CN103812614A - Multi-system orthogonal signal low-density check code coding/decoding method - Google Patents

Abstract

The invention discloses a multi-system orthogonal signal low-density check code coding/decoding method, mainly aiming to solve the problems of weak anti-jamming capability, large number of decoding iteration times, great operand and poor decoding performance in the prior art. The method comprises the following specific implementation steps: (1) generating a multi-system low-density check matrix; (2) generating a code word; (3) performing orthogonal signal modulation; (4) receiving a message from a variable message processing device; (5) receiving an estimated code word; (6) judging whether a check equation is satisfied or not; (7) judging whether a maximum iteration time is reached or not; (8) ending decoding. In the orthogonal signal modulation, very high bit error rate performance can be achieved through less decoding iteration times, and the anti-jamming capability and frequency spectrum utilization ratio of the entire system are increased. By adopting fast Hadamard transform, the operation efficiency and storage efficiency of a decoding algorithm are increased, and the programming complexity of the decoding algorithm on a programmable device is lowered.

Description

M-ary orthogonal signal low-density check code coding/decoding method

Technical field

The invention belongs to communication technical field, further relate to a kind of error control coding, digital modulation and demodulation and soft-decision decoding method in communication system.The method is a kind of M-ary orthogonal signal modulation is combined with loe-density parity-check code and carries out the method for coding and decoding.Can be used for deep space communication, satellite communication, ultra-wideband communication technical field, can realize the reliable communication of high transfer rate and low error rate.

Background technology

At present, in communication system, Turbo code and LDPC code are the error control codings that approaches Shannon tolerance limit, can improve reliability and the spectrum efficiency of system both at home and abroad.

The serially concatenated code modulating method that the Continuous Phase Modulation CPM (Continuous Phase Modulation) that the patented technology " based on the code modulating method of total regression CPM and Turbo product code " (Granted publication number: CN102223204B, number of patent application: CN20110147937) that Xian Electronics Science and Technology University has proposes combines with Turbo product code.The information bit sequence that the method sends needs is carried out Turbo product code coding, coding output is carried out random interleaving by interleaver, bit sequence after interweaving is converted to multi-system symbol sebolic addressing, send continuous phase encoder, memoryless modulator is exported corresponding waveform according to the multi-system symbol sebolic addressing of continuous phase encoder output again.The weak point that this patented technology exists is: adopt interleaver to carry out random interleaving, time delay is large, and whole system realizes complicated.

Declercq D, Fossorier M is at ``Decoding Algorithms for Nonbinary LDPC Codes Over GF (q) ". the coding and decoding method of multi-system BPSK modulation loe-density parity-check code has been proposed in (IEEE Comm.Trans2007,55 (4): 633-643.).The method is carried out BPSK modulation transmissions at transmitting terminal to the loe-density parity-check code generating, first the code word receiving is carried out the initialization of information at receiving terminal, recycling Log-BP algorithm carries out iterative decoding, carry out respectively the renewal of message at check-node and variable node, stop iteration until meet certain iteration stopping condition, output decode results or decoding failure.The weak point that the method exists is: utilize BPSK modulation technique can not meet the demand to the higher rate of information throughput; Adopt the belief propagation algorithm decoding complexity of log-domain large.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the object of the present invention is to provide a kind of M-ary orthogonal signal low-density check code coding/decoding method, can effectively reduce operand and memory space, reduce the error rate, improve spectrum efficiency and the reliability of system simultaneously.

To achieve these goals, the concrete steps that the present invention realizes are as follows:

(1) generate multi-system low-density check matrix:

Adopt progressively limit growing method, generate a binary low density check matrix;

To binary low density check matrix, by random replacement, obtain a multi-system low-density check matrix;

(2) generated codeword:

To multi-system low-density check matrix, by the method for Gaussian elimination, obtain generator matrix;

Input information sequence to be encoded;

Be multiplied by generator matrix with information sequence to be encoded, obtain a multi-system low-density check code word;

(3) orthogonal signalling modulation:

Symbol a in multi-system low-density check code word is mapped to base vector va, obtains symbolic vector sequence;

Symbolic vector sequence is carried out to orthogonal waveforms shaping, obtain orthogonal signalling;

Send orthogonal signalling by transmission channel;

(4) message of acquisition variable message processing unit:

Receive the signal that orthogonal signalling send by channel;

