CN1568575A - Multi-dimensional coding on quasi-close-packet lattices - Google Patents

Abstract

The present invention relates to a method and system for multi-dimensionally coding and/or decoding an information to/from a lattice structure representing bit positions of said coded information in at least two dimensions. Encoding and/or decoding is performed by using a close-packed lattice structure, preferably a quasi-hexagonal lattice structure. In particular, at least partial quasi-hexagonal clusters consisting of one central bit and a plurality of nearest neighboring bits can be defined, and a code constraint can be applied such that for each of said at least partial quasi-hexagonal clusters a predetermined minimum number of said nearest neighboring bits are of the same bit state as said central bit. Thereby, intersymbol interferences can be minimized at a high code efficiency. Furthermore, another code constraint can be applied such that for each of said at least partial quasi-hexagonal clusters a predetermined minimum number of said nearest neighboring bits are of the opposite bit state as said central bit. This constraint provides an advantageous high pass characteristic to avoid large areas of channel bits of the same type.

Description

Multidimensional coding on the accurate closs packing grid

The present invention relates to the method and system that carries out multidimensional coding.

Because at the ubiquity of the computer that connects by the internet, the information age has produced the blast of user's available information all for it.The reduction of storage data cost, and the increase of the memory capacity that takes up room of same midget plant has become the enabler of this revolution.In satisfied existing storage demand, memory technology must be improved so that synchronous with the requirement maintenance of quick growth.

But magnetic or conventional light data storage technology be near its physical restriction, surpasses this and limit each and just may too little or too be difficult to not storing the position separately, and each is separately that to be stored in recording medium with different magnetic or optical change lip-deep here.Volume by medium-be not only in its surface-stored information provides another kind of interesting high-capacity storage way.

Holographic data storage is a kind of way of solid, though this method is just being expected decades ago, but along with the appearance of the cheap technology that enables, the important achievement that studies for a long period of time and make great efforts to obtain, and the development of hologram recording material etc. and obtained nearest progress towards practicality.In holographic data storage, the information of whole page or leaf side by side is deposited in the very thick photosensitive optical material with optical interference pattern.By being intersected, two relevant microbeams realize this point in storage medium.First is called the information that will store that includes of subject beam; Second, be called with reference to bundle, be designed to simple Shu Yizai and for example bear simple bundle with the plane wave front collimation.Synthetic optical interference pattern has caused chemistry and/or the physical change in the photosensitive medium.The duplicate of interference pattern is as the absorptivity of photosensitive medium, refractive index, or the variation in the thickness is stored.When the interference grating that stores during with the irradiation of one of once used two light waves in the recording process, the diffraction that some incident lights are subjected to storing grid makes that another light wave is set up.Store grating with the reference light wave irradiation and rebuild the target light wave, vice versa.

As another kind of three-dimensional or three-dimensional way, the notion of multilayer fluorescence card/dish (FMD/C) is a kind of fabulous breakthrough, and it has solved the degradation of signals problem relevant with the current reflective optical disc technology of DVD (digital video disk) with CD (CD).With CD or DVD the time, the data on the FMD layer are encoded on substrate with a series of geometrical features or volume markings.The capacity of each layer is 4.7 GB (as under the situation of DVD).When using the FMD/C technology, each stores layer and all is coated with transparent fluorescent material, rather than the metallic reflector of CD or DVD.When laser beam is got to mark on the layer, just launch fluorescence.This light of being launched, its wavelength different with the wavelength of incident laser light (shifting to the red end of spectrum slightly) is incoherent in nature, this is opposite with reflection coherent light in the current white light devices.The light of being launched is not subjected to the influence of data markers, and therefore laterally adjoining course is interference-free.In the read-out system of driver, laser beam is filtered.So only detect the fluorescent light of information-carrying.This has just reduced the influence of stray laser and interference.

In above-mentioned and other data-storage system (as the reflective optical disc technology of routine), the purpose of coding and signal processing is, when obtaining, BER (bit error rate) is reduced to enough low level such as important quality factors such as high density and high data rates.This is by the suffered stress of the physical component that makes system channel zero defect point head and shoulders above, and introduces the level that BER reduced to can be handled by error correction (ECC) decoding technique and and then be reduced to extremely low-level that the user can accept (BLER (block error rate) is generally 10 ^-16) modulating-coding and signal processing scheme finish.

