CN102957438B - A kind of Turbo decoder and interpretation method - Google Patents
A kind of Turbo decoder and interpretation method Download PDFInfo
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Abstract
The embodiment of the present invention provides a kind of Turbo decoder and interpretation method, described Turbo decoder comprises the first sub-decoder and the second sub-decoder, the first prior information that first sub-decoder provides according to the first perfect information in current iteration, the first channel information received and the second sub-decoder carries out iterative decoding, generates the first external information and is supplied to the second sub-decoder as the second prior information; Second sub-decoder carries out iterative decoding according to the second perfect information in current iteration, the second channel information received and the second prior information, generate the second external information and be supplied to the first sub-decoder as the first prior information, wherein: the external information that each sub-decoder exports comprises the prior information of another sub-decoder of part input.The Turbo decoder of the embodiment of the present invention and interpretation method, improve the error performance of Turbo decoder, or while keeping error performance constant, reduce the iterations of Turbo decoder thus reduce the computation complexity of Turbo decoding.
Description
Technical field
The present invention relates to Turbo decoder field, particularly relate to a kind of Turbo decoder and the interpretation method that can improve the error performance of Turbo decoder.
Background technology
Traditional Turbo decoder is made up of two sub-decoders (componentdecoder), as shown in Figure 1.In decode procedure, the information that the input and output information of decoder itself and two sub-decoders exchange in an iterative process is each other probabilistic information.A kind of concrete manifestation form of this probabilistic information is bit log-likelihood ratio (Loglikelihoodratio, LLR).
The input Soft Inform ation of Turbo decoder is the LLR of the transmission information bit provided by demodulator.This LLR is a kind of prior information, is defined as L
cH.The LLR relevant to sub-decoder has 4 kinds.Here for sub-decoder 1, the first is the above-mentioned prior information from demodulator (priorLLR) L
cH; The prior information of the second for being provided by sub-decoder 2, the prior information in i-th iteration is defined as
the third is the perfect information (fullLLR) that sub-decoder 1 exports, and the perfect information in i-th iteration is defined as
the 4th kind of external information (extrinsicLLR) being sub-decoder 1 and exporting, the external information in i-th iteration is defined as
relation between these four kinds of information is expressed as
prior information L
cHactual is the prior information directly provided by Received signal strength, and remains constant in iterative decoding process.Note, in order to distinguish, claim L here
cHfor channel information, and specially refer to the prior information that provided by sub-decoder 2 by prior information
four kinds of input/output informations of sub-decoder 2 and the equity of sub-decoder 1, have following relation:
wherein,
for the perfect information that sub-decoder 2 exports in i-th iteration,
for the external information that sub-decoder 2 exports in i-th iteration,
for the prior information provided by sub-decoder 1 in i-th iteration.In addition, according to the feature of Turbo code coding, the information bit sequence of sub-decoder 2 is that the information bit sequence of sub-decoder 1 obtains through interweaving.Definition interleaver is π (), and deinterleaver is π
-1(), then the channel information that sub-decoder 2 uses is expressed as π (L
cH).
Inventor is realizing finding in process of the present invention, and the prior information that sub-decoder 1 passes to sub-decoder 2 is actually the external information that sub-decoder 1 exports, and therefore has
equally, the external information that sub-decoder 2 exports also passes to the prior information of sub-decoder 1 as sub-decoder 1, is expressed as
in addition, perfect information is the full detail relevant to transmitted bit, in non-iterative decoding algorithm, use perfect information, after Turbo iterative decoding terminates, also needs to make hard decision according to perfect information to transmitted bit.And in Turbo iterative decoding process, what exchange between two sub-decoders is external information instead of perfect information, this is the independence in order to keep between two sub-decoders, thus increases the number of times of effective iteration.But while doing like this, also reduce the gain of each iteration to a certain extent.Under the prerequisite that iterations is identical, the reduction of iteration gain likely causes the decline of error performance.Keeping under the prerequisite that error performance is constant, the reduction of iteration gain likely can cause the increase of iterations, and then adds computation complexity.This is that industry does not wish to see.
Above it should be noted that, just conveniently to technical scheme of the present invention, clear, complete explanation is carried out to the introduction of technical background, and facilitate the understanding of those skilled in the art to set forth.Only can not think that technique scheme is conventionally known to one of skill in the art because these schemes have carried out setting forth in background technology part of the present invention.
