CN1359197A - Random extending code selection method reaching shannon limit - Google Patents
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Abstract
The radom spread iterated code method for allaining Shannon limit includes: random spread iterative coding band-spreading and decoding despreading; in the coding structure, firstly adopting random band-spreading method and using any random and pseudo-random sequence as spreading sequence, dthen adopting code of iterative decoding idea (for example Turbo code) as band-spread further code; and in the decoding structure, firstly adopting iterative decoding method (for example Turbo code decoding), then adopting despreading of band-spreading sequence, judging addrss code, finally adopting threshold decision method to obtain final decode data. In the band-width range of at most 30 times band-width of only required inputted data or in the range in which only-required inputted data rate is reduced at most 30 times and under the condition of only having need of interative decoding once or twice said method can attain Shannon limit. It possesses extensive adaptability in various communication systems.
Description
The invention belongs to the channel coding technology field in data communication, the transfer of data, be specifically related to the iterative code of the expansion at random method that a kind of coding modulation technique near shannon limit----reaches shannon limit.
The communication technology is one of field at present with the fastest developing speed, and it is people's live and work necessary tool, also is one of basic platform of present and following social and economic development, mainly comprises optical fiber communication, satellite communication and mobile communication.These all will be the information superhighways of present and future communications, and they and Internet are combined into the infrastructure of people's life, working and learning.And all communication all has common requirement, wishes that exactly speed is fast as much as possible, and transmission quality is high as much as possible, and is many as much as possible for the user who uses.Yet whatsoever communication certainly exists chnnel coding and channel multiplexing technology, because they relate to the key fields such as mass of system, power system capacity and systematic cost of communication.Thereby these are also to be one of main problem of present people's research.
About chnnel coding, Shannon was in his laying a foundation property paper " mathematical principle of communication " [1] in 1948, famous channel coding theorem has been proposed first: be the communication channel of C to any channel capacity, if the desired transmission rate R of communication system is less than C, then there is a coding method, fully big and when using maximum-likelihood decoding as code length n, it is arbitrarily small that the error rate of system can reach.He has used three primary conditions in theorem:
1) adopts random coded;
2) code length n → ∞, promptly code length is tending towards unlimited;
3) best maximum likelihood (ML) method is adopted in decoding.
The proposition of this theory and proof tell the method for our designing optimal sign indicating number to comprise the maximum-likelihood decoding that adopts random coded, adopts the best and adopt code length big as far as possible theoretically.
Simultaneously, Shannon can be written as according to the capacity formula that information theory has proposed famous awgn channel
C
[b/s]＝Wlog
2(1+SNR)＝Wlog
2(1+E
s/N
0)bits/s (1)
If represent channel capacity with the amount of information C that every signal delivered, then it is equivalent to the average information bit number that transmits among the T per signal duration, promptly has
For reliable communication, R is arranged
c＜C is updated in the formula (2), obtains under the 2D signal condition, when giving constant bit rate Rc, about E
b/ N
0Shannon be limited to
The shannon limit formula has indicated the limit of chnnel coding for us.
In decades, be that back two of three primary conditions quoting according to Shannon serve as theme and develop basically in order to construct good sign indicating number near shannon limit.For condition 1) do not give enough attention always, its reason may be because coding and decoding is difficult to produce and control at random.1966, Forney proposed the thought of the series connection sign indicating number of two short code structure length, and its error correcting capability is strong, deciphers also uncomplicated.1972, go out the Justeson sign indicating number with cascade construction by Justeson.1977, Goppa constructed the Goppa sign indicating number on the basis of representing code word with rational fraction.Coppa has proposed Algorithms of Algebraic Geometric Codes at early eighties, systematically be applied to algebro geometric theory and method in the coding theory, make in the original linear code important parameter such as code length, distance and dimension etc. have brand-new geometric meaning, the research of Algorithms of Algebraic Geometric Codes becomes one of research focus in the eighties and the nineties coding field.