Figure 14 shows the typical case's coding and the Signal Processing Element of data-storage system.Circulation from input DI to output DO can comprise interlacing scan 10, error correction code (ECC) and modulating- coding 20,30, signal pre-treatment 40, the storage on the recording medium 50, signal post-processing 60, binary detection 70, and the decoding 80,90 of interlacing scan ECC.ECC encoder 20 adds that on data redundancy so that protection to be provided, makes it not be subjected to the influence of various noise sources.Then the ECC coded data is sent to modulating coder 30, it makes data adapting in channel, and promptly it becomes the unlikely form that is subjected to the channel error error and is easier to detect at the channel output to data processing.Data with modulation are input to tape deck then, for example spatial light modulator etc. and store recording medium 50 into.In retrieval one side, this reading device (for example, charge-coupled device (CCD)) returns the numerical value of pseudo-analog data, and this numerical value must conversion be got back to numerical data (1 of common every pixel).The first step of this process is a post-processing step 60, is called equilibrium, and it is attempted to eliminate and produces in the recording process, still in the distortion of pseudonorm near-field.Then, convert the array of binary digital data to by detector 70 for the array of analogue data.Array of digital data at first is sent to code modulation decoder 80 again, and it carries out the operation opposite with modulating-coding, then is resent to ECC decoder 90.

Between pixel or intersymbol interference (ISI) be the intensity of a concrete pixel near a kind of phenomenon of polluting of the data of pixel.Physically, this phenomenon is that the frequency band limits owing to (light) channel produces, and it comes from optical diffraction, or time dependent aberration in the lens combination, defocuses as disc tilt and laser beam.The way that overcomes this interference is a high spatial frequency of forbidding some pattern by modulating-coding.The code of forbidding a certain pattern high spatial frequency (or more generally, in the set of 0 and 1 fast-changing these patterns of pixel) is called the low pass code, and it can be used for the modulating-coding/decoding of modulating coder 30 and decoder 80.This modulation code forces the information of writing with two dimension district (as the permission page with Hologram Storage) to have limited high spatial frequency content.

2 d code with low-frequency filter characteristics is interesting as being used for the new cubic light record of above-mentioned pattern scheme.But, two dimension (2-D) coding also may be a key issue concerning new route, these new routes are relatively near the optical recording of more conventional pattern, for example the coherent diffraction of service recorder two-dimensional model (mark) in card or CD two dimension district, based on the optical recording technology of reflective optical disc technology.In the prior art, considered on square net, to encode.Particularly, at IEEE journal in 1998, W.Weeks on information theory the 44th volume the 3rd phase 1193-1203 page or leaf, in " capacity of some pattern code and coding gain " literary composition of R.E.Blakut after deliberation the capacity of pattern code.In the literary composition, the square shaped grid considered the constraint of various chessboard in case channels bits read with testing process in obtain low-pass characteristic, thereby reduce the influence of intersymbol interference (ISI).

But, for two-dimensional encoded, in the situation of the one-dimensional coding that coexists, different coding bounds and coding geometrical condition, it is different from the coding on the square net that exists in the prior art, and they may produce more effective storage, thereby can obtain higher storage density.So, in the multidimensional storage is used, also need to improve constantly code efficiency.

In addition, go back presence bit and detect problem in the 2-D coding, this generation to coherent signal is very typical.Come arrogant convex region, promptly the reflected signal in zero level mirror image district with come arrogant recessed district, the reflected signal that promptly is lower than zero level mirror image district (in λ/4 degree of depth, λ represents the radiation wavelength that is used to read) here is duplicate.Thereby, can not be separately in the detection two binary system horizontal zones.In traditional 1-D coding, this problem does not occur, because the diameter of point is always greater than the radial width of recessed district (or mark), and diffraction is also always occurring in the radial direction.Therefore, folded light beam is owing to the diffraction outside centre bore discharges some intensity.In contrast, the problems referred to above also can occur in the 2-D coding, because just do not have diffraction the laser of the focusing on inciding big recessed district or big convex region or other radiants at all.

Therefore, the purpose of this invention is to provide a kind of improved two dimension or multidimensional coding scheme, utilize this scheme can reduce and/or have the error rate that the Da Qu of same (bipolarity) bit-type produces because of intersymbol interference.

By by defined method in the claim 1, by by defined system in the claim 22, and by reaching this purpose by defined record carrier in the claim 32.

According to the present invention, use accurate hexagon network to be used for multidimensional coding.This accurate hexagon grid is for example compared with square net, and its benefit comes from the ingenious combination of code efficiency, also has the influence of time nearest ortho position to intersymbol interference.Use accurate hexagon grid to mean that it may arrange by hexagon ideally, but may have little mesh distortion apart from desirable grid.For example, the angle between each standard shaft of unit cell may strictly not equal 60 degree.The intensity sketch map that more likes used scan laser point between reading duration is arranged in the position that accurate hexagon grid produces.

The hexagon network of high bulk density provides higher code efficiency.In addition, about to having the constraint with the predetermined number of time peri position of central authorities positions identical bits attitude, it is to be used to provide the interference that reduces code frequency spectrum low-pass characteristic, and about to having another or the additional constraint with the predetermined number of time peri position of central authorities positions opposite position attitude, its be used to provide code frequency spectrum high pass characteristic to avoid having the Da Qu of same position attitude.Thereby two kinds of constraints have caused reducing of bit error rate.