The signal receiving is carried out to orthogonal signalling demodulation, obtain vector sequence;

Numbering m using the line number of multi-system low-density check matrix nonzero element as verification message processing unit, the column number of nonzero element is as the numbering n of variable message processing unit;

Vector sequence is sent to variable message processing unit;

According to the following formula, calculate the initial probability of the symbol in multi-system low-density check code word:

$p_n^a=\frac{e^{-\frac{{|y_n-v^{a|}}^2}{2{\mathrm{\σ}}^2}}}{{\mathrm{\Σ}}_{a=0}^{q-1}{e}^{-\frac{{|y_n-v^{a|}}^2}{2{\mathrm{\σ}}^2}}}$

Wherein,

the initial probability that represents the symbol in multi-system low-density check code word, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2, and n represents the numbering of variable message processing unit, n=1,2 ..., N, N represents the multi-system low-density check code word length corresponding with the numbering of variable message processing unit, y _nrepresent the vector sequence after demodulation, v ^arepresent the base vector of the symbol a mapping in multi-system low-density check code word, σ ²represent the noise power of transmission channel;

By the initial probability of the symbol in multi-system low-density check code word, as the message of the variable message processing unit of correspondence code metasymbol;

(5) obtain and estimate code word:

To the message of message processing apparatus, adopt the belief propagation method of quick Hadamard matrix, obtain estimating code word;

(6) judge whether to meet check equations:

Estimation code word is multiplied by multi-system low-density check transpose of a matrix matrix, obtains judgement vector;

Judge whether judgement vector is 0 vector, if so, execution step (8), otherwise, execution step (7);

(7) judge whether to reach maximum iteration time:

Judge whether to reach maximum iteration time, if so, execution step (8), otherwise, execution step (5);

(8) decoding finishes:

The decoding code word of code word as output will be estimated.

The present invention compared with prior art has the following advantages:

First, because the present invention has adopted orthogonal signalling modulation technique in the time that code word is modulated, overcome the deficiency that the mutual interference of each symbol is strong and decoding iterations is many existing in prior art, made the present invention improve the iteration efficiency of decoding computing, reliability, antijamming capability and the spectrum efficiency of system.

Second, because the present invention has adopted fast hadamard transform in the time upgrading check-node, overcome the check-node existing in prior art and upgraded complicated deficiency, make the present invention improve operation efficiency and the storage efficiency of decoding algorithm, reduced the decoding algorithm complexity realizing of programming on programming device.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention;

Fig. 2 is the bit error rate performance simulation result comparison diagram of the present invention and BPSK modulation.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described.

Realize concrete steps of the present invention and be described below for 1 pair by reference to the accompanying drawings:

Step 1, generates multi-system low-density check matrix.

Adopt progressively limit growing method, generate a binary low density check matrix, to random method of replacing for this matrix, obtain a multi-system low-density check matrix, random replacement refers to the nonzero element of binary low density check matrix is replaced with to the nonzero element on finite field gf (q) at random.

The multi-system low-density check matrix adopting in the embodiment of the present invention refers to 16 system low-density check matrixes, q=16.

Step 2, generated codeword.

Multi-system low-density check matrix is carried out to Gaussian elimination, obtain generator matrix, input information sequence to be encoded, be multiplied by generator matrix with information sequence, obtain a multi-system low-density check code word.

The information sequence adopting in the embodiment of the present invention is a random row vector sending, and vector element is the whole elements on finite field gf (16), code word size n=204, and information bit length k=102, code efficiency is 0.5.

Step 3, orthogonal signalling modulation.

Be mapped to base vector v by symbol a ^amode, multi-system low-density check code word is mapped to symbolic vector sequence, then do orthogonal waveforms be shaped, obtain orthogonal signalling, send orthogonal signalling by transmission channel, the orthogonal signalling here refer to that the q kind shaping wave obtaining is orthogonal, wherein, a represents the symbol in multi-system low-density check code word, a=0,1, ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2.

In the embodiment of the present invention, q=16, base vector collection is 16 column vectors in 16 rank unit matrix, and symbol a is mapped as the unit column vector that a+1 element is " 1 ", and for example, symbol 0 is mapped as vector [1000000000000000].

Step 4, the message of acquisition variable message processing unit.