The theoretical proof of Shannon, random code are good sign indicating numbers, but its decoding is but too complicated.Therefore, the random coded theory is as analyzing and the main method that proves coding theorem, do not cause enough attention of people and how to play a role on the structure sign indicating number always for these years.Up to 1993, the discovery of Turbo code just solved this problem preferably, for the application study of Shannon random code theory is laid a good foundation.The appearance of Turbo code is objectively said, is the inevitable outcome of channel decoding development, and it has fully absorbed the achievement in research of modern coding and decoding, comprises random coded thought, concatenated coding, soft input soft output decode and iterative decoding thought etc.Turbo code claims parallel cascade convolution code (PCCC) again, as shown in Figure 1, is proposed in ICC ' 93 meetings by C.Berrou etc.It combines convolution code and random interleaver dexterously, has realized the thought of random coded, simultaneously, adopt soft output iterative decoding to approach maximum-likelihood decoding, reached the performance near the Shannon limit, this excellent properties causes the sensation of information and coding theory circle immediately.The discovery of Turbo code indicates that channel coding theorem and Study on Technology have entered a brand-new stage, and it is through with for a long time with the history of channel rate of cut as the actual capacity limit.
Simultaneously, as the coding modulation technique on the channel of another research direction of channel coding theorem, begin also to have obtained develop rapidly from the eighties.When studying chnnel coding in the past, only study encoder, do not consider modulator, and from information-theoretical angle, error correcting encoder combines with modulator, they finish the task of chnnel coding jointly.Therefore, we should understand chnnel coding under a wider meaning.Coding all belongs to the Design of Signal problem with modulation, and demodulation and decoding belong to the input problem.J.Massey has proposed in 1974 to encode and the as a whole imagination that may improve systematic function for the treatment of is made in modulation.After this, many scholar's research this imagination is committed to the approach of practice.Wherein, the most noticeable is Trellis-coded modulation (TCM) technology [3] that Ungerboeck proposed in nineteen eighty-two, and it has established the research basis of coding modulation technique on the band limited channel, is considered to the developing milestone of chnnel coding.In addition, almost in the same period Japanese scholar Imai has proposed a kind of coding modulation technique that adopts block code, is called BCM.Its performance in fading channel is more outstanding.The major advantage of TCM and BCM is the shared bandwidth of expanding system not when improving system power efficient.In addition, along with the further raising of transmission rate, be the opposing intersymbol interference, people will encode again and combine with multi-carrier modulation technology, and the COFDM technology has been born.Multi-carrier modulation is that the perfection about parallel channel transmission " water filling theorem " embodies in the Shannon information theory, and it has given its application prospects with combining of channel coding technology.At present, CDMA multiple carrier has become one of major technique pillar of broadband wireless communications net.
At present people generally believe, since Turbo code and TCM technology were the eighties, obtained greatest technological contribution in channel coding theorem and the technical research had milestone inthe.They realized respectively near shannon limit coding techniques and coded modulation combine technology.
To the channel multiplexing technology, mainly comprise time division multiplexing at present, frequency division multiplexing and code division multiplexing technology, the use of these multiplexing methods has improved the utilance of channel greatly, improves the capacity of system greatly.In the code division multiplexing field, be exactly the spread spectrum communication that we use always, comprise Direct-Spread and frequency modulation spread spectrum etc.For spread spectrum communication, because optical fiber communication, satellite communication and second generation cdma mobile communication, and be about to become the standard of the third generation and the 4th third-generation mobile communication with extensively.
We use for reference the thought of existing chnnel coding modulation technique and spread spectrum communication, the particularly output of the interleaver designs of Turbo code and soft inputting and soft and the thought of iterative decoding, and the thought that combines of coded modulation, proposed to expand at random alternative manner (Random SpreadingIterative technique, RSI).This method effectively combines chnnel coding and spread-spectrum modulation technique, and confirms that through theory analysis and a large amount of Computer Simulations this coding modulation technique has been issued to shannon limit at limited bandwidth condition
The task of this patent of invention is: proposed a coding modulation technique that reaches shannon limit, this technology is called expands alternative manner at random, expands alternative manner at random and has reflected a kind of novel coded modulation thought, the i.e. combination of band spectrum modulation and chnnel coding.It is a kind of coding techniques, also be a kind of coded modulation technology that combines, this method is in the maximum 30 times bandwidth range that only needs the input data bandwidth or only need input data rate to reduce in maximum 30 times scopes and only need be issued to shannon limit at an iterative decoding of twice.