In addition, can use about having the another kind of code constraints with time peri position of central authorities positions identical bits attitude, according to this constraint, the azimuth contiguous bits of predetermined number is configured to have identical position attitude with central authorities.Therefore, the label size that can realize minimum is write process with simplification.For example, using laser beam recorder (LBR) to be used in read-only (ROM) master record in using, and laser beam is not when writing the enough resolution of less label size, this may be favourable.

In addition, also the visual field shape of reading the thing lens is modified as the readout that equilateral regular hexagon also will improve these mediums from general rectangle.

Other further favourable expansions have all been done qualification in relevant claim.

Below, will give more detailed description to the preferred embodiments of the invention with reference to accompanying drawing, in the accompanying drawing:

Figure 1A and 1B represent the simple accumulation graph of square net structure and hexagon network respectively;

Fig. 2 A to 2C represents the hexagon according to position, preferred embodiment position respectively, and big capacity is trooped, and the trooping of bottom and top boundary;

Fig. 3 illustrates the sketch of expression based on the two-dimensional coding scheme of band;

Fig. 4 illustrates according to preferred embodiment, two-dimensional encoded possible transition between states situation;

Fig. 5 A and 5B illustrate according to first preferred embodiment and (use N _Nn=1), in the disable mode of the big capacity region of band;

Fig. 6 A and 6B illustrate according to first preferred embodiment and (use N _Nn=1), in the disable mode of lace battery limit (BL);

Fig. 7 illustrates according to first preferred embodiment, represents the curve chart of the first type hexagon grid coding maximum size and lower limit;

Fig. 8 illustrates according to first preferred embodiment and represents, the curve chart of the second type hexagon grid coding maximum size and lower limit;

Fig. 9 illustrates according to first preferred embodiment and represents, the curve chart of the 3rd type hexagon grid coding maximum size and lower limit;

Figure 10 A and 10B illustrate respectively according to first preferred embodiment, are illustrated under first and second coding bounds, the curve chart of height of sighting line and user position dimensional characteristic in square and hexagon grid coding;

Figure 11 illustrates according to first preferred embodiment, is illustrated in the height of sighting line of hexagon grid coding under the different code constraint and the curve chart of user position dimensional characteristic;

Figure 12 A and 12B illustrate respectively according to second preferred embodiment, the big disable mode that capacity is trooped and troop in the border;

Figure 13 illustrates according to second preferred embodiment, the curve chart of capacity lower limit during the constraint of expression difference;

Figure 14 illustrates the coding of a routine data storage system and the sketch of treatment element; And

Figure 15 A and 15B illustrate the visual field shape to the pick-up unit of rectangle and equilateral hexagon situation respectively.

Now, the preferred embodiments of the invention are illustrated according to based on two-dimensional coding scheme band, that use accurate hexagon grid.

As everybody knows, the packing ratio that hexagonal lattice provides in crystallography is the highest.For example, its packing ratio is 1/cos (30 °)=1.155, is better than the packing ratio that has same square net apart from a between the arest neighbors lattice point.The latter can be determined by the two-dimentional impulse response scope of the two dimensional channel that is used for writing record or medium 50 apart from a, for example by hologram optical recording or fluorescence optical recording, or is determined by the conventional reflection type optical record with two-dimentional coherent diffraction.

Figure 1A and 1B express the package assembly of square net and hexagon grid respectively.Concerning each lattice point, square and hexagon grid needs size to be a respectively ²And a ²The two dimension district of cos (30 °), it is respectively shown in Figure 1A and 1B.The number at ortho position is b to the hexagon grid recently, and the square shaped grid is 4.Therefore, at first glance, use the hexagon grid as if not have benefit, because it is bigger to produce the number at the nearest ortho position of disturbing between two-dimensional symensional symbol.But the benefit of hexagon grid is for example compared with square net, and it comes from code efficiency and time nearest ortho position taking all factors into consideration the influence of intersymbol interference.

About the further ortho position of bigger distance, the hexagon grid is in distance

(when the arest neighbors distance of positions when being 1) ortho positions are recently arranged six times, in distance 2 ortho positions are recently being arranged six times times.The square shaped grid is in distance

Obtain ortho position recently four times, obtain ortho position recently four times times in distance 2.

Under two-dimensional encoded situation, be arranged in full-scale hexagon in the big capacity hexagon grid and troop position, seven positions or address are arranged, and a central authorities position and six arest neighbors address.For simplicity, when the accurate hexagon on relating to accurate hexagon grid is trooped, also use term " hexagon is trooped ".But, on the border that is used for based on the two-dimensional space band of band coding, appearance but be the part size or the trooping of border.

Fig. 2 A to 2C expresses the position, position that big capacity troops on the hexagon grid respectively and troops, and bottom boundaries is trooped and top boundary is trooped.Be in the locational channel bit X in position _iNumbering as follows.

