CN1430353A - Minimum Eustachian distance maximized constellation mapping cascade error-correction coding method - Google Patents

Abstract

A constellation mapping cascaded error-correcting encode method with maximizing the minimal Euclidean distance includes encoding the input digital signals by systen convolution code, random bit interleaving processing to data, and performing mQAM modulation to data. The sign constellation mapping relative conforms with the maximization of minimal Euclidean distance between correlative codes. The sign constellation mapping code as the internal code of cascaded error-correcting code and said system conveolution code constitute a cascaded system convolution code. It has high error-correcting performance with less iteractive operations.

Description

The maximized constellation mapping cascade error-correction coding method of minimum Eustachian distance

Technical field

The invention belongs to digital information transmission technical field, be specifically related to a kind of constellation mapping cascade error-correction coding method.

Background technology

In Digital Video Communication, owing to wireless channel, fiber channel etc. all are the logical type channels of band,, modulates base-band digital, so that in the channel of determining, transmit so believing the ` needs.Modulation is a functional transformation process in essence, and it is mapped as the carrier waveform with certain attribute with binary sequence waiting for transmission (finished chnnel coding usually and formed signal frame).Concerning carrier wave, the attribute that can change comprises amplitude, frequency and phase place.Therefore basic digital modulation mode also comprises three kinds, i.e. amplitude shift keying (ASK), frequency shift keying (FSK) and phase shift keying (PSK).Existing form of digital modulation can be regarded the distortion and the combination of these three kinds of citation forms as.In Digital Video Communication, adopt the linear modulation demodulation techniques usually, promptly the frequency spectrum of modulation signal is that the linearity of digital baseband signal frequency spectrum is moved.

Figure 1 shows that linear modulation demodulation model.It is divided into two basic function module with modulation: Base-Band Processing and frequency spectrum shift.Because Digital Video Communication is the bandwidth efficient system, so adopt the modulation of M system usually.This moment, baseband processing module was from binary sequence { a _nIn once extract k=log ₂M bit formation group carried out base band shaping filtering to each group, again from M=2 ^kThe individual analog carrier waveform { s that is complementary with the characteristic of channel _i, i=1,2 ... select one of them to finish frequency spectrum shift by the mapping relations of determining among the M}, the bandwidth constraints that makes transmission signals is with carrier frequency f _cOn the frequency range for the center.

The same with the vector space notion in the linear algebra, signal waveform collection { s _i, i=1,2 ... M} constitutes a signal space.Each element s that signal waveform is concentrated _i(t), the orthonormal basis function { φ that can produce with one group of Gram-Schmidt method _j(t), j=1,2 ... the linear combination of N} obtains, that is: $s_i\left(t\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{s}_{\mathrm{ij}}{\mathrm{\φ}}_j\left(t\right)$ Like this, just with M signal waveform { s _i(t) } set up mapping relations one by one with M N dimensional vector, that is to say, signal waveform s _i(t) be mapped to the some s in N dimensional signal space equivalently _i=[s _I1, s _I2..., s _IN].In fact, the linearly modulated signal that adopts in the digital communication can be easily with two orthonormal basis functions under the condition of rectangular pulse ${\mathrm{\φ}}_1\left(t\right)=\sqrt{\frac{2}{T_s}}\cos 2\mathrm{\π}{f}_{c}t$ ${\mathrm{\φ}}_2\left(t\right)=-\sqrt{\frac{2}{T_s}}\sin 2\mathrm{\π}{f}_{c}t$ Launch.T in the formula _sRepresentation signal waveform s _i(t) duration.Like this, just can in a 2 d plane picture, show by mapping relations the linear modulation waveform Here it is planisphere.Fig. 2 has made the signal constellation which of 64QAM modulation, traditionally the I axle is called in-phase component, and the Q axle is called quadrature component, and for the 64QAM modulation, I, Q component are represented the digital information of 3 bits respectively.

Therefore, the sign map of constellation is an important step of digital modulation, normal natural sign mapping and the Gray's sign map of adopting of traditional 64QAM modulation, shown in table 1 and 2, therefore, the sign map in the digital modulation also can be regarded as a kind of coding, and just it does not adopt memory.

