CN102903378B - For the two-dimentional run length constraint coding/decoding device and method of elongated code check - Google Patents
For the two-dimentional run length constraint coding/decoding device and method of elongated code check Download PDFInfo
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Abstract
The invention provides the two-dimentional run length constraint coding/decoding device and method for elongated code check, this device comprises encoder, described scrambler comprises one-dimensional data stream buffering and grouping module, 2 × 2 code word generation modules, two-dimentional word cell array structure module, 2 × 2 code words write two-dimentional word cell array module, writes two-dimentional word cell array module two-dimensional data array is exported to 2-D data pen recorder finally by 2 × 2 code words wherein; Described demoder comprises two-dimensional array buffer module, two-dimentional word cell page constructing module, two-dimentional word cell read module, 2 × 2 code words to one-dimensional data mapping block, one-dimensional data stream Knockdown block, exports finally by one-dimensional data stream Knockdown block wherein.The present invention can solve two-dimensional data array in both the horizontal and vertical directions, and between adjacent data 1, the run length of data 0 is minimum equals the 1 maximum technical matters equaling the two-dimensional data array structure of 3.
Description
Technical field
The invention belongs to field of data storage and the communications field.Be specifically related to work as by binary data storage in the molecular plane of rectangular grid, no matter in the horizontal direction or in vertical both direction, at adjacent data " 1 " between, the run length of data " 0 " is minimum equals 1, is no more than at most decoding method and the operative installations thereof of 3.The present invention is a kind of coding and decoding technology of elongated code check, and the type of two-dimension codeword length namely exported and the one-dimensional data length ratio of input change along with initial conditions change, and code check is change.
Background technology
In the tape and CD storage technique of current main-stream, data are along track (Track) record on a storage medium.In these storeies, for improving the reliability of storage system, usually necessary constrained is done to binary data sequence.Wherein common restriction is RLL (d, k) run length constraint (Runlength Limited Constraint), and d represents that, between continuous data " 1 ", the run length minimum value of " 0 ", k represents its maximal value.Most high-transmission frequency can be controlled, to reach the object reducing intersymbol interference by choosing suitable parameter d; When reading data, parameter k then can guarantee there are enough jump frequencies to meet the demand controlled clock synchronous.Famous Miller code, i.e. modified frequency modulation code MFM(U.S. Patent number 3,108,261, date of publication on October 22nd, 1963), be exactly one of them representative.In MFM code, between adjacent data " 1 ", the run length of " 0 " at least equals 1, is no more than 3 at most.
Occurred in recent years with the novel memory devices of two-dimentional page mode record data, such as holographic memory, two-dimentional CD and two-dimensional pattern record etc.This kind of storer has a common feature: data store on the recording medium according to the mode of the two-dimentional page at every turn, when reading data, is also carry out according to the mode of the whole page of whole page.Fig. 1 describes the layout signal of binary bits data in this New Two Dimensional storer of 8 × 8.In this example, square grid represents 1 bit data information, i.e. black representative " 1 ", white representative " 0 ", there are 4 bit informations and itself direct neighbor (namely usually said upper and lower, left and right) in every bit binary data bit " 0 " or " 1 ".Be similar to the constrained that binary sequence is made in one-dimension storage technology, in the storer of this two-dimentional page record, also need in row (horizontal) direction and column (vertical) direction, to do constrained to two-dimensional data array.Be not difficult to find out, above-mentioned modified frequency modulation code (MFM), just no longer valid under this two-dimensional case, namely the two-dimensional binary data array be made up of data " 0 " and " 1 " in the row direction with column direction can not meet when d=1 and k=3 time simultaneously, equal 1 to the run length of data " 0 " is minimum, be no more than at most the restriction requirement of 3.Patented claim 201110148840.9 propose a kind of with protection word along the coding method of two-dimensional lattice diagonal line; method based on this patent can construct the minimum value that the scale-of-two rectangle data array that is made up of data " 1 " and data " 0 " can meet the run length of data " 0 " in row (horizontal) direction and column (vertical) direction both direction simultaneously and equal 1, is no more than at most the two-dimensional data array of 3.But the technology that this patent provides is cbr (constant bit rate), the ratio of code word size and input data is fixed values, and namely code check equals 0.25.
Summary of the invention
Technical matters to be solved by this invention is: the coding and decoding device and the using method that are provided for the two-dimentional run length constraint of elongated code check, decoding method of the present invention and device can solve by " 0 " and the two-dimensional data array that " 1 " is formed in level (line direction) with in vertical (column direction) both direction, between adjacent data " 1 ", the run length of data " 0 " is minimum equals 1, the maximum technical matters equaling the two-dimensional data array structure of 3, the code check provided relative to patent 201110148840.9 equals 0.25, average encoder bit rate of the present invention approximately improves about 12.3%, reach about 0.2808.