In big capacity is trooped, the numbering i=0 of central authorities position, and six ortho positions the most contiguous are i=1 by its azimuthal order number consecutively ... 6.Strip edge not exclusively or the border of portion size troop, seven positions or a position, position of trooping with big capacity are compared, it has only five positions or position, position to form.Central authorities positions also is numbering i=0, and the nearest ortho position number consecutively of adjacency is i=1 on four azimuths ... 4.

Hereinafter, defined the new normal codes constraint that is used for the hexagon network, it relates to the troop arest neighbors position of middle position of complete or portion size hexagon.

According to first embodiment, these constraints have a double purpose.The first, make these constraints be suitable for the low-pass characteristic of code frequency spectrum, the second, make it be suitable for realizing reducing the minimum mark size that write-channel requires.Particularly, by two parameters these constraints are described:

(i) has nearest ortho position (N with the same types or the attitude of the position that is in central grid position _Nn) minimal amount; And

The (ii) nearest ortho position (N of adjacency on the azimuth _Ac) minimal amount, 1≤N wherein _Ac≤ N _Nn

Parameter N _NnThe low-pass characteristic that provides helps the influence that reduces to disturb between two-dimensional symensional symbol.This point is easy to see below.Each has six nearest ortho positions.Suppose that two-dimentional impulse response function (IRF) is f0 at the numerical value of middle position, the numerical value in the arest neighbors position is f1.So, if there is N just with same pattern _Nn(it is a minimal amount) recently during the ortho position, just obtained the waveform minimum value at given grid position.This minimum value is provided by following formula:

f0-(6-2N _nn)f1 (1)

Consider the minimum mark size restrictions of write-channel, operation parameter N _AcFor example, constraint N _Nn=2, N _Ac=1 will allow not two nearest ortho positions on azimuth in succession.Thereby, have the 2T mark (on different azimuths, and having a channels bits shared) of one dimension, and to write be very difficult.But, work as N _Nn=2, N _Ac=2 o'clock, the nearest ortho position of adjacency on two same pattern azimuths should be arranged at least, this just means that one dimension 2T mark forbids.And minimum mark is the triangle morpheme with same pattern in this case.Concerning two-dimentional write-channel, with N _Ac=1 situation is compared, and this may be favourable, but, because constraint is stricter under latter event, must face corresponding rate loss problem.

Above-mentioned constraint can be used as the big capacity-constrained that full-scale big capacity troops and is defined.Two conditions of capacity-constrained provide as follows like this, greatly:

$|6x_0+{\mathrm{\Σ}}_{i=1}^6{x}_i|\≥2N_{\mathrm{nn}}---\left(2\right)$

$\∃J\∈\{\mathrm{0,1},...5\}:|x_0+{\mathrm{\Σ}}_{i=1}^{N_{\mathrm{ac}}}{x}_{i+J}|=N_{\mathrm{ac}}+1---\left(3\right)$

Notice that the subscript of 6 positions is all the time between numerical value 1 and 6 on the accurate hexagon cluster boundaries; When subscript i+J was outside this scope in relational expression (3), i+J just was reduced to 1/6 so, so it is within desired 1 to 6 scope.Similarly, constraint can be used as the code constraints of trooping on the portion size border and is defined above.So two conditions of big capacity-constrained provide as follows:

$|6x_0+{\mathrm{\Σ}}_{i=1}^4{x}_i|\≥2(N_{\mathrm{nn}}+1)---\left(4\right)$

$\∃J\∈\{\mathrm{0,1},...4-N_{\mathrm{ac}}\}:|x_0+{\mathrm{\Σ}}_{i=1}^{N_{\mathrm{ac}}}{x}_{i+J}|=N_{\mathrm{ac}}+1---\left(5\right)$

Thereby trooping constrains in band boundaries and also is met, although actual bit is in adjacent encoding strip thereof.Boundary constraint can make band be stacked on mutually on each other the top and without any the situation of violating constraint, because these constraints are met borderline not exclusively trooping.

Fig. 3 illustrates the sketch of expression based on the two-dimensional coding scheme of band.The two dimension district is split up into band.Band aligns in the horizontal direction, and is N by quantity _rMesh row form.Be coded on the horizontal direction and carry out, and in fact become one-dimensional coding.Code word is not striden the border of super band.Code word can be based on by N _rIndividual row and N _cThe two dimension district that individual row are formed.To make the connection of in the vertical direction band not violate above-mentioned relevant constraint of crossing over band boundaries when constituting band.

In order to derive capacity and in order to design valid code, must to derive the finite state machine (FSM) as the basis, it drives the generation of two-dimensional sequence.Because all constraints that propose at present all only relate to peri position, consider based on two states that attach to and cover all row of band on the hexagon grid just enough.The number of this state is exactly 2 ^2NrBy the transition from the given state to the NextState, just exported the channels bits of a permutation.According to definition, last row of first state are identical with first row of follow-up state.