Receive signal, carry out orthogonal signalling demodulation, obtain vector sequence y, then device is numbered, concrete operations are the numbering m using the line number of multi-system low-density check matrix nonzero element as verification message processing unit, the column number of nonzero element, as the numbering n of variable message processing unit, is finally sent to vector sequence variable message processing unit, calculates according to the following formula the initial probability of the symbol in multi-system low-density check code word:

$p_n^a=\frac{e^{-\frac{{|y_n-v^{a|}}^2}{2{\mathrm{\σ}}^2}}}{{\mathrm{\Σ}}_{a=0}^{q-1}{e}^{-\frac{{|y_n-v^{a|}}^2}{2{\mathrm{\σ}}^2}}}$

Wherein, the initial probability that represents the symbol in multi-system low-density check code word, a represents the symbol of multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2, and n represents the numbering of variable message processing unit, n=1,2 ..., N, N represents the multi-system low-density check code word length corresponding with the numbering of variable message processing unit, y _nrepresent the vector sequence after demodulation, v ^arepresent the base vector of the symbol a mapping of multi-system low-density check code word, σ ²represent the noise power of transmission channel.

Next step obtains estimates that code word is an interative computation process, set in advance a maximum iteration time, iteration is by mutual pass-along message between variable message processing unit and verification message processing unit each time, upgrade the message of variable message processing unit and the message of verification message processing unit, and symbol is adjudicated.

Step 5, obtains and estimates code word.

The information updating step of verification message processing unit is as follows:

The first step, the order increasing progressively successively according to symbol value, by the message of each variable message processing unit, forms a q dimension variable message vector

wherein,

be illustrated in except m verification message processing unit, under the known condition of the message of other verification message processing unit being connected with n variable message processing unit and the initial probability of symbol, n variable message processing unit passed to the message of m verification message processing unit, a represents the symbol in multi-system low-density check code word, a=0,1, ..., q-1, q represents the system number of multi-system loe-density parity-check code, q value is 2 multiple, and n represents the numbering of variable message processing unit, and m represents the numbering of verification message processing unit.

Second step, rearranges the element in variable message vector, and queueing discipline is using a+1 element in variable message vector as displacement message vector

b (b=a/h _mn+ 1) individual element, wherein, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, b=1,2 ..., q, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2, represent the element in displacement message vector, h _mnrepresent m verification message processing unit and n the multi-system low-density check matrix element that variable message processing unit is corresponding, a/h _mncomputing on finite field gf (q), carry out.

The 3rd step, carries out fast hadamard transform to displacement message vector, obtains current verification message vector

fast hadamard transform comprises direct transform and inverse transformation, and concrete operations are undertaken by following two formulas

${{\mathrm{FQ}}_{\mathrm{mn}}^a}^{\&prime;}=\mathrm{FHT}({{\mathrm{<figure-callout\; id="0"\; label="Q\; nm"\; filenames="HDA0000472379880000021.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{\mathrm{nm}}^{}}^{\&prime;},{Q_{\mathrm{nm}}^1}^{\&prime;},...,{Q_{\mathrm{nm}}^{q-1}}^{\&prime;})$

$R_{\mathrm{mn}}^a=\mathrm{IFHT}[\left(\underset{n^{\&prime;}\&Element;N\left(m\right)\backslash n}{\mathrm{\&Pi;}}{{\mathrm{FQ}}_{n^{\&prime;}\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="HDA0000472379880000021.png"\; state="\{\{state\}\}">m</figure-callout>}}^0}^{\&prime;}\right),\left(\underset{n^{\&prime;}\&Element;N\left(m\right)\backslash n}{\mathrm{\&Pi;}}{{\mathrm{FQ}}_{n^{\&prime;}m}^1}^{\&prime;}\right),...,\left(\underset{n^{\&prime;}\&Element;N\left(m\right)\backslash n}{\mathrm{\&Pi;}}{{\mathrm{FQ}}_{n^{\&prime;}}^{q-1}}^{\&prime;}\right)]$

Wherein,

being illustrated in symbol is a, except the message of n variable message processing unit, under the known condition of the message of other variable message processing unit that are connected with m verification message processing unit, m verification message processing unit passed to the message of n variable message processing unit, n represents the numbering of variable message processing unit, m represents the numbering of verification message processing unit, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2

represent the element in displacement message vector,

represent the intermediate variable after quick Hadamard direct transform, N (m) { n} represents except n variable message processing unit, processes the set of other variable message processing unit that are connected with m verification message.