In order to reach foregoing invention object, the technical scheme that the present invention takes is: for the coding and decoding device of elongated code check two dimension run length constraint, comprise encoder, described scrambler comprises:
One-dimensional data stream buffering and grouping module, this module, while buffer accepts one-dimensional data stream, is one group according to 2 bits and is divided into several one-dimensional data words;
2 × 2 code word generation modules, this module is according to coding and decoding rule list, several one-dimensional data words that one-dimensional data stream buffering and grouping module divide being generated corresponding 2 × 2 two-dimensional constrains code words, being input to according to successively producing order 2 × 2 word cell buffer zones that 2 × 2 code words write two-dimentional word cell array module;
Two dimension word cell array structure module, two-dimensional array is divided into the two-dimentional word cell array that several two-dimentional word cells being 2 × 2 by size form by this module, and each two-dimentional word cell write zone bit of juxtaposition two dimension word cell array equals to write mark;
2 × 2 code words write two-dimentional word cell array module, 2 × 2 two-dimensional constrains codeword sequences in 2 × 2 code word generation modules read from the buffer zone of this module according to sequencing by this module, and capable along two-dimentional word cell array diagonal, line by line 2 × 2 two-dimensional constrains code words are written in two-dimentional word cell array;
Four modules of above-mentioned scrambler connect successively, write two-dimentional word cell array module two-dimensional data array is exported to 2-D data pen recorder finally by 2 × 2 code words wherein;
Described demoder comprises:
Two-dimensional array buffer module, it is the two-dimensional data array of 2N × 2M that this module is mainly used in temporarily depositing the size read from 2-D data pen recorder;
Two dimension word cell page constructing module, it is the two-dimentional word cell array of the N × M of minimum reading unit that this module is mainly used in the 2N × 2M two-dimensional data array in two-dimensional array buffer module to be divided into by 2 × 2, and it is readable mark that each word cell of juxtaposition two dimension word cell array reads zone bit;
Two dimension word cell read module, this module is mainly used in reading 2 × 2 suitable two-dimensional constrains code words from two-dimentional word cell array, and temporarily deposits 2 × 2 produced two-dimensional constrains codeword sequences;
2 × 2 code words are to one-dimensional data mapping block, this module is mainly used in reading 2 × 2 two-dimensional constrains codeword sequences from two-dimentional word cell read module, according to coding and decoding rule list, 2 × 2 two-dimensional constrains code words are decoded into according to precedence the one-dimensional data word that size equals 2 bits;
One-dimensional data stream Knockdown block, the 2 bit one-dimensional data words that this module is mainly used in 2 × 2 code words produce to one-dimensional data mapping block are assembled into one-dimensional data stream according to the sequencing produced;
Five modules of above-mentioned demoder connect successively, export finally by one-dimensional data stream Knockdown block wherein.
The decoding method of the coding and decoding device of the described two-dimentional run length constraint for elongated code check, realizes cataloged procedure by scrambler, comprises the following steps successively:
S101) the binary one-dimensional data stream of input is one group by every 2 bits and is divided into some one dimension 2 bit data word equably by one-dimensional data stream buffering and grouping module, and the data buffer this 2 bit data word being input to 2 × 2 code word generation modules is kept in;
S102) 2 × 2 code word generation modules read one dimension 2 bit data word one by one from data buffer, and one dimension 2 bit data word is changed into 2 × 2 two-dimensional constrains code words by the output scheme choosing encoding and decoding rule list;
S103) two-dimentional word cell array structure module is according to the storage size of 2-D data pen recorder, by size be 2N × 2M a two-dimensional data array with 2 × 2 word cell be one group, be divided into the two-dimentional word cell array comprising 2 × 2 identical two-dimentional word cells of N × M size, each 2 × 2 two-dimentional word cell writes of juxtaposition are masked as true, and wherein N and M is positive integer;
S104) 2 × 2 code words write 2 × 2 two-dimensional constrains code words that step S102 obtains by two-dimentional word cell array module, the two-dimentional word cell of obtain with step S103 2 × 2 is benchmark, successively two-dimensional constrains code word write size is equaled in the two-dimentional word cell of 2 × 2 along two-dimentional word cell array diagonal direction from the upper right corner to the lower left corner, carry out selective filling according to the direct neighbor two dimension word cell of encoding and decoding rule list to the right of the two-dimentional word cell of current write and below simultaneously; If the two-dimentional word cell of this diagonal lines is all written into, enter next step, if all two-dimensional constrains code words have been filled complete, directly terminate cataloged procedure;
S105) judged whether that next diagonal lines not yet writes, if having, gone to step S104; If all 2 × 2 two-dimentional word cells of this two-dimentional word cell page have write full two-dimensional constrains code word, then enter next step;
S106) judge whether uncoded one-dimensional data word in addition, if having, go to step S102; Otherwise end cataloged procedure.