Fig. 4 expresses N _rState during=b situation " i " (409b gets 1), and a follow-up state " j " that may or allow.Can infer that according to Fig. 4 last row of state " i " match with first row of state " j ".In addition, the constraint of expression all is met in equation (2) to (4).

In capacity derivation and two dimensional channel or modulation code design, more vital is connection matrix D, and it is that a size is 2 ^2Nr* 2 ^2NrSquare matrix, N _StBe the number of possible state, it is with N _St≤ 2 ^2NrBe boundary.At state " i " with corresponding state " j " during as its follow-up state, the matrix element D of connection matrix D _IjBe set to " 1 ".Every other matrix element corresponding to the follow-up state of non-permission all places " 0 ".Like this, the transition from state " i " to state " j " allows, if following condition is met:

1) last row of state " i " are identical with first row of state " j ";

2) transition between states can not cause the constraint fault (big capacity-constrained) that big capacity is trooped.These constraints are the unique constraints that will consider when the derivation maximum size;

3) band does not connect and can cause that constraint breaks rules in band boundaries.Therefore, application boundary constraint makes it possible to carry out piling up of band and irrelevant with the content of adjacent ribbons.These constraints need for the lower limit of derivation capacity.

Fig. 5 A and 5B express N _Nn=1 o'clock, two representative instances of forbidding or non-permission pattern in the big capacity region of band.In this case, when when state " i " transits to state " j ", just having violated N _Nn=1 constraint.The position is not minded in parameter " X " expression, and it can place bit value arbitrarily.Coding staff is to being correct.

Fig. 6 A and 6B express N _Nn=1 o'clock, two representative instances of forbidding or non-permission pattern in the lace battery limit (BL).In this case, when when state " i " transits to state " j ", concerning opposite position, also violated N _Nn=1 constraint.

Fig. 7 to 9 expresses in bar bandwidth difference, when promptly line number does not wait, and the various various computing results of code capacity.The upper limit is limited by the capacity that has only big capacity-constrained, and this just means that band can not freely connect.Lower limit limits big capacity and boundary constraint, and promptly band can freely connect, but this will need extra extra order, and it has reduced available capacity.

At N shown in Figure 7 _Nn=1, N _AcSingle file (the N of=1 situation _r=1) under the situation, the situation of lower limit is equivalent to one dimension run-length restriction (RLL) coding of d=1 run length constraint.The minimum run length of d=1 rll encoder (2T) can only obtain in the horizontal direction.Move to two row (N from delegation _r=2) time the remarkable increase of (lower limit) capacity be because, minimum run length constraint (2T) can also become with the band horizontal axis on the incline direction of 60 ° and hexagonal angle degree to obtain now.

Fig. 8 expresses at N _Nn=2, N _AcThe relation of capacity and strip width characteristic under=1 the situation, Fig. 1 expresses at N _Nn=2, N _AcThe relation of capacity and strip width characteristic under=2 situations.In both cases, the minimal amount at the nearest ortho position of same pattern or state equals 2.At N _AcUnder=1 situation, two nearest ortho positions of same pattern not necessarily are in succession the azimuth.At N _AcUnder=2 situations, two nearest ortho positions of same pattern are in succession the azimuth.Can infer that from Fig. 8 and 9 higher constraint has caused the reduction of upper and lower bound.

Figure 10 A and 10B express the curve chart that goes out according to numerical computations, and it is N corresponding to Fig. 8 and 9 pairs of line numbers that these curves illustrate capacity _r=8, prescribe a time limit the relation of height of sighting line and user's position dimensional characteristic based on the following of band coding situation.Dotted line is used for the hexagon grid, realizes being used for conventional square net.It is the Gaussian function (normalized on two dimensions) of two dimension that impulse response function is assumed to.As parameter, the center set point value of two-dimentional IRF is expressed as the constant horizontal line at top in Figure 10 A and 10B.Should be pointed out that actual range of interest comprises positive height of sighting line.Therefore, two dimensional channel is actually dead letter road to the height (being similar to the cut-off frequency of one dimension channel) beyond zero sight line.Thereby, as desired, can improve height of sighting line by two-dimensional encoded on the hexagon grid.By the nearest ortho position that connects on the same state azimuth is added that constraint can be further improved.

Figure 11 shows curve chart, and it is expressed only to hexagon grid coding and N _NnThe relation of=0,1,2 o'clock height of sighting line and user's position dimensional characteristic.By the resulting coding increment of height of sighting line is the obvious direction that increases this constraint.Realize this point by the low-pass characteristic that improves the two dimensional channel code.