Summary of the invention
In order to solve problem pointed in above-mentioned prior art, embodiments provide a kind of Turbo decoder and interpretation method, to improve the error performance of Turbo decoder, or while keeping error performance constant, reduce the iterations of Turbo decoder thus the computation complexity of reduction Turbo decoding.
According to an aspect of the embodiment of the present invention, provide a kind of Turbo decoder, described Turbo decoder comprises the first sub-decoder and the second sub-decoder, the first prior information that described first sub-decoder provides according to the first perfect information in current iteration, the first channel information received and described second sub-decoder carries out iterative decoding, generates the first external information and is supplied to described second sub-decoder as the second prior information; Described second sub-decoder carries out iterative decoding according to the second perfect information in current iteration, the second channel information received and described second prior information, generate the second external information and be supplied to described first sub-decoder as the first prior information, wherein: the external information that each sub-decoder exports comprises the prior information of another sub-decoder of part input.
In one embodiment, the first external information that described first sub-decoder exports is the difference of the product of described first perfect information and described first channel information and described first prior information and the first multiplicative coefficient factor; The second external information that described second sub-decoder exports is the difference of the product of described second perfect information and described second channel information and described second prior information and the second multiplicative coefficient factor; Wherein, described first multiplicative coefficient factor and described second multiplicative coefficient factor be respectively be not equal to 1 from 0 to 1 arbitrary value.
According to another aspect of the embodiment of the present invention, additionally provide a kind of Turbo interpretation method, wherein, described method comprises:
The first prior information that first sub-decoder provides according to the first perfect information in current iteration, the first channel information received and the second sub-decoder carries out iterative decoding, generates the first external information and is supplied to described second sub-decoder as the second prior information;
Described second sub-decoder carries out iterative decoding according to the second perfect information in current iteration, the second channel information received and described second prior information, generates the second external information and is supplied to described first sub-decoder as the first prior information;
Wherein, the external information that each sub-decoder exports comprises the prior information of another sub-decoder of part input.
In one embodiment, the first external information that described first sub-decoder exports is the difference of the product of described first perfect information and described first channel information and described first prior information and the first multiplicative coefficient factor; The second external information that described second sub-decoder exports is the difference of the product of described second perfect information and described second channel information and described second prior information and the second multiplicative coefficient factor; Wherein, described first multiplicative coefficient factor and described second multiplicative coefficient factor be respectively be not equal to 1 from 0 to 1 arbitrary value.
The beneficial effect of the embodiment of the present invention is: by retaining the prior information of another sub-decoder of part input in the external information that exports at each sub-decoder, have modified the share of prior information in the interactive information of two sub-decoders, which thereby enhance the error performance of Turbo decoder, or while keeping error performance constant, reduce the iterations of Turbo decoder thus reduce the computation complexity of Turbo decoding.
With reference to explanation hereinafter and accompanying drawing, disclose in detail particular implementation of the present invention, specifying principle of the present invention can adopted mode.Should be appreciated that, thus embodiments of the present invention are not restricted in scope.In the spirit of claims and the scope of clause, embodiments of the present invention comprise many changes, amendment and are equal to.
The feature described for a kind of execution mode and/or illustrate can use in one or more other execution mode in same or similar mode, combined with the feature in other execution mode, or substitutes the feature in other execution mode.
Should emphasize, term " comprises/comprises " existence referring to feature, one integral piece, step or assembly when using herein, but does not get rid of the existence or additional of one or more further feature, one integral piece, step or assembly.
Accompanying drawing explanation
With reference to following accompanying drawing a lot of aspects that the present invention may be better understood.Parts in accompanying drawing are not proportional draftings, and just in order to illustrate principle of the present invention.For the ease of illustrating and describing some parts of the present invention, in accompanying drawing, corresponding part may be exaggerated or reduce.The element described in an accompanying drawing of the present invention or a kind of execution mode and feature can combine with the element shown in one or more other accompanying drawing or execution mode and feature.In addition, in the accompanying drawings, similar label represents parts corresponding in several accompanying drawing, and can be used for instruction more than the corresponding component used in a kind of execution mode.In the accompanying drawings:
In the accompanying drawings:
Fig. 1 is the composition schematic diagram of traditional Turbo decoder;
Fig. 2 is the composition schematic diagram of the Turbo decoder of the embodiment of the present invention;
The iterative information that Fig. 3 (a) is-4.2dB for different Turbo decoder SNR under Gaussian channel shifts schematic diagram;
The iterative information that Fig. 3 (b) is-3.8dB for different Turbo decoder SNR under Gaussian channel shifts schematic diagram;
Fig. 4 is the throughput curve schematic diagram of different Turbo decoder under Gaussian channel condition;
Fig. 5 is the flow chart of the Turbo interpretation method of the embodiment of the present invention.