The decoding method of the described coding and decoding device for the constraint of elongated code check two dimension run length, realizes decode procedure by demoder, comprises the following steps successively:
S201) two-dimensional data array read from 2-D data pen recorder is temporarily left in 2-D data buffer module;
S202) two-dimentional word cell page constructing module reads size is the two-dimensional data array of 2N × 2M, this two-dimensional data array is evenly divided for minimum reading unit with 2 × 2, formation is contained in the two-dimentional word cell array of 2 × 2 identical two-dimentional word cells of N × M size, it is that readable mark is true that each two-dimentional word cell of juxtaposition two dimension word cell array reads zone bit, and wherein N and M is positive integer;
S203) two-dimentional word cell read module with 2 × 2 two-dimentional word cells of this two-dimentional word cell array for benchmark, according to encoder encodes order, along the diagonal lines of two-dimentional word cell array, reading mark selectivity successively according to each two-dimentional word cell from the upper right corner to the lower left corner reads the two-dimensional constrains code word in two-dimentional word cell array, if the two-dimensional constrains code word of this row is all read, enter next step, if the two-dimensional constrains code word of current two-dimentional word cell array has read complete, then go to step S205;
S204) the not yet decoding of next diagonal lines has been judged whether, if go to step S203; If the two-dimensional constrains code word of all diagonal lines of this two-dimentional word cell page is all read, enter next step;
S205) 2 × 2 code words are to the one-dimensional data mapping block decoding table corresponding according to selected encoding and decoding table, 2 × 2 two-dimensional constrains code words read from two-dimentional word cell read module are decoded into corresponding one dimension 2 bit data word according to generation order, after completing, enter next step;
S206) one dimension 2 bit data word obtained is assembled according to corresponding decoding precedence by one-dimensional data stream Knockdown block, and obtain corresponding one dimension binary data stream, decoding completes.
Described method, the method that the right of step S104 to the two-dimentional word cell of current write 2 × 2 two-dimentional word cell adjacent with below carries out selective filling is:
If the two-dimensional constrains code word a) being written to current 2 × 2 two-dimentional word cells does not belong to diagonal matrix or sub-diagonal matrix, then judge and the right of direct neighbor of current 2 × 2 two-dimentional word cells, the two-dimentional word cell in below write mark true and false; If true, be the two-dimensional constrains code word of diagonal matrix or sub-diagonal matrix at the two-dimentional word cell position Filling power corresponding with this zone bit; If false or undefined, then do not fill two-dimensional constrains code word;
After completing above-mentioned ablation process, the two-dimentional word cell write of putting current 2 × 2 two-dimentional word cells and filling two-dimensional constrains code word is masked as vacation, again can not be allowed write two-dimensional constrains code word after representing these positions;
If the two-dimensional constrains code word b) being written to current 2 × 2 two-dimentional word cells belongs to diagonal matrix or sub-diagonal matrix, after current two-dimentional word cell position writes this two-dimensional constrains code word, it is false for being write traffic sign placement.
5. method according to claim 3, is characterized in that, the method for the two-dimensional constrains code word that step S203 selectivity reads in two-dimentional word cell page is:
If a) the two-dimentional word cell of current reading reads zone bit is true, then read the two-dimensional constrains code word in this two-dimentional word cell, the reading of this two-dimentional word cell of juxtaposition is masked as vacation, is not allowed to read namely; If the two-dimensional constrains code word of current reading does not belong to diagonal matrix or sub-diagonal matrix, the adjacent right of current reading word cell position is set in the lump, the two-dimentional word cell of below reads and be masked as vacation, namely do not allow to read;
If b) the two-dimentional word cell of current reading reads zone bit is false, then proceed to the data in the next one two dimension word cell reading this two-dimentional word cell place diagonal lines.
Technique effect of the present invention is as described below:
1) scrambler is elongated code check.The code check of scrambler is the bit number of output codons and the ratio of enter code word bit number, code check is higher, presentation code effect is better, in the present invention, data in coding stage, according to the context situation of scrambler, one dimension 2 bit data word is output into the different two-dimensional constrains code word of length, the coding method of this avriable length codes, the relevance between the abundant sharp adjacent data of energy, the therefore more existing coding method of code check
,average bit rate will exceed 12.3%.
2) coding and decoding rule list is simple.In the present invention, one dimension 2 bit data word, according to data forward-backward correlation, can choose different output intents to meet constrained condition.By simple decoding equation, the decoding of one dimension 2 bit data word can be realized.
Accompanying drawing explanation
Fig. 1 is 8 × 8 two-dimensional data array meeting the constraint of (1,3) run length in the two directions.
Fig. 2 is 2 × 2 molecular two-dimentional word cells of square grid.
Fig. 3 is two-dimentional word cell array co-ordinates and diagonal lines numbering schematic diagram.
Fig. 4 is the read/write sequential schematic of data in two-dimentional word cell array.
Fig. 5 is the coordinate schematic diagram calculating code check.
Fig. 6 is the scrambler theory diagram of variable code rate.
Fig. 7 is the code translator theory diagram of variable code rate.
Fig. 8 is the two-dimensional data array constructed embodiment based on table 1,2 the first coding and decoding rule.
Fig. 9 changes schematic diagram based on the two-dimentional word cell array of table 1,2 the first coding and decoding rule at cataloged procedure.
Figure 10 is the two-dimentional word cell array decoding embodiment based on table 1,2 the first coding and decoding rule.