This patent has proposed to expand at random alternative manner by to the improvement of spectrum spreading method and the thoughts such as the design that interweaves, parallel cascade, the soft input of soft output and iteration thought of reference Turbo code.
This method is to put forward on the encoding and decoding algorithm basis of using for reference Turbo code, and becomes the technology that a kind of coded modulation combines.Under finite bandwidth or finite rate, reached shannon limit.
Below be detailed description to this method:
Band spectrum modulation is a kind of multiplexing modulator approach, also can be regarded as simultaneously a kind of channel coding method, can be described as extended coding at random, under the situation of spreading factor several times and tens times, is a kind of tamed spread spectrum method, bit sign for input, become the n position behind the extended coding at random by integral multiple, i.e. (n, 1) coding, concerning spread spectrum, promptly be that spreading factor is the band spectrum modulation of G=n.
In traditional spread spectrum system (as 3GPP), at transmitting terminal generally is just to carry out band spectrum modulation afterwards in chnnel coding (this paper adopts the Turbo coding thinking), by after receiving terminal generally is despreading, deciphering (adopting Turbo decoding thought) behind the channel again, as shown in Figure 2, frequency expansion sequence is sequence spreading at random, among the figure, frequency expansion sequence is at random or pseudo random sequence (as being the m sequence, Gold sequence or chaos sequence etc.).
In this patent, we have proposed carries out earlier carrying out chnnel coding again behind the extended coding (spread spectrum) at random, at receiving terminal, earlier to carrying out despreading decoding after the channel decoding again.As shown in Figure 3.
This thought is the coding thinking that a kind of extended coding at random and Turbo code coding combines, and also can be the coded modulation thought that combines with subsequently Turbo coding.
In the drawings, why adopt the Turbo code coding and decoding, be because more subsequently expand the interleaving technology that will adopt Turbo code in the iterative technique at random, concatenation technology and iterative decoding technology reach shannon limit in the hope of the performance of combination modulating-coding.In fact in this thought, can be other iterative decoding, as the LDPC code encoding method.
The coding of described iterative decoding thought is selected Turbo code or LDPC sign indicating number.One, the structured flowchart of this method
Expand at random alternative manner comprise expand at random the iterative technique coding spread spectrum and the decoding despreading.
Its coding spread spectrum such as Fig. 4, structured flowchart such as Fig. 5 of decoding despreading.
In coding structure, at first adopt spectrum spreading method at random, and available usefulness any at random with pseudo random sequence as sequence spreading, the coding (as Turbo code) that adopts iterative decoding thought again is as the further coding behind the spread spectrum.In decoding architecture, at first adopt the interpretation method of iterative decoding (as Turbo code), adopt the despreading of random sequence again, and judge address code, adopt the threshold judgement method to draw final decoding data at last.Two, the algorithm of this method is realized
The algorithm of expanding alternative manner at random is embodied as:
At coded portion:
Data b for input
k(k=1 ..., M), signal element is to be T the duration
b, data rate is R
b(R
b=1/T
b) the rectangular signal of 0 and 1 value, its power spectral density mainly is distributed in (f
b,+f
b) frequency band in B
b=2f
b, bandwidth B
b=2f
b
For sequence spreading L
In=[1,2, Λ, T], its code element is to be T the duration
a, bit rate is R
a(R
a=1/T
a) the rectangular signal of 0 and 1 value, its power spectral density mainly is distributed in (f
a,+f
a) frequency band in, f
a=1/T
a, bandwidth B
a=2f
a
The data sequence that obtains after the expansion of input data through L position spread symbols, its code element x
k(k=1 ..., N) being is T the duration
a, bit rate is R
a(R
a=1/T
a) the rectangular signal of 0 and 1 value, its power spectral density mainly is distributed in (f
a,+f
a) frequency band in, f
a=1/T
a, bandwidth B
a=2f
a
Spreading gain can be expressed as:
Through behind the spread spectrum, and enter the Turbo code encoder, the Turbo code encryption algorithm is seen document " error correction coding of close shannon limit: Turbo code " (Proc.IEEE ICC ' 93-pp:1064-1070).