Embodiment
For making the object of the embodiment of the present invention, technical scheme and advantage clearly understand, below in conjunction with embodiment and accompanying drawing, the embodiment of the present invention is described in further details.At this, schematic description and description of the present invention is for explaining the present invention, but not as a limitation of the invention.
In order to obtain better compromise between perfect information (complete information) and external information (independence between sub-decoder), thus improve the error performance of Turbo decoder further, the Turbo decoder of the embodiment of the present invention, improves the interactive information (being also external information) between two sub-decoders.In existing Turbo decoder, in order to thoroughly keep independence, when calculating the interactive information between two sub-decoders, cut whole prior information.The embodiment of the present invention adds a multiplicative coefficient factor in interactive information computing formula, this factor be interval [0,1) in arbitrary value, for revising the share of the prior information in interactive information.
With reference to the accompanying drawings the preferred embodiment of the present invention is described.
Embodiment 1
The composition schematic diagram of a kind of Turbo decoder that Fig. 2 provides for the embodiment of the present invention, please refer to Fig. 2, this Turbo decoder comprises: the first sub-decoder 21 and the second sub-decoder 22, wherein:
First sub-decoder 21 according in current iteration the first perfect information (
i is iterations), the first channel information (L of receiving
cH) and the second sub-decoder 22 provide the first prior information (
i is iterations) carry out iterative decoding, generate the first external information (
i is iterations) as the second prior information (
i is iterations) be supplied to the second sub-decoder 22.
Second sub-decoder 22 according in current iteration the second perfect information (
i is iterations), the second channel information (π (L that receives
cH)) and the first sub-decoder 21 provide the second prior information (
i is iterations) carry out iterative decoding, generate the second external information (
i is iterations) as the first prior information (
i is iterations) be supplied to the first sub-decoder 21.
In the present embodiment, the external information that each sub-decoder exports comprises the prior information of another sub-decoder of part input.Such as, first sub-decoder 21 export the first external information (
i is iterations) in comprise a part of second sub-decoder 22 input the first prior information (
i is iterations); Second sub-decoder 22 export the second external information (
i is iterations) in comprise a part of first sub-decoder 21 input the second prior information (
i is iterations).
In the present embodiment, by multiplicative coefficient factor α (α ∈ [0,1)) ratio of the prior information of another sub-decoder input that comprises of the external information that regulates each sub-decoder to export.Such as, the first external information that the first sub-decoder 21 exports is the difference of the product of the first perfect information and the first channel information and the first prior information and the first multiplicative coefficient factor, is also
wherein,
be the first multiplicative coefficient factor, it is the multiplicative coefficient factor that the first sub-decoder 21 uses when i-th iteration; The second external information that second sub-decoder 22 exports is the difference of the product of the second perfect information and second channel information and the second prior information and the second multiplicative coefficient factor, is also
wherein,
be the second multiplicative coefficient factor, it is the multiplicative coefficient factor that the second sub-decoder 22 uses when i-th iteration.Wherein, the first multiplicative coefficient factor
with the second multiplicative coefficient factor
be respectively be not equal to 1 from 0 to 1 arbitrary value.
In the present embodiment, the first multiplicative coefficient factor can be identical with the second multiplicative coefficient factor, also can be different.That is, these two sub-decoders 21 with 22 multiplicative coefficient factor can identical also can be different from each other.Such as
Or
In the present embodiment, when the different iterations of Turbo decoder, the first multiplicative coefficient factor can be identical value or different values.Such as
(k is positive integer), or
same, when the different iterations of Turbo decoder, the second multiplicative coefficient factor also can be identical value or different values.Such as
(k is positive integer), or
In the Turbo decoder of the embodiment of the present invention, as shown in Figure 2, also comprise interleaver 23,24 and deinterleaver 25, because its principle of dealing with problems is identical with deinterleaver with the interleaver of existing Turbo decoder, do not repeat them here.