Figure 11 is the change schematic diagram of two-dimentional word cell array in decode procedure based on table 1,2 the first coding and decoding rule.
Figure 12 is the two-dimensional data array constructed embodiment based on table 3,4 the second coding and decoding rules.
Figure 13 is the two-dimentional word cell array decoding embodiment based on table 3,4 the second coding and decoding rules.
Figure 14 is two-dimensional constrains code word the first adjacent type diagonally.
Figure 15 is two-dimensional constrains code word the second adjacent type diagonally.
Figure 16 is two-dimensional constrains code word the third adjacent type diagonally.
Figure 17 is two-dimensional constrains code word the 4th kind of adjacent type diagonally.
Embodiment
For the problem that background technology proposes, the invention provides the decoding method of the two-dimentional run length constraint of two kinds of elongated code checks, can, in two-dimensional data storage with under the environment communicated, make binary bits information meet preassigned constrained condition.Namely when binary data " 0 " and " 1 " are written in the molecular array of rectangular grid, also can construct between adjacent data " 1 ", no matter be in row (horizontal) direction or column (vertical) direction, the run length of data " 0 " is minimum equals 1, is no more than at most the binary data array of 3.Be with patent 201110148840.9 difference: the present invention is a kind of coding and decoding technology of elongated code check, the type of two-dimension codeword length namely exported and the one-dimensional data length ratio of input change along with initial conditions change, and code check is elongated.Take the technical scheme that the present invention provides, make full use of the relation between two-dimensional rectangle grid and two-dimensional constrains code word, and maximization make use of this relation; The average bit rate of coding then brings up to 0.2808 from 0.25 of patent 201110148840.9, and code check improves about 12.3%.In other words, under equal conditions, the present invention is taked can to improve the system memory size of about 12.3%.
The present invention is applicable to the data-storage system of binary data according to the square grid record of two dimension.The Typical Representative of storage system has the two-dimentional novel memory devices such as holographic, holographic storer, two-dimentional CD.A goal of the invention of the present invention is to provide the coding method of the two-dimentional run length constraint of two kinds of elongated code checks.Another object of the present invention is to provide two kinds of coding/decoding methods of the corresponding two-dimentional run length constraint with the coding method of two kinds of elongated code checks.Another object of the present invention is to provide corresponding Code And Decode device.
Two-dimentional run length (1,3) the constraint coding and decoding method of elongated code check, for the first the coding and decoding rule shown in table 1,2, comprises the steps:
The coding schedule of the first coding and decoding rule of table 1
The decoding table of the first coding and decoding rule of table 2
The first step: be one group according to dibit by the one dimension binary data stream of input, is divided into several one dimension 2 bit data word of size, the value of each one dimension 2 bit data word have following 4 kinds may: 00,01,10,11.And one dimension 2 bit data word is input to one-dimensional data buffer zone keeps in, go to step two;
Second step: 2-D data page size being equaled 2N × 2M is one group with 2 × 2, is divided into the two-dimentional word cell page that N × M size is identical, and each word cell write of juxtaposition two dimension word cell array is masked as true, then goes to step three;
3rd step: read one dimension 2 bit data word sequence from the one dimension buffer zone of step one, and according to table 1, 2 or table 3, the output scheme three of coding and decoding rule list described in 4, by the one dimension 2 bit data word sequence of buffer zone one by one coding mapping become the two-dimensional constrains codeword sequence of 2 × 2, then by the two-dimentional word cell array diagonal standard of behaviour that this two-dimensional constrains codeword sequence of 2 × 2 produces with step 2, along 45 ° of diagonal lines of two-dimentional word cell array, successively this two-dimensional constrains code word of 2 × 2 is write in the corresponding word cell of two-dimentional word cell array from the upper right corner to the lower left corner line by line, go to step four,
The coding schedule of table 3 the second coding and decoding rule
The decoding table of table 4 the second coding and decoding rule
4th step: on the basis of step (3), if the two-dimentional word cell array co-ordinates of current write is
, and write is masked as true, 2 × 2 two-dimensional constrains code words to be written are simultaneously
if (step (3) takes the second coding and decoding rule described in table 3,4, then
with
replace), then in position
write
time, and judge
with
the write zone bit of two two-dimentional word cell positions is true and false, if false, skips over, otherwise
with
two positions optionally writes two-dimensional constrains code word
(when step (3) takes the second coding and decoding rule described in table 3,4, then
with
replace), the write finally resetting each two-dimentional word cell corresponding coordinate position of this step is masked as vacation, goes to step five;
;
;
(A)
;
;
(B)
5th step: if the two-dimensional array of cells coordinate of current write is
, and 2 × 2 two-dimensional constrains code words to be written are, directly in position
write (if step (3) takes table 3,4 coding and decoding rules, then two places of step (5)
all use
replace), the write of this coordinate of juxtaposition is masked as vacation, represents that this coordinate write data, goes to step six;
6th step: repeat step 4, until all 2 × 2 two-dimensional constrains words that step (2) produces are written to the two-dimentional word cell array of N × M.