Write-channel limit the size that its characteristics are the minimum two-dimensional marker that will write.Obviously, in this respect, constraint N _Nn=and N _AcThe=2nd, the most interesting.The shape of minimum mark is different to the hexagon grid coding with the square net coding.In both cases, minimum shape is the triangle that 3 channels bits are arranged.In the previous case, this is shaped as the equilateral triangle of equilateral isogonism, in the later case, and owing to its shape is with half square triangle that obtains, so be not too favourable from this shape in the aspect of writing.The relative size of the minimum mark of same constraint is depended on ratio to each self-capacity of hexagon grid and square net coding.Work as N _Nn=2 and N _Ac=2 o'clock, this ratio equaled 1.60, and this is favourable to the hexagon grid.

In traditional one dimension rll encoder, the spot diameter of the radiation beam of read apparatus is always greater than the radial width in optical recording or the recessed district of medium.Therefore, obtaining diffraction in the radial direction, this has just caused in reflecting bundle intensity and can detectedly lose.But, according in first preferred embodiment above-mentioned two-dimensional encoded, the big recessed district that is made up of some ortho positions may appear.Thereby, in big recessed district, there is not diffraction to take place, also just can not detect loss of strength.

According to second preferred embodiment, by two dimensional channel or modulation code additional or other constraint avoided the big regional channel position of same pattern.Can realize this constraint by a single parameter that produces the 2 d code high pass characteristic.

Particularly, use parameter M _NnIntroduce high pass constraint, it expresses the minimal amount at nearest ortho position, and this nearest ortho position is compared with the troop channels bits bit value of middle position of hexagon, and it must have opposite bit-type or position attitude.

Troop for big capacity, can be above-mentioned high pass constrained parameters M _NnWith low pass constrained parameters N _NnIn the following single-relation formula that provides, combine:

$2N_{\mathrm{nn}}\≤|6x_0+{\mathrm{\Σ}}_{j=1}^6{x}_j|\≥12-2M_{\mathrm{nn}}---\left(6\right)$

Trooped in the border two constrained parameters M _NnAnd N _NnProduce two relational expressions given below:

$2N_{\mathrm{nn}}\≤|4x_0+{\mathrm{\Σ}}_{j=1}^4{x}_j|---\left(7\right)$

$|8x_0+{\mathrm{\Σ}}_{j=1}^4{x}_j|\≤12-2M_{\mathrm{nn}}---\left(8\right)$

Figure 12 A and 12B express respectively that one of them should have (M under the situation of opposite pattern or state at least at nearest ortho position _Nn=1), big capacity is trooped and the example of the disable mode that bottom boundaries is trooped.In the position of central grid position, its value is x (i.e. " 0 " or " 1 "), and the position of all peripheries all has same numerical value.Thereby top high pass constraint is not met.

As for code capacity, owing to extra high pass constraint is had in the face of additional capacitance loss.To constraint N _Nn=1, M _Nn=1 situation, this capacitance loss are concerning the band with triplex row, and the code with map 8-9 is impossible, and this map is to N _Nn=1, M _Nn=0 situation is possible.

Concerning the few two-dimensional ribbon there of every band line number, high pass constrains in and is applied to when big capacity is trooped and troop in the border, consequently quite expends capacity.Therefore, the constraint combination of trooping different with the border cluster selection to big capacity may be favourable.On the one hand, high pass constraint can only be used for big capacity troops, and on the other hand, the high pass constraint can be used for that big capacity is trooped and or top or bottom boundary troop.

The constraint N that graphical representation shown in Figure 13 is trooped to big capacity and border _Nn=1, and to different situations M _Nn=1 o'clock, the relation of capacity and strip width characteristic, these different situations promptly are, do not troop to any, only big capacity is trooped, big capacity is trooped and only trooped in top or bottom boundary, and big capacity is trooped and the border of two kinds of patterns troop (order that occurs from the top to bottom by curve in the curve chart).Can infer that from Figure 13 the application that increases the high pass constraint has reduced code capacity.

With N _NnAnd M _NnThe actual code structure that constraint combines has caused the increase of complexity in the Code Design.As actual code, at constraint N to big capacity and two borders _Nn=1, to the constraint M on big capacity and any border _Nn, can generate code at=1 o'clock with 8-9 map to band based on triplex row.In addition, at constraint N to a large amount of appearances and two borders _Nn=1, only to big capacity not to the constraint M on any border _Nn, can generate code at=1 o'clock with 11-12 map to band based on triplex row.

In the superincumbent preferred embodiment.For position state or pattern, for example same constraint has been considered in mark and non-marked or recessed district and convex region.But, to decide according to the characteristic of write-channel, the two kinds of patterns or the state of contraposition apply asymmetric constraint, and promptly different constraints may be favourable.Also have; to not being in single band boundaries but the situation of trooping in the border on the border, 20 district that is the boundary with a certain boundary belt; having less constraint coding on than recessed position in the position, convex region may be effectively, in any case because the protection zone all comprises bigger convex region.In addition, to the selected horizontal direction of two-dimensional ribbon there can be [100] direction or [110] direction of hexagon grid.

