, March, 1999).

The first decoding module D and the second decoding module F can also use a minimum sum decoding algorithm or a posterior probability decoding algorithm, and they can respectively adopt the same or different decoding algorithms, and the minimum sum decoding algorithm and the posterior probability decoding algorithm can be See the US "International Institute of Electronics and Electrical Engineers Consumer Electronics Journal (Communication Journal)" (IEEETransactions on Communications, vol.47, NO.5, p673-680, May, 1999) and the US "International Institute of Electronics and Electrical Engineers Consumer Electronics Journal" (Communication Journal)" (IEEE Transactions on Communications, vol.53, NO.8, p1288-1298, August, 2005).

5. Simulation performance

Utilize software to carry out performance emulation, under additive Gaussian white noise (AWGN) channel condition and binary phase-shift keying (BPSK) modulation mode, compare the system form low-density code and system form of the parallel concatenated structure that the method of the present invention constructs Performance of low-density codes in systematic form corresponding to matrix H.

Figure 5 shows the performance simulation comparison curves of the system-form low-density code and the system-form low-density code of the parallel concatenated structure: the poor performance curve d represents the performance of the system-form low-density code with a code length of 1125 and a code rate of 0.4 , better performance. Curve e represents the performance of the system form low-density code with a code length of 2475 and a code rate of 0.455 constructed by the method of the present invention. It can be seen from the simulation results in FIG. 5 that the performance of the systematic low-density code with the parallel cascaded structure constructed by the method of the present invention is about 1.5 dB higher than that of the systematic low-density code.

6. Comparison of Computational Complexity

Since the two system form matrices in the parallel cascaded structure are exactly the same, it does not lead to an increase in storage space. Although the encoding operation amount of the systematic low-density code of the parallel cascaded structure is twice that of the original systematic low-density code, but because the encoding operation amount of the systematic low-density code itself is very low, the systematic form of the parallel cascaded structure is low. Compared with ordinary low-density codes, the encoding calculation amount of density codes is still very low. The modulus 2 calculation amount of the system form low-density code with code length 1125 and code rate 0.4 is 3375 times, and the storage space needs 33750 bits; the code length is 2475 and code rate 0.455. 2 The calculation amount is 6750 times, and the storage space requires 33750 bits.

The method of the present invention utilizes the designed interleaver to concatenate two systematic form low-density codes in parallel, and introduces more verification relations for the coding sequence, so the performance is greatly improved compared with the systematic form low-density code; The concatenation operation will not destroy the structure of the system form matrix used for concatenation, so the constructed system form low-density code with parallel concatenation structure retains the advantages of simple structure and low coding complexity of the system form low-density code to the greatest extent , has a simple structure that is very favorable for hardware implementation. The system-form low-density code with parallel cascading structure constructed by the invention is very suitable for application in systems with relatively tight resources and certain requirements for error correction performance.

Claims (1)

1. A method for constructing a systematic low-density code of a parallel cascaded structure, comprising: constructing a systematic low-density code and an interleaver, the check matrix H of the systematic low-density code having a size of m×n, Where m<n, the left side of the parity check matrix H is an initial matrix H ₁ with a size of m×(nm), and the right side is an identity matrix I with a size of m×m; It is characterized by: The following method is used to design an interleaver that minimizes the correlation between the two check sequences: first perform column exchange on the initial matrix H ₁ , and then calculate the column exchanged exchange matrix H ₁ ′ and the initial matrix H by the following formula Column-heavy correlation between ₁ : ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}$ $W=\underset{i}{\mathrm{\&Sigma;}}{C}_i,1\&le;i\&le;\mathrm{no}-m$ (1) Among them, m and n respectively represent the number of rows and columns of the check matrix H, C _i represents the column re-correlation coefficient between the i-th column of the exchange matrix H ₁ ' and the i-th column of the initial matrix H ₁ , and W represents the exchange The column re-correlation coefficient of matrix H ₁ ' and initial matrix H ₁ ; Finally, the column exchange order corresponding to the case where W is the smallest is used as the interleaving order of the interleaver; Utilize this interleaver to concatenate the encoders of two structured systematic low-density codes in parallel as encoders, and the two encoders used for parallel concatenation are respectively the first encoder and the second encoder, which The two encoders are exactly the same; the original coded sequence is interleaved to obtain the interleaved coded sequence, and then the original coded sequence and the interleaved coded sequence are encoded by the first encoder and the second encoder at the same time, respectively, to obtain the original check sequence and interleaved check sequence; finally, these three sequences are combined in the order of the original coded sequence, original check sequence and interleaved check sequence as a complete coded frame; Utilizing the interleaver and the corresponding deinterleaver to connect the decoders of the two systematic low-density codes in series as a decoder, the two decoders used in series are respectively the first decoder and the second decoder, These two decoders use the same or different conventional low-density code decoding algorithms, including sum product decoding algorithm, minimum sum decoding algorithm or posterior probability decoding algorithm; The confidence degree of the test sequence is decoded, and then the confidence degree of the original coded sequence output by the first decoder is processed by the interleaver to obtain the confidence degree of the interleaved coded sequence, and then the confidence degree of the interleaved coded sequence and the interleaved coded sequence are obtained by the second decoder. The confidence degree of the check sequence is decoded, and then the confidence degree of the interleaved coded sequence output by the second decoder is processed by the deinterleaver to obtain the confidence degree of the updated original coded sequence, and then according to this process between the two decoders Iterate until the decoding termination condition is satisfied, that is, a systematic low-density code with a parallel cascaded structure is constructed.

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