(the first the coding and decoding rule for described in table 1,2) decoding procedure is as follows:
The first step: read size and equal the binary data array of 2N × 2M, is a two-dimentional word cell by two-dimensional data array with 2 × 2, is divided into the two-dimentional word cell array of N × M, each word cell of this two-dimentional word cell array of juxtaposition read be masked as true;
Second step: 45 ° of diagonal line along two-dimentional word cell array read two-dimensional constrains code word successively line by line from the upper right corner to the lower left corner;
3rd step: on the basis of step 2, if changing coordinates
reading is masked as very, then read corresponding 2 × 2 two-dimensional constrains code words, judge whether to equal simultaneously
, if so, then put coordinate
with
reading be masked as vacation;
4th step: read the true and false of zone bit according to two-dimentional each word cell of word cell array, judge whether all two-dimentional word cells of two-dimentional word cell array are all read, if go to step five, otherwise go to step two;
5th step: 2 × 2 two-dimensional constrains code words that step 3 is obtained according to table 1,2 or table 3,4 decoding table be decoded into one dimension 2 bit data word;
6th step: one dimension 2 bit data word step 5 obtained is assembled into one-dimensional data stream according to the precedence generated and exports, and decoding completes.
To achieve these goals, present invention also offers the scrambler realizing above-mentioned data-encoding scheme, comprising:
One-dimensional data stream buffering and grouping module, Data Placement, while buffering one-dimensional data stream, according to the size of two-dimensional array, is become several one dimension 2 bit data word by this module;
2 × 2 code word generation modules, this module according to table 1,2 or table 3,4 described in the output scheme three of coding and decoding rule list, several one dimension 2 bit data word of one-dimensional data stream buffering and grouping module being generated corresponding 2 × 2 two-dimensional constrains code words, being input to according to successively producing order 2 × 2 word cell buffer zones that 2 × 2 code words write two-dimentional word cell array module;
Two dimension word cell array structure module, two-dimensional array is divided into several word cell arrays be made up of 2 × 2 arrays by this module, and each two-dimentional word cell write zone bit of juxtaposition two dimension word cell array equals to write mark " 0 ";
2 × 2 code words write two-dimentional word cell array module, 2 × 2 two-dimensional constrains codeword sequences in 2 × 2 code word generation modules read from the buffer zone of this module according to sequencing by this module, and along the diagonal lines of two-dimentional word cell array 45 °, line by line 2 × 2 two-dimensional constrains code words are written in two-dimensional array;
To achieve these goals, present invention also offers the scrambler realizing above-mentioned data decoding method, comprising:
Two-dimensional array buffer module, this module is mainly used in temporarily depositing the 2N × 2M two-dimensional data array read from 2-D data pen recorder;
Two dimension word cell page constructing module, it is the two-dimentional word cell array of the N × M of minimum reading unit that this module is mainly used in the 2N × 2M two-dimensional data array in two-dimensional array buffer module to be divided into by 2 × 2, and it is readable mark " 0 " that each word cell of juxtaposition two dimension word cell array reads zone bit;
Two dimension word cell read module, this module is mainly used in reading 2 × 2 suitable two-dimensional constrains code words from current two-dimentional word cell array, and temporarily deposits whole 2 × 2 two-dimensional constrains code words that this two-dimentional word cell array produces;
2 × 2 code words are to one-dimensional data mapping block, this module is mainly used in reading 2 × 2 two-dimensional constrains code words according to successively producing order from two-dimentional word cell read module, according to table 1,2 or table 3,4 described in the decoding table of coding and decoding rule, 2 × 2 two-dimensional constrains code words are decoded into according to precedence the one-dimensional data word that size equals 2 bits;
One-dimensional data stream Knockdown block, the 2 bit one-dimensional data words that this module is mainly used in 2 × 2 code words produce to one-dimensional data mapping block are assembled into one-dimensional data stream according to the sequencing produced.
Below in conjunction with drawings and Examples, the present invention is described in further detail:
As shown in Figure 1, describe the two-dimensional data array produced according to the present invention, no matter this two-dimensional data array is in the horizontal direction or in vertical direction, between adjacent data " 1 ", the run length of data " 0 " all meets and minimumly equals 1, is no more than at most the constraint condition of 3.The left figure of Fig. 1 is the logging mode of 2-D data at holographic memory, and the right is the figure pattern of binary data array.
As shown in Figure 2, the two-dimentional word cell of 2 × 2 square grid systems is least unit of coding and decoding two-dimensional data array.
As shown in Figure 3, two-dimentional word cell array co-ordinates and diagonal lines numbering schematic diagram is described.In figure, each base unit of array is two-dimentional word cell, this two-dimentional word cell 2 × 2 square grid compositions as shown in Figure 2.
As shown in Figure 4, description is the read/write orders of data at two-dimentional word cell array.Namely, in two-dimentional word cell, the read/write of data is all carry out line by line along the diagonal line of 45 °, 45 ° of cornerwise every a line, is all carry out read/write to data in order from the upper right corner toward the lower left corner.