By the Turbo decoder of the embodiment of the present invention, the prior information of another sub-decoder of part input is remained in the external information that each sub-decoder exports, instead of all cut, thus, between perfect information (complete information) and external information (independence between sub-decoder), achieve better compromise, improve the error performance of Turbo decoder.From another one angle, by the Turbo decoder of the embodiment of the present invention, while maintenance error performance is constant, reduces the iterations of Turbo decoder thus reduce the computation complexity of Turbo decoding.
In order to the effect of the Turbo decoder of the outstanding embodiment of the present invention, below in conjunction with accompanying drawing, this is illustrated.
Fig. 3 (a) and Fig. 3 (b) give that code length is 6144, code check is 1/6, generator polynomial is [15,13] the Turbo decoder of oct, under Gaussian channel, signal to noise ratio snr is respectively the iterative information transfer schematic diagram of-4.2dB and-3.8dB.Wherein, the curve of multiplicative coefficient factor α=1 is the curve of existing Turbo decoder, to cut the prior information of another whole sub-decoders, as stated in the Background Art in the external information also namely exported at each sub-decoder; The curve of multiplicative coefficient factor α=0.92 is the curve of the Turbo decoder of the embodiment of the present invention, remains the prior information of another sub-decoder of part input in the external information also namely exported at each sub-decoder.Can be found out by Fig. 3 (a) and Fig. 3 (b), under the prerequisite of same iterations, the output information amount of the Turbo decoder of the embodiment of the present invention is greater than the Turbo decoder described in background technology, and also namely the decoding effect of the Turbo decoder of the embodiment of the present invention is better than the Turbo decoder described in background technology.
Fig. 4 gives that code length is 2048, code check be 1/2 generator polynomial is [15,13]
octturbo decoder, the throughput curve under Gaussian channel.As seen from Figure 4, same iteration 8 times, the Turbo decoder of the embodiment of the present invention will significantly better than existing Turbo decoder, and in low signal-to-noise ratio district, and the performance that the performance that the Turbo decoder iteration of the embodiment of the present invention is 7 times and existing Turbo decoder iteration are 8 times is consistent.
The embodiment of the present invention additionally provides a kind of Turbo interpretation method, as described in the following examples 2.The principle of dealing with problems due to this Turbo interpretation method is similar to the Turbo decoder of above-described embodiment 1, and therefore the enforcement of this Turbo interpretation method see the enforcement of the Turbo decoder of embodiment 1, can repeat part and repeat no more.
Embodiment 2
The flow chart of a kind of Turbo interpretation method that Fig. 5 provides for the embodiment of the present invention, please refer to Fig. 5, the method comprises:
Step 501: the first prior information that the first sub-decoder provides according to the first perfect information in current iteration, the first channel information received and the second sub-decoder carries out iterative decoding, generates the first external information and is supplied to described second sub-decoder as the second prior information;
Step 502: described second sub-decoder carries out iterative decoding according to the second perfect information in current iteration, the second channel information received and described second prior information, generates the second external information and is supplied to described first sub-decoder as the first prior information;
Wherein, the external information that each sub-decoder exports comprises the prior information of another sub-decoder of part input.
In the present embodiment, the first external information that described first sub-decoder exports is the difference of the product of described first perfect information and described first channel information and described first prior information and the first multiplicative coefficient factor; The second external information that described second sub-decoder exports is the difference of the product of described second perfect information and described second channel information and described second prior information and the second multiplicative coefficient factor; Wherein, described first multiplicative coefficient factor and described second multiplicative coefficient factor be respectively be not equal to 1 from 0 to 1 arbitrary value.
In one embodiment, described first multiplicative coefficient factor is identical or different with described second multiplicative coefficient factor.
In one embodiment, described first multiplicative coefficient factor is identical value or different values when the different iterations of described Turbo decoder.
In one embodiment, described second multiplicative coefficient factor is identical value or different values when the different iterations of described Turbo decoder.