Mapping of table 1 64QAM natural sign and Euclidean distance thereof

Sign map		Euclidean distance
											Symbol	Bit	Known bits	Related symbol	Euclidean distance	Known bits	Related symbol	Euclidean distance	Known bits	Related symbol	Euclidean distance
0	000	×00	100	4	00×	001	1	0×0	010	2
											1	001	000		00?0	000
2	010		×01		001	4			01×								010	1	0×1	001	2
		3		011			101			011	011
4	100				×10				110			4	10×	101	1	1×0	110			2
		5	101	010			100	100
6	110								×11	011	4		11×	110			1	1×1	101		2
		7	111	111		111	111

Table 2 64QAM Gray's sign map and Euclidean distance thereof

Sign map		Euclidean distance
											Symbol	Bit	Known bits	Related symbol	Euclidean distance	Known bits	Related symbol	Euclidean distance	Known bits	Related symbol	Euclidean distance
0	000	×00	100	7	00×	001	1	0×0	010	3
											1	001	000		000	000
2	011		×01		001	5			01×								010	1	0×1	001	1
		3		010			101			011	011
4	110				×10				110			1	10×	101	1	1×0	110			3
		5	111	010			100	100
6	101								×11	011	3		11×	110			1	1×1	101		1
		7	100	111		111	111

Through after the Channel Transmission, the demodulator of receiving terminal is finished the inverse process of modulator, promptly carries out filtering and down-conversion at first to received signal, and it is reverted to baseband signal, finishes functions such as matched filtering and signal decision again in base band.

Disturb and noise owing to exist in the transmission channel, actual reception to constellation point can depart from desirable constellation point position, therefore, need carry out signal decision.It is that equiprobability occurs that traditional QAM demodulation is based on the hypothesis constellation point, and does not adopt repeatedly iterative processing method, and signal decision output result has only symbolic information (soft-decision or hard decision output), the probabilistic information that does not have this symbol to occur.Therefore, traditional QAM demodulation is the signal determining that receives the nearest constellation point of Euclidean distance.

I component with 64QAM shown in Figure 3 is example (the Q axle is set up equally), bring in for reception and to say, 3 bit informations of I component representative all are unknown, and the probability that hypothesis constellation point A～H occurs is etc. general, if the constellation point that receives is positioned at the R place, then nearest according to Euclidean distance judgement principle is the data of R judgement for the constellation point representative at D place.

But the probability of occurrence of constellation point is not etc. general in the reality.

In addition, in digital transmission system, no matter the Channel Transmission of signal by what media types because the ` that declines of signal subtracts, distortion and various interference, all can make the data that receive go wrong inevitably.Therefore, the digital communication system of any reality all needs to take the error code correction measure, general forward direction error code correction FEC (Forward ErrorCorrect) method that adopts, it is at transmitting terminal data to be added by certain rule to hold complementary unit, forms the error correcting code with error correcting capability.After receiving terminal is received code word, decipher, zero defect is arranged, if wrong then correction automatically to determine to receive in the code word by the rule of predesignating.FEC can have a variety of classification according to the starting point difference.Error correction coding commonly used in Digital Transmission has block code (for example Read-Solomon RS sign indicating number, BCH code) and convolution code etc.

Wherein, the coding/decoding method of convolution code mainly contains two kinds of algebraic decoding and probabilistic decodings.Algebraic decoding is deciphered according to the Algebraic Structure of convolution code self, calculates simple; Probabilistic decoding is then considered channel statistic property when calculating, calculate complexity, but the error correction effect is much better, is widely used.

Suppose that coded sequence is C _m=(c _M1, c _M2), through Channel Transmission, the signal that receiving terminal is received is R (analog signal or digital signal depend on the definition to channel), receiving terminal can be sought conditional probability P (C with following a well mapped-out plan in all possible sign indicating number sequence so _m| R) one of maximum, think that it is most probable transmission sequence.That is: ${\tilde{C}}_m=\mathrm{Arg}\left\{\underset{C_m}{\mathrm{MAX}}P\left(C_m\right|R)\right\}$ This decision rule is called maximum a posteriori probability (MAP) criterion.Yet, because conditional probability P (C _m| value R) and transmitting terminal coded sequence C _mProbability of happening relevant, and the probability of happening of coded sequence is difficult to obtain, so maximum posteriori criterion is difficult to utilization in traditional convolutional code decoder algorithm.

According to the Bayes formula, have: $P\left(C_m\right|R)=\frac{p\left(R\right|C_m)P\left(C_m\right)}{p\left(R\right)}$ Suppose unknown P (C _m) be equiprobability, find to seek maximum posterior probability P (C this moment _m| R) be equivalent to the likelihood probability P (R|C that seeks maximum _m).At this moment decision rule is modified to: ${\tilde{C}}_m=\mathrm{Arg}\left\{\underset{C_m}{\mathrm{MAX}}P\left(C_m\right|R)\right\}$ Maximum-likelihood criterion that Here it is (ML).Likelihood probability P (R|C _m) only relevant with the characteristic of channel, and with the statistical probability that sends code word irrelevant (suppose be etc. general).