As shown in table 1,2, the coding schedule of the first coding and decoding rule that what table 1 provided is, in this coding schedule, based on context one-dimensional data word 00,01,10 has 3 kinds of scheme two-dimensional constrains code words can export for coding; One-dimensional data word 11 only has a kind of two-dimensional constrains code word to export for coding.What table 2 provided is based on the decoding rule table described in table 1 corresponding to coding rule.In this decoding rule table, if 2 bit one-dimensional data words are used
represent, the two-dimensional constrains code word of 2 × 2 is used
represent.Based on this coding and decoding rule, the two-dimensional constrains code word basic coding equation of 2 × 2 is as follows:
Wherein ×
1~ ×
2for the individual bit position of one-dimensional data word.Y
11~ Y
22for the bit of type of two-dimension codeword.Same according to this basic coding equation, in the process of decoding, the decoding equation of one dimension 2 bit data word is as follows:
；
Shown in A, what formula A provided is on the basis of the first coding and decoding rule list described in table 1,2, to the classification that the two-dimensional constrains code words of 42 × 2 are carried out.
,
,
these 3 two-dimensional constrains words are classes, use respectively
,
with
represent;
be divided into Equations of The Second Kind separately, use
representing, for convenience of describing, being called for short diagonal matrix.
What table 3,4 provided is the second coding and decoding rule.The basic coding table that what table 3 provided is based on the second coding and decoding rule, in this coding rule, based on context one-dimensional data word 00,01,10 adopts 3 kinds of other two-dimensional constrains code word schemes to export for coding; One-dimensional data word 11 also only has a kind of coding output scheme selective with the first scheme is the same.The decoding table that what table 4 provided is based on coding rule described in table 3.If one dimension 2 bit data word is still used
represent, the two-dimensional constrains code word of 2 × 2 is still used
represent.Based on this second coding and decoding rule, the two-dimensional constrains code word basic coding equation of 2 × 2 is as follows:
According to the basic coding and decoding rule of this second, the second decoding equation of one dimension 2 bit data word is as follows:
；
Shown in B, what formula B provided is on the basis of the second coding and decoding rule list described in table 3,4, to the classification that the two-dimensional constrains code words of 42 × 2 are carried out,
,
,
these 3 two-dimensional constrains words are classes, use respectively
,
with
represent;
be divided into Equations of The Second Kind separately, use
representing, for convenience of describing, being called for short sub-diagonal matrix.
As shown in Figure 5, this Figure illustrates based on table 1,2 and table 3,4 two kinds of coding and decoding rules on, how to calculate the average bit rate of these two kinds of variable length encoding methods.Namely coordinate in cell array is calculated
the probability of appearance write two-dimensional constrains code word
.For the first coding and decoding method described in table 1,2, the average bit rate of concrete calculation code method is as follows
:
First by one dimension binary data sequence according to one group between two, divide, then according to one dimension to two-dimensional map relation, successively one dimension 2 bit data word is mapped to the two-dimentional word cell of 2 × 2, by one dimension binary data sequence change into two dimension 2 × 2 word cell data sequences.Problem for convenience of description, for the first variable code rate method, becomes two classes by the two-dimentional word cell Data Placement of 2 × 2
, namely two dimension 2 × 2 word cell data sequences by
by forming.Here
, and
;
.
Generally,
probability equal
, and
probability equal
.After above-mentioned mapping transformation, one dimension binary data sequence changes into two-dimentional word cell data sequence.Obviously, after above-mentioned conversion, the array sequence entropy of 42 × 2 two-dimensional constrains code word compositions equals
, namely
.In two-dimensional array of cells, use
represent the write value of certain unit, wherein
.Equal at two-dimensional array of cells coordinate
write value use
represent.Be simultaneously write line by line according to 45 ° of diagonal lines because 2 × 2 two-dimensional constrains code words are written to two-dimentional word cell array, therefore in diagonal angle N-th row, diagonally there are four kinds of adjacent type as shown in Figure 14 ~ Figure 17 in 2 × 2 two-dimensional constrains code words.In the first type of Figure 14
,
; In Figure 15 the second type,
; In the third type of Figure 16
,
; In Figure 17 Four types
, wherein i=1,2,3.The average bit rate of obvious scrambler
Wherein
represent at an arbitrary position
the probability of write two-dimensional constrains code word.According to the precedence of write two-dimensional cell data, in position
any write two-dimensional constrains code word
, according to constraint condition, namely in position
and position
on cell data value should equal simultaneously
.Have in conjunction with Figure of description 5:
, namely there is following equation consolidated equation (2), (3), (4), (5), (6), (7), (8):
Wherein
.Solve an equation
, have
Substitute into equation (1), namely
Usual binary data stream is independent identically distributed, and namely the probability of " 0 " and " 1 " all equals 1/2, then when described in binary data stream table 1,2, the first coding and decoding rule takes output scheme three to be converted into two-dimensional constrains codeword sequence, and two-dimensional constrains code word
the probability occurred equals
, according to computing formula (11) above, the therefore average bit rate of variable code rate
.Obviously take the second table 3,4 the average bit rate that obtains of coding and decoding rule and method the same with first method.