By the Turbo interpretation method of the embodiment of the present invention, the prior information of another sub-decoder of part input is remained in the external information that each sub-decoder exports, instead of all cut, thus, between perfect information (complete information) and external information (independence between sub-decoder), achieve better compromise, improve the error performance of Turbo decoder.From another one angle, by the Turbo interpretation method of the embodiment of the present invention, while maintenance error performance is constant, reduces the iterations of Turbo decoder thus reduce the computation complexity of Turbo decoding.
More than describe the preferred embodiment of the present invention with reference to the accompanying drawings.Many feature and advantage of these execution modes are clearly according to this detailed description book, and therefore claims are intended to all these feature and advantage fallen in its true spirit and scope covering these execution modes.In addition, owing to those skilled in the art will find apparent that a lot of amendment and changing, therefore not embodiments of the present invention to be limited to precision architecture that is illustrated and that describe and operation, but can contain and fall into all suitable modifications within the scope of it and equivalent.
Should be appreciated that each several part of the present invention can realize with hardware, software, firmware or their combination.In the above-described embodiment, multiple step or method can with to store in memory and the software performed by suitable instruction execution system or firmware realize.Such as, if realized with hardware, the same in another embodiment, any one in the following technology can known altogether with this area or their combination realize: the discrete logic with the logic gates for realizing logic function to data-signal, there is the application-specific integrated circuit (ASIC) of suitable combinational logic gate circuit, programmable gate array (PGA), field programmable gate array (FPGA) etc.
To describe or frame can be understood in flow chart or in this any process otherwise described or method, represent and comprise one or more for realizing the module of the code of the executable instruction of the step in specific logical function or process, fragment or part, and the scope of the preferred embodiment of the present invention comprises other realization, wherein, can not according to order that is shown or that discuss, comprise according to involved function by the mode while of basic or by contrary order, carry out n-back test, this should those skilled in the art described by the present invention understand.
In flow charts represent or in this logic otherwise described and/or step, such as, the sequencing list of the executable instruction for realizing logic function can be considered to, may be embodied in any computer-readable medium, for instruction execution system, device or equipment (as computer based system, comprise the system of processor or other can from instruction execution system, device or equipment instruction fetch and perform the system of instruction) use, or to use in conjunction with these instruction execution systems, device or equipment.With regard to this specification, " computer-readable medium " can be anyly can to comprise, store, communicate, propagate or transmission procedure for instruction execution system, device or equipment or the device that uses in conjunction with these instruction execution systems, device or equipment.Computer-readable medium can be such as but be not limited to electronics, magnetic, optical, electrical magnetic, infrared or semiconductor system, device, equipment or propagation medium.The example more specifically (non-exhaustive list) of computer-readable medium comprises following: the electrical connection section (electronic installation) with one or more wiring, portable computer diskette box (magnetic device), random access memory (RAM) (electronic installation), read-only memory (ROM) (electronic installation), Erasable Programmable Read Only Memory EPROM (EPROM or flash memory) (electronic installation), optical fiber (electro-optical device), and portable optic disk read-only memory (CDROM) (Optical devices).In addition, computer-readable medium can be even paper or other suitable media that can print described program thereon, because can such as by carrying out optical scanner to paper or other media, then carry out editing, decipher or carry out process with other suitable method if desired and electronically obtain described program, be then stored in computer storage.
Above-mentioned explanatory note and accompanying drawing show various different feature of the present invention.Should be appreciated that those of ordinary skill in the art describe and each step illustrative and process in the accompanying drawings above can preparing suitable computer code to realize.It is also understood that above-described various terminal, computer, server, network etc. can be any types, and described computer code can be prepared according to disclosure and realize the present invention to utilize described device.
Particular implementation of the present invention is disclosed at this.Those of ordinary skill in the art will readily appreciate that, the present invention has other application in other circumstances.In fact, also there is many execution modes and realization.Claims are absolutely not in order to limit the scope of the present invention to above-mentioned embodiment.In addition, arbitrarily for " for ... device " to quote be all the explaination that device in order to describe key element and claim adds function, and specifically do not use arbitrarily " for ... device " the key element quoted do not wish to be understood to that device adds the element of function, even if this claim includes the word of " device ".