When sorted in the territory, these territories are for being loaded with for example zone on the recording medium of the recessed district at least two dimensions (20 record) or mark of stored information, show above, use the accurate closs packing grid of picture in the hexagon grid can access possible highest region territory storage density.In addition, this can also be used to improving reading of this record data, especially read about the record data of pick-up unit arrangement, pick-up unit can be to read optical system, it comprises the object lens that are used to make the imaging on image plane of institute's deposit data, wherein arranges detector means that sense data is detected in image plane.Because detector means has only been utilized a part of circular image plane, and the circular field of view VF of object lens is not effectively utilized.Therefore, when Figure 15 A expresses and the territory sorted in square net according to rectangular coordinate system, be used for the arrangement of reading object lens that 2D reads, especially limit the arrangement situation of the circular field of view VF of image plane.Within the VF of the visual field, show square visual field VF with detector means _SqCorresponding to squared region, the square visual field VF of detector means _SqDetermine by the detector element in the image plane.

As can be drawn from Figure 15, except area packing density is low, the square visual field VF of detector means _SqOnly utilize 2/ π of object lens circular field of view VF, be about 64%.Yet if data field D is arranged in the accurate hexagon network of introducing here, the density of data storage will increase, but because the square visual field VF of detector means _SqAnd the mismatch between the accurate hexagon grid of data field, seamless reading will be impossible.This has just caused reading difficulty and read-out speed is reduced.

Therefore, in Figure 15 B, introduced detector means hexagon visual field VF in object lens circular field of view VF _Hex, it is an equilateral hexagon in the present embodiment.This has just obtained the higher density of data storage, compares with square net, increased about 15%, in addition because the higher higher read-out speed of having got back of utilization ratio of object lens visual field VF.Especially, can use the 30 °/π of 3cos of visual field VF, about 83%.This is to be bordering on 30% growth, and with two effects, promptly the accurate hexagon graticule mesh of data field is arranged and detector means hexagon visual field VF _HexEffect add together, total raising is near 50%.In addition, also provide and between reading duration, obtained these equilateral hexagon visuals field VF _HexThe possibility of seamless combination.

Should be noted that only to read out in along by accurate hexagon network they [100], when three directions one of in may directions that [010] or [110] grid direction limited are carried out, could between reading duration, obtain maximum data rate.In these cases, (pattern is (100 when a grid plan of only being filled by " recessed district "-territory (or convex region-position), (010), or (110) with only by a grid plan of " convex region "-territory (or convex region-position) filling when staggered, just provided high spatial frequency.Certainly, this high spatial frequency must be lower than the cut-off frequency that pick-up unit is read optical system.

The most tangible way of carrying out the reproduction of 2D data structure in the detector means visual field is that the appropriate area on the recording medium that contains data field is carried out coherent illumination.By selection, these zones can be carried out continuous scanning or be scanned in mode step by step.Under first kind of situation, the data field in the disk image plane moves by the read detector array, and like this, the data in a concrete territory must be collected by different detector-segments in the different time intervals, so that obtain enough luminous energy from this concrete territory.Under second kind of situation, data field is fixed at certain hour to detector array, at this moment between in data-signal in the visual field can distinguish addition or sum total.Read after the data field in a certain concrete visual field, pick-up unit must move to the adjacent visual field, or the like.

Yet except fluorescence was read, coherent illumination had cut-off frequency, and its cut-off frequency is half of incoherent irradiation cut-off frequency.The array that the each point that utilizes incoherent irradiation can produce the grating by the pick-up unit illuminated portion is formed scans along the edge of hexgonal structure.Should be pointed out that adjacent point may be not overlapping.Therefore, track space will be more much smaller than the distance in succession.In order to read adjacent track at one time, these points will tilt to place with respect to track.Point of irradiation within the pick-up unit object lens visual field can distribute in a different manner.But maximal density obtains with the distribution on the accurate hexagon grid.

Note, above-mentioned hexgonal structure based on multidimensional coding can be used on any data-storage system, such as two-dimensional optical storage, or require the accumulator system of any other kind of high pass and/or low pass code characteristic, in two-dimensional optical storage, used hologram optical recording, fluorescence optical recording, the optical recording of page type, conventional but with two-dimensional encoded reflection type optical memory, or the like.Particularly, the present invention also is intended to relate to the record carrier that is used in these data storage systems, and for example CD uses above-mentioned multidimensional coding scheme to write or stored information on these record carriers.In addition, described encoding scheme can be applicable to any multidimensional coding of unnecessary two dimensions.For example, under three-dimensional dimension, can utilize accurate closely packed network.Under three-dimensional situation, this closely packed network can be a face-centered cubic lattice, is also referred to as the FCC grid, or it can be the close heap lattice of hexagonal, is also referred to as the HCP grid.Therefore, the present invention is any modification that will relate within the claims scope.