The convolutional code decoder algorithm based on maximum-likelihood criterion that is widely adopted at present is the Viterbi algorithm of Viterbi proposition in 1967.

But, same, the P (C of the unknown in the reality _m) neither wait general.

Above-mentioned is the situation of single error correcting code, takes another look at the situation of cascaded code below.According to Coding Theory, just can infinitely approach channel capacity with the sufficiently long random coded of code length n, still along with the increase of n, the complexity of decoder and amount of calculation index increase, and are difficult to accept.1966, Fomey proposed the thought of concatenated coding (being made of " RS sign indicating number+matrix interweaves+convolution code ") in its thesis for the doctorate.His thinking is: if encoder, channel and decoder integral body are regarded as the channel of a broad sense, this channel also has error code, therefore can also make further coding to its.Thus, he constitutes a long code at the subcode series connection that two code lengths are short, just can exchange the very big raising of error correcting capability for the limited increase of complexity.

Development along with coding techniques, various " good sign indicating numbers " near the Shannon coding efficiency limit have been proposed in recent years, circulatory system convolution code PCCC for example in parallel (being the Turbo code that the Frenchman proposes), series circulation systematic convolutional code SCCC, Turbo product code TPC and low-density checksum LDPC etc.Why these sign indicating numbers become " good sign indicating number ", are because their decoding algorithm has adopted iterative algorithm, in each iterative process, constantly obtain more transmitting terminal coded sequence C _mThe knowledge of probability of happening obtains conditional probability P (C _m| R), promptly adopted the above-mentioned maximum a posteriori probability of mentioning (MAP) decoding algorithm.

Wherein, series circulation systematic convolutional code SCCC encoder constitutes as shown in Figure 4, form by outer code system encoder for convolution codes, ISN random interleaver and ISN systematic convolutional code encoder etc., in order to solve in the iterative decoding algorithm inside and outside the serial concatenation of codes information problem of transmission between the sign indicating number, require two-layer sign indicating number to be systematic code.Therefore, SCCC has adopted two systematic convolutional code encoders.Simultaneously, do not restrain or converge in order to prevent iterative decoding algorithm away from the optimal solution place, do not comprise the information of using when separating this yard last time in the soft information of feedback that requirement is used when carrying out inner decoding for the second time, so, SCCC has adopted a random interleaver, make that the correlation of adjacent-symbol is very low, eliminate positive feedback, realize iterative decoding.

Therefore, compare with the serial concatenation of codes that traditional Forney proposes, the maximum inside and outside sign indicating number of SCCC sign indicating number that is not both all adopts systematic convolutional code and interleaver to adopt random interleaver.

Adopt series circulation systematic convolutional code SCCC to improve the error-resilient performance of system, but, reduced the efficiency of transmission of system owing to increased redundancy.

Summary of the invention

The objective of the invention is to have proposed the maximized constellation mapping cascade error-correction coding method of a kind of minimum Eustachian distance at adopting above-mentioned series circulation systematic convolutional code SCCC in M-ary orthogonal amplitude modulation(PAM) (mQAM) system, the ISN that the method is encoded as SCCC with the constellation symbol mapped of mQAM modulation, redefined the sign map relation based on the maximum a posteriori probability iterative decoding algorithm, made that the minimum Eustachian distance between constellation point maximizes.Than natural code mapping and Gray code mapping, the present invention only needs the iteration of limited number of time just can obtain good error-correcting performance when improving code efficiency.

The invention provides the maximized constellation mapping cascade error-correction coding method of a kind of minimum Eustachian distance, it is characterized in that, may further comprise the steps:

1) digital signal of input is carried out the systematic convolutional code coding;

2) data that systematic convolutional code coding back is formed are carried out the random bit interleaving treatment;

3) data behind the random interleaving are carried out the mQAM modulation, its symbol constellation mapping code is as the ISN of cascade error correction coding, and the symbol constellation mapping relations satisfy the minimum Eustachian distance maximization between the relevant code word; Above-mentioned three steps constitute the serially concatenated systematic convolutional code, and the signal of its output is the signal after the error correction.