As shown in Figure 6, encoder encodes process is as follows: first one-dimensional data stream is input to one-dimensional data stream buffering and grouping module.This module is while buffering one-dimensional data stream, and Data Placement is become the grouping that several length are equal, packet size equals 2 bit data word.After one-dimensional data flows through grouping module, first packet size being equaled 2 bits is input to 2 × 2 code word generation modules, and then according to table 1,2 or table 3,4 described in the basic coding table of coding and decoding rule list, first generate the two-dimensional constrains code word of 2 × 2, and 2 × 2 two-dimensional constrains codeword sequences formed are input to the two-dimentional word cell that 2 × 2 code words write two-dimentional word cell array module and are cached.On the other hand, two-dimentional word cell array structure module forms a two-dimentional word cell according to 2 × 2 grid, and two-dimensional array size being equaled 2N × 2M is divided into the two-dimentional word cell array of N × M.The generation of two-dimensional data array writes array module by type of two-dimension codeword to have come.After completing aforesaid operations, 2 × 2 code words write two-dimentional word cell array module from the buffer memory of this module, read 2 × 2 constraint code words, and according to table 1,2 or table 3,4 Basic Encoding Rules, along the diagonal lines of Fig. 3 two dimension word cell array 45 ° line by line by 2 × 2 constraint code words writes.In the ablation process of each diagonal lines, the order of write, according to described in Fig. 4, namely writes from the upper left corner that current diagonal is capable toward the lower right corner one by one.According to the classification of formula A or formula B to 2 × 2 two-dimensional constrains code words, choose in the two-dimentional word cell of respective two-dimensional constraint code word write correspondence position, thus realize one-dimensional data stream encryption to become two-dimensional data array.For the first coding and decoding rule described in table 1,2, its coding step comprises:
(1) be one group by the one-dimensional data stream of input according to 2 bits, be divided into several one-dimensional data words;
(2) output scheme three of the one dimension 2 bit data word coding and decoding rule list according to table 1,2 step (1) produced, is encoded into the two-dimensional constrains code word of 2 × 2 by the one-dimensional data word of 2 bits;
(3) formed a two-dimentional word cell with 2 × 2 grid, by the N × M two dimension word cell array of two-dimentional 2N × 2M array partition in units of two-dimentional word cell, each word cell of juxtaposition two dimension word cell array can be write and be masked as true " 0 ";
(4) on the two-dimentional word cell array basis that step (3) is formed, 2 × 2 two-dimensional constrains codeword sequences that step (2) is obtained, according to the classification of formula A to 2 × 2 two-dimensional constrains code words, along two-dimentional word cell array 45 ° of diagonal lines, write data successively from the upper right corner toward direction, the lower left corner line by line;
(5) on the basis of step (4), if the two-dimentional word cell array co-ordinates of current write is
, and 2 × 2 two-dimensional constrains code words to be written are
, in position
write
time, judge
with
the write zone bit of two positions is true and false, if false, skips over, otherwise
with
two positions optionally writes two-dimensional constrains code word, and the write resetting corresponding coordinate position is masked as vacation " 1 ", represents that the write operation of these positions completes, goes to step (6);
(6) if the two-dimentional word cell array co-ordinates of current write is
, and 2 × 2 two-dimensional constrains code words to be written are, directly in position
write, the write of this coordinate of juxtaposition is masked as vacation " 1 ", represents that this position write operation completes;
(7) step (4) is repeated, until all 2 × 2 two-dimensional constrains words that step (2) produces are written to the two-dimentional word cell array of N × M;
As shown in Figure 7, scrambler decode procedure is as follows: first read two-dimensional data array from two-dimentional pen recorder, then data are read page by page from two-dimensional array buffer module, be input to two-dimentional word cell page constructing module, be a two-dimentional word cell according to 2 × 2, two-dimensional data array is divided into two-dimentional word cell page, then the two-dimentional word cell page after division is input to the two-dimensional constrains code word that two-dimentional word cell read module reads 2 × 2, two-dimensional constrains code word is input to 2 × 2 code words to one-dimensional data mapping block, obtain corresponding one dimension 2 bit data word, one dimension 2 bit data word is input to one-dimensional data stream Knockdown block, one dimension original data stream is assembled into according to the precedence of 2 bit data word, thus complete the conversion of two-dimensional constrains array to one-dimensional data stream, realize decode procedure.Still for the first coding and decoding rule described in table 1,2, its decoding procedure comprises:
(1) read two-dimensional data array from two-dimentional pen recorder, and two-dimensional array is input to the preservation of two-dimensional array buffer module;
(2) be an elementary cell by two-dimensional data array according to 2 × 2, be divided into corresponding two-dimentional word cell array, the reading of the corresponding two-dimentional word cell array of juxtaposition is masked as very;
(3) along two-dimentional word cell array 45 ° of diagonal line line by line incremental manner from the upper right corner to the lower left corner, read two-dimensional constrains code word;
(4) on the basis of step (3), if changing coordinates
reading is masked as very, then read corresponding 2 × 2 two-dimensional constrains code words, judge whether to equal simultaneously
, if so, then put coordinate
with
reading be masked as vacation, otherwise continue step (3) and read the two-dimensional constrains code word of next coordinate, until read complete two-dimentional word cell array, then go to step (5);
(5) 2 × 2 two-dimensional constrains codeword sequences step (4) obtained, one by one according to table 1,2 decoding table be decoded into one dimension 2 bit data word;
(6) one dimension 2 bit data word step (5) obtained is assembled into one-dimensional data stream according to precedence and exports, and decoding completes.