Claims (26)

1. With information multidimensional ground coding and/or decode to/from the method for network, this network has been represented the position, position of described coded message at least on two dimensions, described method comprises the step of using accurate closs packing network to carry out multidimensional coding and/or decoding.
2. 2. according to the process of claim 1 wherein that described accurate closs packing network is based on accurate hexagon grid.
3. 3. according to the method for claim 2, the step that wherein said method further comprises is:

   A) limit by trooping to the accurate hexagon of small part that a central authorities position and a plurality of arest neighbors position are formed; And

   B) use the first code constraint, make concerning each described troop to the accurate hexagon of small part, the nearest ortho position of predetermined minimal amount has the identical state in position with central authorities.
4. 4. according to the method for claim 3, the preset minimum number at wherein said nearest ortho position is less than or equal to three.
5. 5. according to the method for claim 2, its step that also comprises is:

   A) limit by trooping to the accurate hexagon of small part that a central authorities position and a plurality of arest neighbors position are formed; And

   B) use the first code constraint, make concerning each described troop to the accurate hexagon of small part, the nearest ortho position of predetermined minimal amount has the opposite state in position with central authorities.
6. 6. according to the method for claim 5, wherein the preset minimum number at ortho position is one recently.
7. 7. according to the method for any one claim in the claim 3 to 6, wherein said coding and/or decoding are based on the two-dimensional encoded of band and/or decoding, and described trooping to the accurate hexagon of small part comprises that big capacity is trooped and troop in the border, big capacity is trooped six nearest ortho positions is arranged, the border troop four nearest ortho positions are arranged and be in encode and/or decode along the edge of encoding strip thereof.
8. 8. according to the method for any one claim in the claim 7, wherein encoding strip thereof is directed on [100] or [110] of accurate hexagon network direction.
9. 9. according to the method for any one claim in the claim 1 to 8, wherein the visual field of pick-up unit is a hexagon.
10. 10. according to the method for claim 9, wherein said hexagon is an equilateral hexagon.
11. 11. according to 9 or 10 method of claim, wherein use detector means to read the storage data, arrange detector means in the checkout gear image plane, to produce and store the corresponding signal of data.
12. 12., wherein read with pick-up unit and carry out containing moving continuously on the grid of storing data according to the method for claim 11.
13. 13. according to the method for claim 12, wherein said storage data detect by the detection signal of collecting the different sections of detector means in the different time intervals.
14. 14., wherein read with pick-up unit and move and carry out containing stepping on the grid of storing data according to the method for claim 9 or 10.
15. 15. according to the method for claim 14, wherein said storage data detect by at certain hour the signal of each detector-segments being sued for peace.
16. 16. according to the method for any one claim in the claim 12 to 15, wherein moving of pick-up unit carried out along [100] of containing the accurate hexagon network of storing data or [110] direction.
17. 17. with information multidimensional ground coding and/or decode to/from the system of network, this network has been represented the position, position of described coded message at least on two dimensions, described device comprises code device (30) and/or decoding device (80), arrange these devices to encode respectively and/or decode, by using accurate hexagon network to limit by trooping to the accurate hexagon of small part that a central authorities position and a plurality of arest neighbors position are formed, and application code constraint make concerning each described troop to the accurate hexagon of small part, the nearest ortho position of predetermined minimal amount has the identical state in position with central authorities.
18. 18. with information multidimensional ground coding and/or decode to/from the system of network, this network has been represented the position, position of described coded message at least on two dimensions, described device comprises coding device (30) and/or decoding device (80), arrange these devices to encode respectively and/or decode, by using accurate hexagon network to limit by trooping to the accurate hexagon of small part that a central authorities position and a plurality of arest neighbors position are formed, and application code constraint make concerning each described troop to the accurate hexagon of small part, the nearest ortho position of predetermined minimal amount has the opposite state in position with central authorities.
19. 19. according to the system of claim 17 or 18, wherein said system is a data-storage system.
20. 20. according to the system of any one claim in the claim 17 to 19, wherein the pick-up unit visual field is shaped as hexagon.
21. 21. according to the system of claim 20, wherein said hexagon is an equilateral hexagon.
22. 22., wherein store reading of data and undertaken by the detector plane in the pick-up unit image plane according to the system of any one claim in the claim 17 to 21.
23. 23. according to the system of any one claim in the claim 17 to 22, wherein said reading with pick-up unit moving continuously on medium carried out.
24. 24. according to the system of claim 23, wherein Cun Chu data are read by collect the detected signal of different detector-segments at interval at different time.
25. 25., wherein read to move and carry out with the stepping of pick-up unit according to the system of any one claim in the claim 17 to 22.
26. 26. according to the system of claim 25, wherein Cun Chu data are read by at certain hour the signal of each detector-segments being sued for peace.

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