Above-mentioned mQAM modulation can be the 64QAM modulation, and its symbol constellation mapping relations are: 000 → 0; 101 → 1; 010 → 2; 111 → 3; 100 → 4; 001 → 5; 110 → 6; 011 → 7.

Described systematic convolutional code can be the systematic convolutional code of various code rate.

Described systematic convolutional code can be the circulatory system convolution code of 2/3 code check.

The circulatory system convolution code of described 2/3 code check can be punchinged by the circulatory system convolution code of 1/2 code check and be obtained, and per 4 of the circulatory system convolution code sequence of 1/2 code check is divided into one group, deletes the 4th circulatory system convolution code that obtains described 2/3 code check.

The denominator generator polynomial of the circulatory system convolution code of described 1/2 code check can be G ₁(x)=1+x+x ³, the molecule generator polynomial can be G ₂(x)=1+x ²+ x ³

Described mQAM modulation 128QAM and 256QAM.

Characteristics of the present invention:

The present invention be directed to the cascade circulatory system convolution code in the mQAM modulating system and proposed the maximized constellation mapping cascade error-correction coding method of a kind of minimum Eustachian distance, make that the minimum Eustachian distance between constellation point maximizes.Than natural code mapping and Gray code mapping, the present invention only needs the iteration of limited number of time just can obtain good error-correcting performance.

The present invention can be applicable in the digital communication system, also can be applicable in the digital television broadcastings such as ground and wired, satellite.

Description of drawings

Fig. 1 is a linear modulation demodulation model.

Fig. 2 is the 64QAM planisphere.

Fig. 3 is traditional 64QAM constellation point judgement schematic diagram.

Fig. 4 is a series circulation systematic convolutional code SCCC encoder block diagram.

Fig. 5 is used for the overall pie graph of embodiment of sending and receiving end for the present invention.

Fig. 6 is the circulatory system encoder for convolution codes structural representation of 1/2 code check that adopts in the present embodiment.

Fig. 7 is a 64QAM constellation point judgement schematic diagram in the present embodiment.

Fig. 8 is the transmitting terminal block diagram of the ground digital multimedia TV broad cast system of employing present embodiment.

Fig. 9 is the receiving terminal block diagram of the ground digital multimedia TV broad cast system of employing present embodiment.

Figure 10 is the Computer Simulation performance of the ground digital multimedia TV broad cast system of employing present embodiment.

Figure 11 is the Computer Simulation performance of the system of employing natural code sign map.

Figure 12 is the Computer Simulation performance of the system of employing Gray code sign map.

Embodiment

Below in conjunction with accompanying drawing specific embodiments of the invention are described in detail.

The maximized constellation mapping cascade error-correction coding method of minimum Eustachian distance of the present invention be used to the to make a start performing step of embodiment is as follows:

1. the digital signal of input is carried out optional preliminary treatment (being the RS error correction coding in the present embodiment)

2. carry out 2/3 code check systematic code coding;

3. the data that 2/3 code check systematic convolutional code coding back is formed are carried out the random bit interleaving treatment;

4. the data behind the random interleaving are carried out the QAM modulation, the minimum Eustachian distance maximization is satisfied in its symbol constellation mapping;

5.QAM the signal after the modulation can further carry out the OFDM modulation, and then through giving Channel Transmission after the processing such as shaping filter, baseband signal frame up conversion.

The present invention is used for sending out receiving end embodiment as shown in Figure 5, as previously described, the constellation symbol mapped that mQAM modulates can be regarded a kind of coding that does not have storage as, and it is used as the ISN of SCCC coding, with the circulatory system convolution code formation serially concatenated systemic circulation convolution code SCCC as outer sign indicating number.

In an embodiment of the present invention, the systematic convolutional code of 2/3 code check among Fig. 5 is to obtain by the symbol of deleting some in female sign indicating number output sequence regularly.Female sign indicating number employing 1/2 code check circulatory system convolution code (recursive systematic convolutional code RSC), has 8 states, and its molecule, denominator generator polynomial are respectively:

G ₁(x)=1+x+x ³(molecule: 15Octal)

G ₂(x)=1+x ²+ x ³(denominator: 13Octal) circulatory system convolution code maker of 1/2 code check as shown in Figure 6.An input bit U generates two output bits: information bit I and check bit P.

Circulatory system convolution code to above-mentioned 1/2 code check is deleted regularly, thereby improves the efficiency of transmission of channel effectively.In embodiments of the present invention, 2/3 rate convolutional code adopts deletion (punchinging) convolution code.Per 4 of the convolution code sequence of above-mentioned 1/2 code check is divided into one group, deletes the 4th and obtain deleting convolution code.