In the decoding part, the sequence of input is at first by the Turbo code decoder, this decoding algorithm is still seen document " near the error correction coding of shannon limit: Turbo code " (Proc.IEEEICC ' 93-pp:1064-1070), and the despreading through the at random sequence spreading the same with coded portion is that mould 2 adds again.Enter thresholding on the one hand and decipher, threshold decoding adopts the integration interpretation method, on the other hand for multi-user system, enters address comparator, draws spectrum-spreading address code.Three, the hardware of this method is realized
Independently spread spectrum and despreading and Turbo code coding and realization of decoding prior art achieve a solution, and embody this patent RSI thought expand at random with this that relevant hardware algorithm of iterative technique is realized and system's realization also is that prior art is soluble, should all be effective extensions of this patent.Any hardware designs based on this thought and technology all is the extension of this technology.
This method effectively combines chnnel coding and spread-spectrum modulation technique, and confirms that through theory analysis and a large amount of Computer Simulations this coding modulation technique has been issued to shannon limit at limited bandwidth condition.
Below the effect of this method is analyzed:
For input data sequence b={b
k}
M, k=1,2, Λ M, the average signal energy of the unit's of establishing bit is E
b, when not adopting that extended coding promptly only adopts traditional Turbo code at random, interleaver sizes is M, through behind the channel, its signal interference ratio is E
b/ n
0, n here
0One-sided power spectrum density for noise.Through extended coding at random, be encoded to (n, 1) (the expansion gain is G) after, become data sequence X={x
l}
N, l=1,2, Λ N, wherein:
N=G * M interleaver sizes becomes N, and through behind the channel, its signal interference ratio is:
E
x/n
0＝(E
b/n
0)×(1/G)
Long information sequence for N is through (2,1, v) convolution coding can regard 2 as
NIndividual code word, code length are the block code of 2 (v+N), the bit error rate P of convolution code
bUnder maximum-likelihood decoding (ML) and Gaussian channel, have:
In the formula, w
d 0For information sequence first " 1 " " zero " constantly, code distance is the weight of all information sequences of d, R is a bit rate, d is the convolution code distance, d
FreeBe free code distance.
For be made of code check two RSC sign indicating numbers is 1/3 Turbo code, and component coder is handled in extra ending and reached nought state, and Turbo code is equivalent to (3N+2v, N) block code, v is the component code code registers, and N is an information sequence length, and is identical with interleaver sizes.By the encoder behind the interleaver 2, for whole Turbo code, its bit error rate is:
Compare with (4) formula, differ factor N, illustrate that Turbo code is reduced to 1/N with convolution code error rate under identical signal to noise ratio, explained that from the Turbo code code distance interleaver brings the reason of decoding gain 1/N like this.And Turbo code considers that mainly in the input code weight be 2 o'clock minimum distance d
FreeTo the Turbo code Effect on Performance, therefore, error rate limit can further be reduced to:
The input data b
k(k=1 ..., M) pass through L (L=G) position code element a at random
l(l=1 ..., obtain data sequence x after expansion N) (spread spectrum)
l(i=1 ..., N), through obtaining y after the Turbo code coding and decoding
l(i=1 ..., N), because the effect of random sequence spread spectrum and the effect of Turbo code encoder and interleaver, can be similar to the free code distance d after the Turbo code of thinking behind spread spectrum (expansion) coding is at random encoded
Free sFor:
The y that obtains through the Turbo code coding and decoding of extended coding at random
i, its error rate is:
The sheet y that obtains through the Turbo code coding and decoding of spread spectrum coding at random
i(i=1 ..., N), pass through random sequence a again
l(l=1 ..., despreading N), and the process threshold decoding obtains final output sequence d
k(k=1 ..., M), because the effect of threshold decoding makes the error rate of final output sequence further drop to P
x(G-1)/(2G) (G〉I), therefore the final output error rate through the Turbo code coding and decoding of spread spectrum coding and despreading at random is:
Compare with (6) formula, compare with general Turbo code coding and decoding based on the Turbo code coding and decoding of spread spectrum coding at random, its error rate limit has reduced 2G
2/ (G-1) (G〉I) doubly, obviously its effect is tangible.