Although illustrate and describe the present invention for certain preferred embodiments or multiple execution mode, obviously, those skilled in the art are reading and can expect the modification that is equal to and modified example when understanding specification and accompanying drawing.Especially for the various functions performed by above-mentioned key element (parts, assembly, device, form), unless otherwise noted, wish that (namely the term (comprising quoting of " device ") for describing these key elements corresponds to any key element of the concrete function performing described key element, function equivalent), even if this key element is structurally different from the open structure performing this function in illustrated illustrative embodiments of the present invention or multiple execution mode.In addition, although below in several illustrative execution mode only one or more describes specific features of the present invention, as required and from the viewpoint of to any given or embody rule is favourable, but this feature can be combined with one or more other features of other execution modes.
Claims (8)
1. a Turbo decoder, described Turbo decoder comprises the first sub-decoder and the second sub-decoder, the first prior information that described first sub-decoder provides according to the first perfect information in current iteration, the first channel information received and described second sub-decoder carries out iterative decoding, generates the first external information and is supplied to described second sub-decoder as the second prior information; Described second sub-decoder carries out iterative decoding according to the second perfect information in current iteration, the second channel information received and described second prior information, generates the second external information and is supplied to described first sub-decoder as the first prior information,
Wherein:
The external information that each sub-decoder exports comprises the prior information of another sub-decoder of part input;
Wherein:
The first external information that described first sub-decoder exports is the difference of the product of described first perfect information and described first channel information and described first prior information and the first multiplicative coefficient factor;
The second external information that described second sub-decoder exports is the difference of the product of described second perfect information and described second channel information and described second prior information and the second multiplicative coefficient factor;
Wherein, described first multiplicative coefficient factor and described second multiplicative coefficient factor be respectively be not equal to 1 from 0 to 1 arbitrary value.
2. Turbo decoder according to claim 1, wherein, described first multiplicative coefficient factor is identical or different with described second multiplicative coefficient factor.
3. Turbo decoder according to claim 1, wherein, described first multiplicative coefficient factor is identical value or different values when the different iterations of described Turbo decoder.
4. Turbo decoder according to claim 1, wherein, described second multiplicative coefficient factor is identical value or different values when the different iterations of described Turbo decoder.
5. a Turbo interpretation method, wherein, described method comprises:
The first prior information that first sub-decoder provides according to the first perfect information in current iteration, the first channel information received and the second sub-decoder carries out iterative decoding, generates the first external information and is supplied to described second sub-decoder as the second prior information;
Described second sub-decoder carries out iterative decoding according to the second perfect information in current iteration, the second channel information received and described second prior information, generates the second external information and is supplied to described first sub-decoder as the first prior information;
Wherein, the external information that each sub-decoder exports comprises the prior information of another sub-decoder of part input;
Wherein:
The first external information that described first sub-decoder exports is the difference of the product of described first perfect information and described first channel information and described first prior information and the first multiplicative coefficient factor;
The second external information that described second sub-decoder exports is the difference of the product of described second perfect information and described second channel information and described second prior information and the second multiplicative coefficient factor;
Wherein, described first multiplicative coefficient factor and described second multiplicative coefficient factor be respectively be not equal to 1 from 0 to 1 arbitrary value.
6. Turbo interpretation method according to claim 5, wherein, described first multiplicative coefficient factor is identical or different with described second multiplicative coefficient factor.
7. Turbo interpretation method according to claim 5, wherein, described first multiplicative coefficient factor is identical value or different values when the different iterations of described Turbo decoder.
8. Turbo interpretation method according to claim 5, wherein, described second multiplicative coefficient factor is identical value or different values when the different iterations of described Turbo decoder.
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| CN1419743A (en) * | 2000-05-05 | 2003-05-21 | 诺基亚公司 | Scaled-feedback turbo decoder |
| CN101479945A (en) * | 2006-06-27 | 2009-07-08 | Nxp股份有限公司 | Turbo decoder with extrinsic information scaling modules |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN1419743A (en) * | 2000-05-05 | 2003-05-21 | 诺基亚公司 | Scaled-feedback turbo decoder |
| CN101479945A (en) * | 2006-06-27 | 2009-07-08 | Nxp股份有限公司 | Turbo decoder with extrinsic information scaling modules |
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| Title |
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| A PRACTICAL ALGORITHM FOR TURBO-DECODING ENHANCEMENT;Dejan Spasov等;《Proceedings of the 2004 International Symposium on Circuits and Systems,2004》;20040526;第4卷;第623页左栏第12-20行、第28-30行，图1 * |
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