If the sign indicating number sequence of 1/2 code check is:

Then deleting convolution code is:

The result is equivalent to import 2 bit informations, through being output as 3 bits after this deletion convolution code, has promptly realized 2/3 code check systemic circulation convolution code.

Before carrying out the symbol constellation mapping, carry out the bit random interleaving to bit stream, Bit Interleave is undertaken by tabling look-up.Interleaver is selected pseudo random interleaver, and when interleaver was fully big, correlation was very little between the sign indicating number sequence before and after interweaving, and error correction coding is had be similar to the characteristic of long code at random, has also avoided when iterative decoding owing to correlation forms positive feedback by force.Simultaneously, interleaver has changed the distribution of weight of code word, makes the distribution of code word weight in the coding output sequence even as far as possible, reduces very light in weight or very heavy code word as far as possible, make the code word of generation have considerably less comparatively speaking neighbour, that is to say that the code word of generation is disperseed very much.

Signal behind the random interleaving is given the mQAM modulator of back, finishes the constellation symbol mapped coding, and this part sees that ` makes the ISN of error correction coding of the present invention.

In decoding end, present embodiment has adopted the general iterative decoding of maximum a posteriori (MAP-ID) algorithm.

At first demodulation map decode is started working earlier, and do not have priori to sending sequence this moment, after map decoding calculates, obtains external information LE _1kInformation symbol sequence { the x that receives _kAnd external information LE _1kBe adjusted into the order of encoding through one with the same random interleaver of making a start, be sent to 2/3 code check systematic convolutional code decoder subsequently at 2/3 code check systematic convolutional code.The external information LE that 2/3 code check systematic convolutional code decoder provides the demodulation map decoding _1kBe used as own priori to the transmission sequence and finish decoding, output sends the priori and the external information LE of sequence _2k, finish iteration one time.

LE _2kBe sent to the demodulation map decoder again after the process reciprocal cross is knitted, be used as priori equally, beginning new round iteration.Through the several times iteration or after output is stable, provide court verdict.

Therefore, in the general iterative decoding of above-mentioned maximum a posteriori (MAP-ID) process, obtain the symbolic information of soft output, obtain conditional probability information simultaneously.Modulate for the 64QAM in the embodiment of the invention, after through the MAP-ID decoding, can determine 2 bits in the 3 entrained bit informations of I (and Q) component, promptly from last 8 constellation point of I axle, select 2, C as shown in Figure 7 and D point is for example determined among 2 constellation point C and the E which transmission of making a start by the 3rd bit more at last.

In order to adjudicate more reliably is C point or E point, and the distance between these 2 is big more so, then is not easy to declare mistake more.Therefore, so just should be according to maximum Euclidean distance criterion decision for the 3rd the bit judgement of 64QAM, the mapping code principle that is 64QAM should be in the minimum Eustachian distance maximization that makes under the situation of known 2 bits between relevant two code words, according to this principle, obtain the 64QAM modulation symbol constellation mapping table of the present embodiment shown in the table 3, and Euclidean distance.Can see that the minimum Eustachian distance of present embodiment is 2 from table, and foregoing natural code sign map and Gray code sign map be shown in the table 1 and table 2 of front, their minimum Eustachian distance all is 1.

The 64QAM sign map and the Euclidean distance thereof of table 3 present embodiment

Sign map		Euclidean distance
											Symbol	Bit	Known bits	Related symbol	Euclidean distance	Known bits	Related symbol	Euclidean distance	Known bits	Related symbol	Euclidean distance
0	000	×00	100	4	00×	001	5	0×0	010	2

??1	??101		??000			??000			??000
											??2	??010	??×01	??001	??4	??01×	??010	??5	??0×1	??001	??2
??3	??111	??101		??011	??011
						??4	??100	??×10	??110	??4	??10×	??101		??3		??1×0	??110			??2
??5	??001	??010		??100	??100
						??6	??110		??×11		??011	??4	??11×		??110		??3	??1×1	??101		??2
??7	??011	??111		??111	??111

The ground digital multimedia TV broad cast emission system composition frame chart of a described method of employing present embodiment as shown in Figure 8.The MPEG TS code stream of input can be a video, audio frequency, figure, multimedia messagess such as data, in order to resist the error code that produces in the transmission course, TS stream at first passes through RS sign indicating number error correction coding, give the maximized constellation mapping cascade error-correcting coder of minimum Eustachian distance that has of the present invention then, modulator becomes the digital QAM modulation signal, give the OFDM multi-carrier modulation again, multiple connections such as last and PN sequence are after D/A converter module, be converted to suitable analog signal, the radio frequency module receives this analog signal, and the result after the processing gives transmitting antenna or other signal transmitter.