The information updating step of variable message processing unit is as follows:

The first step, rearranges the element in current verification message vector, and queueing discipline is using a+1 element in current verification message vector as decommutation message vector

c (c=a*h _mn+ 1) individual element, wherein, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, c=1,2 ..., q, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2,

represent the element in decommutation message vector, h _mnrepresent m verification message processing unit and n the multi-system low-density check matrix element that variable message processing unit is corresponding, a*h _mncomputing on finite field gf (q), carry out.

Second step, first select except m verification message processing unit, a+1 element in the corresponding decommutation message of other verification message processing unit vector being connected with n variable message processing unit, then tires out multiple elements of selecting to take advantage of, then be multiplied by initial probability

with normalization factor α _nm, the finant product obtaining is as in n variable message vector

renewal value, the operation of this process can illustrate with following formula:

$Q_{\mathrm{nm}}^a={\mathrm{\&alpha;}}_{\mathrm{nm}}{p}_n^a\underset{m^{\&prime;}\&Element;M\left(n\right)\backslash m}{\mathrm{\&Pi;}}{R_{m^{\&prime;}n}^a}^{\&prime;}$

Wherein, m represents the numbering of verification message processing unit, and n represents the numbering of variable message processing unit, and a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2

represent the initial probability of the symbol in multi-system low-density check code word, be illustrated in except m verification message processing unit, under the known condition of the message of other verification message processing unit being connected with n variable message processing unit and the initial probability of symbol, n variable message processing unit passed to the message of m verification message processing unit, M (n) { m} represents except m verification message processing unit, the set of other verification message processing unit that are connected with n variable message processing unit

represent the element in decommutation message vector, α _nmrepresent by the definite normalization factor of variable message vector, i.e. α _nmmake

Codeword decision step is as follows:

The first step, first selects a+1 element in the corresponding decommutation message of the complete verification message processing apparatus vector being connected with n variable message processing unit, then multiple elements of selecting is tired out and is taken advantage of, then be multiplied by initial probability

with normalization factor β _n, the finant product obtaining is as the posterior probability vector of n variable message processing unit

middle element

renewal value, the operation of this process can illustrate with following formula:

$Q_n^a={\mathrm{\&beta;}}_n{P}_n^a\underset{m\&Element;M\left(n\right)}{\mathrm{\&Pi;}}{R_{\mathrm{mn}}^a}^{\&prime;}$

Wherein, n represents the numbering of variable message processing unit, and a represents the symbol in multi-system low-density check code word, a=0, and 1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2,

represent the initial probability of the symbol in multi-system low-density check code word,

the posterior probability that represents the symbol in multi-system low-density check code word, m ∈ M (n) represents the set of the verification message processing unit being connected with n variable message processing unit,

represent the element in decommutation message vector, β _nrepresent by the definite normalization factor of posterior probability vector, i.e. β _nmake

Second step, by posterior probability vector

in the corresponding Position Number of greatest member subtract 1, the difference obtaining is as the estimation of the symbol in multi-system low-density check code word, the operation of this process can illustrate with following formula:

${\hat{c}}_n=\arg \underset{a}{\max }{Q}_n^a$

Wherein,

the posterior probability that represents the symbol in multi-system low-density check code word, a represents the symbol in multi-system low-density check code word, a=0,1, ..., q-1, q represents the system number of multi-system loe-density parity-check code, q value is 2 multiple, and n represents the numbering of variable message processing unit

represent the estimation of symbol.

The 3rd step, estimates code word by one of the estimation composition of the symbol in multi-system low-density check code word.

Maximum iteration time 50 times in the embodiment of the present invention, a/h _mncomputing and a*h _mncomputing all on finite field gf (16), carry out.

Step 6, judges whether to meet check equations.

Estimate that code word is multiplied by multi-system low-density check transpose of a matrix matrix, obtain judgement vector, judge whether this judgement vector is 0 vector, if so, execution step (8), otherwise, execution step (7).

Multiplying in the embodiment of the present invention is carried out on finite field gf (16)

Step 7, judges whether to reach maximum iteration time.

Judge whether to reach maximum iteration time, if so, execution step (8), otherwise, execution step (5).

Step 8, decoding finishes.

The decoding code word of code word as output will be estimated.