We have carried out a large amount of emulation simultaneously, see the simulation result of Fig. 6.This result shows, is below 1/20 at code check, and the RSI code performance has reached shannon limit, and emulation shows iterative decoding, only needs an iteration just can reach such effect.
Therefore, all illustrated from theoretical and emulation and expanded the outstanding coding and decoding effect of iterative technique at random.
The advantage of this technology is:
The one, channel coding technology is combined with spread-spectrum modulation technique.
The 2nd, adopt random coded that list entries is played scrambler, can improve the code weight characteristic of input information, make the real pseudorandom permutation of input data, can improve the quality of system's bit timing recovery, improve the performance of systems such as frame synchronization and adaptive time domain equalization;
The 3rd, improve the interleaver gain, improve the correlation and the code weight of interleaver front and back;
The 4th, adopt soft inputting and soft output interative encode method;
The 5th, by threshold decoding, further error correction reduces the error rate;
The 6th, iterative decoding number of times few (only needing once) just can be issued to shannon limit in certain speed, has reduced the time delay and the complexity of system significantly.
In a word, the use of this technology makes system can adjust the error rate as required, and in only needing maximum 30 times bandwidth range of the rate bandwidth of raising information own and only just can reach shannon limit under needs one twice the iterative decoding.
Expanding iterative technique at random is a kind of coding techniques, also is a kind of coded modulation technology that combines, and also is a kind of coded modulation thought simultaneously.Be a technological break-through of chnnel coding.
Confirm that by a large amount of computer simulation experiments and theory analysis expand iterative technique at random and have huge superiority, the practical application of this technology will bring leap to communication, and society and the economic worth that can't estimate arranged.
Description of drawings:
Figure 1A is a Turbo code encoder block diagram;
Figure 1B is a Turrbo code decoder block diagram;
Fig. 2 is general spread spectrum and coding and decoding method figure;
Fig. 3 expands alternative manner figure at random;
Fig. 4 is the coding structure figure that expands alternative manner at random;
Fig. 5 is the decoding architecture figure that expands alternative manner at random;
Fig. 6 utilizes the simulation result of expanding alternative manner at random and comparison diagram (Pe≤10 of shannon limit
-5).Simulation system parameters is as follows: Turbo code is translated agate and is adopted the Map decoding algorithm, being encoded to code check is 1/2 convolution code, spread spectrum adopts chaos spread spectrum sequence, and promptly Logistic chaotic maps Xn+1=4Xn (1-Xn) is as band spectrum modulation, and channel is an additive white Gaussian noise channel.
Fig. 7 is the communication system applications figure that expands alternative manner at random.Among the figure, can embed the above-mentioned iterative technique of expanding at random in chnnel coding and the channel decoding module, obviously this technology has adaptability widely in various communication systems, has important practical value.
Claims (3)
1. reach the iterative code of the expansion at random method of shannon limit, it is characterized in that comprising and expand iteration coding spread spectrum and decoding despreading at random; In coding structure, at first adopt spectrum spreading method at random, and with any at random with pseudo random sequence as sequence spreading, the further coding of the coding that adopts iterative decoding thought again after as spread spectrum; In decoding architecture, at first adopt the interpretation method of iterative decoding, adopt the despreading of random sequence again, and judge address code, adopt the threshold judgement method to draw final decoding data at last.
2. the iterative code of the expansion at random method that reaches shannon limit according to claim 1 is characterized in that the coding of iterative decoding thought is selected Turbo code or LDPC sign indicating number.