The ground digital multimedia TV broad cast receiving system principle composition frame chart of a described method of employing present embodiment as shown in Figure 9.Antenna or other signal receiver receive modulation signal, give after down conversion module carries out frequency translation, give analog-to-digital conversion and become digital signal, pass through the demodulation of OFDM multicarrier then.Digital signal after the OFDM demodulation through of the present invention have the maximized constellation mapping cascade of minimum Eustachian distance error correction decode method and handle after, give back RS decoder, recover MPEG TS code stream at last.

Computer Simulation test to the ground digital multimedia TV broad cast receiving system of above-mentioned employing present embodiment method is carried out draws following result, and Figure 10 is the Computer Simulation performance of the ground digital multimedia TV broad cast system of employing present embodiment; Figure 11 is the Computer Simulation performance of the system of employing natural code sign map; Figure 12 is the Computer Simulation performance of the system of employing Gray code sign map.As we can see from the figure, through after 4 iteration, adopt the SNR～BER performance of the system of present embodiment just to become fine, curve is precipitous, and through after 8 iteration, SNR～BER curve becomes more precipitous; And the SNR～BER performance of the system of employing Gray symbol constellation mapping is the poorest, no matter iteration several times, its each bar curve all concentrates in together basically, and descends slowly; Adopt the SNR～BER performance of the system of natural code sign map slightly to be better than Gray code sign map system.

On the basis of computer artificial result, realized adopting the function model machine of the ground digital multimedia TV broad cast receiving system of the described method of present embodiment with FPGA.

In conjunction with the accompanying drawings specific embodiments of the invention are had been described in detail above; but the present invention is not restricted to the foregoing description; under the spirit and scope situation of the claim that does not break away from the application; those skilled in the art can make various modifications or remodeling; for example 2/3 code check systematic convolutional code is revised as 3/4 systematic convolutional code; the 64QAM modulation modification is 256QAM etc., all should belong to protection scope of the present invention.

Claims (7)

1, the maximized constellation mapping cascade error-correction coding method of a kind of minimum Eustachian distance is characterized in that, may further comprise the steps:

1) digital signal of input is carried out the systematic convolutional code coding;

2) data that systematic convolutional code coding back is formed are carried out the random bit interleaving treatment;

3) data behind the random interleaving are carried out the mQAM modulation, its symbol constellation mapping code is as the ISN of cascade error correction coding, and the symbol constellation mapping relations satisfy the minimum Eustachian distance maximization between the relevant code word.

2, the maximized constellation mapping cascade error-correction coding method of minimum Eustachian distance as claimed in claim 1 is characterized in that: said mQAM is modulated to the 64QAM modulation, and its symbol constellation mapping relations are: 000 → 0; 101 → 1; 010 → 2; 111 → 3; 100 → 4; 001 → 5; 110 → 6; 011 → 7.

3, the maximized constellation mapping cascade error-correction coding method of minimum Eustachian distance as claimed in claim 1, it is characterized in that: described systematic convolutional code is the systematic convolutional code of various code rate.

4, the maximized constellation mapping cascade error-correction coding method of minimum Eustachian distance as claimed in claim 3 is characterized in that, described systematic convolutional code is the circulatory system convolution code of 2/3 code check.

5, the maximized constellation mapping cascade error-correction coding method of minimum Eustachian distance as claimed in claim 4, it is characterized in that, the circulatory system convolution code of described 2/3 code check is to be punchinged by the circulatory system convolution code of 1/2 code check to obtain, per 4 of the circulatory system convolution code sequence of 1/2 code check is divided into one group, deletes the 4th circulatory system convolution code that obtains described 2/3 code check.

6, the maximized constellation mapping cascade error-correction coding method of minimum Eustachian distance as claimed in claim 5 is characterized in that further comprising that the denominator generator polynomial of the circulatory system convolution code of described 1/2 code check is G ₁(x)=1+x+x ³, the molecule generator polynomial is G ₂(x)=1+x ²+ x ³

7, the maximized constellation mapping cascade error-correction coding method of minimum Eustachian distance as claimed in claim 1, it is characterized in that: described mQAM is modulated to 128QAM and 256QAM.

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