Effect of the present invention can further illustrate by following emulation:

Emulation of the present invention is used Matlab7.1 simulation software, system parameters is consistent with parameter used in embodiment, emulation 3000 times, code element energy is erg-ten, code efficiency is 0.5, multi-system low-density check matrix 102 row 204 are listed as, 16 irregular system loe-density parity-check codes, maximum iteration time 50 times, transmission channel is additive white Gaussian noise channel, and the performance of BER curve obtaining is as shown in curve in Fig. 21, and in Fig. 2, transverse axis represents bit signal to noise ratio, unit decibel, the longitudinal axis represents bit error rate.

Use Matlab7.1 simulation software, only change modulation system, adopt BPSK modulation, simulated conditions and other parameters are consistent with the parameter in embodiment, and the performance of BER curve obtaining is as shown in curve in Fig. 22.

From the simulation result of Fig. 2, under same bits signal to noise ratio condition, bit error rate of the present invention is starkly lower than the bit error rate under BPSK modulation; The present invention is 1 × 10 in bit error rate ^-3time, approximately there is the gain of 1dB compared with BPSK modulation, visible the present invention has improved the reliability of system significantly than BPSK modulation technique.

Claims (5)

1. M-ary orthogonal signal low-density check code coding/decoding method, comprises the steps:

(1) generate multi-system low-density check matrix:

(1a) adopt progressively limit growing method, generate a binary low density check matrix;

(1b), to binary low density check matrix, by random replacement, obtain a multi-system low-density check matrix;

(2) generated codeword:

(2a) to multi-system low-density check matrix, by the method for Gaussian elimination, obtain generator matrix;

(2b) input information sequence to be encoded;

(2c) be multiplied by generator matrix with information sequence to be encoded, obtain a multi-system low-density check code word;

(3) orthogonal signalling modulation:

(3a) the symbol a in multi-system low-density check code word is mapped to base vector va, obtains symbolic vector sequence;

(3b) symbolic vector sequence is carried out to orthogonal waveforms shaping, obtain orthogonal signalling;

(3c) send orthogonal signalling by transmission channel;

(4) message of acquisition variable message processing unit:

(4a) receive the signal that orthogonal signalling send by channel;

(4b) signal receiving is carried out to orthogonal signalling demodulation, obtain vector sequence;

(4c) the numbering m using the line number of multi-system low-density check matrix nonzero element as verification message processing unit, the column number of nonzero element is as the numbering n of variable message processing unit;

(4d) vector sequence is sent to variable message processing unit;

(4e) calculate according to the following formula, the initial probability of the symbol in multi-system low-density check code word:

Wherein,

the initial probability that represents the symbol in multi-system low-density check code word, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2, and n represents the numbering of variable message processing unit, n=1,2 ..., N, N represents the multi-system low-density check code word length corresponding with the numbering of variable message processing unit, y _nrepresent the vector sequence after demodulation, v ^arepresent the base vector of the symbol a mapping in multi-system low-density check code word, σ ²represent the noise power of transmission channel;

(4f) by the initial probability of the symbol in multi-system low-density check code word, as the message of the variable message processing unit of correspondence code metasymbol;

(5) obtain and estimate code word:

To the message of message processing apparatus, adopt the belief propagation method of quick Hadamard matrix, obtain estimating code word;

(6) judge whether to meet check equations:

(6a) estimation code word is multiplied by multi-system low-density check transpose of a matrix matrix, obtains judgement vector;

(6b) judge whether judgement vector is 0 vector, if so, execution step (8), otherwise, execution step (7);

(7) judge whether to reach maximum iteration time:

Judge whether to reach maximum iteration time, if so, execution step (8), otherwise, execution step (5);

(8) decoding finishes:

The decoding code word of code word as output will be estimated.

2. M-ary orthogonal signal low-density check code coding/decoding method according to claim 1, it is characterized in that, random replacement described in step (1b) refers to, the nonzero element of binary low density check matrix is replaced to the nonzero element on finite field gf (q) at random, wherein, GF (q) represents finite field, and q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2.

3. M-ary orthogonal signal low-density check code coding/decoding method according to claim 1, it is characterized in that, information sequence to be encoded described in step (2b) is row vector, vector element is all elements on finite field gf (q), wherein, GF (q) represents finite field, and q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2.