3. the iterative code of the expansion at random method that reaches shannon limit according to claim 1 and 2 is characterized in that the algorithm of this method is embodied as:
(1) at coded portion:
Data b for input
k(k=1 ..., M), signal element is to be T the duration
b, data rate is R
b(R
b=1/T
b) the rectangular signal of 0 and 1 value, its power spectral density mainly is distributed in (f
b,+f
b) frequency band in B
b=2f
b, bandwidth B
b=2f
b
For sequence spreading L
InIts code element of=[1,2, Λ, T] is to be T the duration
a, bit rate is R
a(R
a=1/T
a) the rectangular signal of 0 and 1 value, its power spectral density mainly is distributed in (f
a,+f
a) frequency band in, f=1/T
aBandwidth B
a=2f
a
The data sequence that obtains after the expansion of input data through L position spread symbols, its code element x
k(k=1 ..., N) being is T the duration
a, bit rate is R
a(R
a=1/T
a) the rectangular signal of 0 and 1 value, its power spectral density mainly is distributed in (f
a,+f
a) frequency band in, f
a=1/T
a, bandwidth B
a=2f
a
Spreading gain can be expressed as:
Through behind the spread spectrum, enter and have iteration and translate the encoder of thought and encode;
(2) in the decoding part: the sequence of input is at first by the iterative code decoder for decoding, and the despreading through the at random sequence spreading the same with coded portion is that mould 2 adds again.Enter thresholding on the one hand and decipher, threshold decoding adopts the integration interpretation method, on the other hand for multi-user system, enters address comparator, draws spectrum-spreading address code.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101924565A (en) * | 2004-04-02 | 2010-12-22 | 北方电讯网络有限公司 | LDPC encoder, decoder, system and method |
| CN103208997A (en) * | 2013-05-03 | 2013-07-17 | 北京理工大学 | Codec structure capable of realizing simultaneous input, decoding and output |
| CN104811211A (en) * | 2015-05-13 | 2015-07-29 | 广东省电信规划设计院有限公司 | Construction method and device of Turbo code interleaver |
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2001
- 2001-06-21 CN CNB011085681A patent/CN1166073C/en not_active Expired - Fee Related
Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101924565A (en) * | 2004-04-02 | 2010-12-22 | 北方电讯网络有限公司 | LDPC encoder, decoder, system and method |
| CN101924565B (en) * | 2004-04-02 | 2014-10-15 | 苹果公司 | LDPC encoders, decoders, systems and methods |
| CN103208997A (en) * | 2013-05-03 | 2013-07-17 | 北京理工大学 | Codec structure capable of realizing simultaneous input, decoding and output |
| CN103208997B (en) * | 2013-05-03 | 2019-09-24 | 北京理工大学 | It is a kind of while input/while decoding/side output encoder and decoder structure |
| CN104811211A (en) * | 2015-05-13 | 2015-07-29 | 广东省电信规划设计院有限公司 | Construction method and device of Turbo code interleaver |
| CN104811211B (en) * | 2015-05-13 | 2018-04-20 | 广东省电信规划设计院有限公司 | The building method and device of Turbo code interleaver |
| CN107180206A (en) * | 2016-03-11 | 2017-09-19 | 中国电子科技集团公司电子科学研究院 | A kind of solid state hard disk secure control method and device based on CDMA |
| CN107180206B (en) * | 2016-03-11 | 2020-01-14 | 中国电子科技集团公司电子科学研究院 | Solid state disk safety control method and device based on CDMA |
| CN109657478A (en) * | 2018-12-20 | 2019-04-19 | 中国人民解放军战略支援部队信息工程大学 | A kind of quantization method and system of isomerism |
| CN109657478B (en) * | 2018-12-20 | 2023-12-19 | 中国人民解放军战略支援部队信息工程大学 | Isomerization quantification method and system |
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Owner name: ZHANG HONGYU Free format text: FORMER OWNER: ZHANG HONGYU; WANG LIN Effective date: 20070810 Owner name: SHENZHEN HONGYU CHUANGXIN SCIENCE CO., LTD. Free format text: FORMER OWNER: ZHANG HONGYU Effective date: 20070810 |
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Effective date of registration: 20070810 Address after: 518000, room 1210, Fangda building, South Science and technology road, Shenzhen, Nanshan District Patentee after: Shenzhen Hongyu Creative Technology Ltd. Address before: 610054 Department of Opto electronics technology, Chengdu University of Electronic Science and technology of Sichuan Patentee before: Zhang Hongyu Effective date of registration: 20070810 Address after: 610054 Department of Opto electronics technology, Chengdu University of Electronic Science and technology of Sichuan Patentee after: Zhang Hongyu Address before: 610054 Department of Opto electronics technology, Chengdu University of Electronic Science and technology of Sichuan Co-patentee before: Wang Lin Patentee before: Zhang Hongyu |
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