4. M-ary orthogonal signal low-density check code coding/decoding method according to claim 1, is characterized in that, the belief propagation method of the quick Hadamard matrix described in step (5), comprises the steps:

The first step, by the message of each variable message processing unit, forms a q dimension variable message vector wherein,

be illustrated in except m verification message processing unit, under the known condition of the message of other verification message processing unit being connected with n variable message processing unit and the initial probability of symbol, n variable message processing unit passed to the message of m verification message processing unit, a represents the symbol in multi-system low-density check code word, a=0,1, ..., q-1, q represents the system number of multi-system loe-density parity-check code, q value is 2 multiple, and n represents the numbering of variable message processing unit, and m represents the numbering of verification message processing unit;

Second step, the b (b=a/h using a+1 element in variable message vector as displacement message vector _mn+ 1) individual element, wherein a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, b=1,2 ..., q, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2, h _mnrepresent m verification message processing unit and n the multi-system low-density check matrix element that variable message processing unit is corresponding, a/h _mncomputing on finite field gf (q), carry out;

The 3rd step, carries out fast hadamard transform to displacement message vector, obtains current verification message vector

wherein,

being illustrated in symbol is a, except the message of n variable message processing unit, under the known condition of the message of other variable message processing unit that are connected with m verification message processing unit, m verification message processing unit passed to the message of n variable message processing unit, n represents the numbering of variable message processing unit, m represents the numbering of verification message processing unit, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2;

The 4th step, the c (c=a*h using a+1 element in current verification message vector as decommutation message vector _mn+ 1) individual element, wherein, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, c=1,2 ..., q, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2, h _mnrepresent m verification message processing unit and n the multi-system low-density check matrix element that variable message processing unit is corresponding, a*h _mncomputing on finite field gf (q), carry out;

The 5th step, selects except m verification message processing unit, a+1 element in the corresponding decommutation message of other verification message processing unit vector being connected with n variable message processing unit, wherein, m represents the numbering of verification message processing unit, and n represents the numbering of variable message processing unit, and a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2;

The 6th step, tires out multiple elements of selecting in the 5th step to take advantage of, and obtains the part accumulation message except m verification message processing unit, and wherein, m represents the numbering of verification message processing unit;

The 7th step, is multiplied by initial probability by part accumulation message

with normalization factor α _nm, obtain in n variable message vector

renewal value, wherein,

represent the initial probability of the symbol in multi-system low-density check code word, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2, and m represents the numbering of verification message processing unit, n represents the numbering of variable message processing unit

be illustrated in except m verification message processing unit, under the known condition of the message of other verification message processing unit being connected with n variable message processing unit and the initial probability of symbol, n variable message processing unit passed to the message of m verification message processing unit, α _nmrepresent by the definite normalization factor of variable message vector;

The 8th step, select a+1 element in the corresponding decommutation message of the complete verification message processing apparatus vector being connected with n variable message processing unit, wherein, m represents the numbering of verification message processing unit, n represents the numbering of variable message processing unit, a represents the symbol in multi-system low-density check code word, a=0,1, ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2;

The 9th step, tires out multiple elements of selecting in the 8th step to take advantage of, and obtains whole accumulation message of verification message processing unit;

The tenth step, is multiplied by initial probability by whole accumulation message

with normalization factor β _n, obtain the posterior probability vector of n variable message processing unit

middle element

renewal value, wherein,

the initial probability that represents the symbol in multi-system low-density check code word, a represents the symbol in multi-system low-density check code word, a=0,1, ..., q-1, q represents the system number of multi-system loe-density parity-check code, q value is 2 multiple, and n represents the numbering of variable message processing unit

represent the posterior probability of the symbol in multi-system low-density check code word, β _nrepresent by the definite normalization factor of posterior probability vector;

The 11 step, by posterior probability vector

in the corresponding Position Number of greatest member subtract 1, the difference obtaining is as the estimation of the symbol in multi-system low-density check code word, wherein, the posterior probability that represents the symbol in multi-system low-density check code word, a represents the symbol in multi-system low-density check code word, a=0,1 ..., q-1, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2, and n represents the numbering of variable message processing unit;

The 12 step, estimates code word by one of the estimation composition of the symbol in multi-system low-density check code word.

5. M-ary orthogonal signal low-density check code coding/decoding method according to claim 1, it is characterized in that, described in step (6a) multiplying on finite field gf (q), carry out, wherein, GF (q) represents finite field, q represents the system number of multi-system loe-density parity-check code, the multiple that q value is 2.

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