In order to the application process of coding rule is described, Fig. 8 and Fig. 9 lists the encoding embodiments 1 of the first the coding and decoding rule that the present invention is based on described in table 1,2.Figure 10 and Figure 11 lists the decoding embodiment 2 of the first the coding and decoding rule that the present invention is based on described in table 1,2.Embodiment 1 and embodiment 2 are all according to the coding and decoding rule list described by table 1,2 and the classification of the two-dimensional constrains code word described in formula A, and the size of two-dimensional array equals 8 × 8, and corresponding two-dimentional word cell array size equals 4 × 4.If according to table 3,4 and the second coding and decoding rule list described in formula B and two-dimensional constrains code word analyze, its coding&decoding embodiment is shown in Figure 12 and Figure 13.
Encoding embodiments 1:
Fig. 8 gives concrete cataloged procedure.One-dimensional data stream 00110111111011001011 according to sequencing from right to left 2 bits be one group and carry out combination and be divided into 10 2 bit data word, these 10 one dimension 2 bit data word are as follows: 11,01,00,11,01,11,11,10,11,00.According to table 1,2, the output scheme three of basic coding table carries out encoding the two-dimensional constrains codeword sequence of generation 10 2 × 2, and 2 × 2 two-dimensional constrains code words of generation are as follows according to corresponding relation arrangement:
，
，
，
，
，
，
，
，
，
Then by 4 × 4 two-dimentional word cell arrays of the front construction of above-mentioned 10 2 × 2 two-dimensional constrains code word writes.Before enforcement, by each unit write mark position 0 of 4 × 4 two-dimentional word cell arrays, namely unit zone bit equals 0, and represent that the unit of current location can write data, equaling 1 expression can not write.Then first by the two-dimensional constrains code word of first 2 × 2
along in the two-dimentional word cell of two-dimentional word cell array diagonal the 0th row write coordinate (0,0), the two-dimentional word cell array after write is as shown in Fig. 9 (1).Then by the two-dimensional constrains code word of the 2nd 2 × 2
be written to the two-dimentional word cell position that diagonal line the 1st row-coordinate equals (0,1), simultaneously according to formula A,
belong to
, because the write mark at coordinate (1,1) and (0,2) place equals 0, therefore write in the word cell position of coordinate (1,1) and (0,2)
, simultaneously by the write mark position 1 at (1,1) and (0,2) this two place, namely one-dimensional data word 01 at this moment according to table 1,2 coding rule and according to output scheme one, be encoded into
.After write the 2nd one dimension 2 bit data word 01, two-dimentional word cell array is as shown in Fig. 9 (2).By the 3rd 2 × 2 two-dimensional constrains code words
continue to be written in corresponding word cell array along 45 ° of diagonal line the 1st row, i.e. coordinate (1,0) place.Due to
also belong to
, and the write mark of coordinate (1,1) equals 1, and the write mark of coordinate (2,0) equals 0, therefore according to coding rule, will
be written to word cell array co-ordinates (1,0) place, then write at coordinate (2,0) place
, on the other hand, because the write mark of coordinate (1,1) equals 1, therefore in the present case, skip at coordinate (1,1) place.After completing said process, the write mark of this two places coordinate is put 1.Namely, when one dimension 2 bit data word 00 is write array, the basic coding schedule of the first coding and decoding rule according to table 1,2, according to output scheme two, 00 is encoded into
, namely after write the 3rd one dimension 2 bit data word 00, two-dimentional word cell array is as shown in Fig. 9 (3).Because array diagonal the 2nd row has not had vacant position, therefore the 4th 2 × 2 two-dimensional constrains code words
array diagonal the 3rd row (0,3) at the writing position coordinate of two-dimentional word cell array.Due to
belong to
, therefore one dimension 2 bit data word 11 basic coding schedule of the first coding and decoding rule according to table 1,2, is encoded into
, namely after the 4th one dimension 2 bit data word 00 is by the two-dimentional word cell array of coding write, two-dimentional word cell array then becomes as shown in Fig. 9 (4).Repeat said process until the 10th 2 bit data word 00 are written to (3 of two-dimentional word array unit diagonal angle the 6th row, 3) place, because now two-dimentional word cell array is fully written, therefore 00 according to table 1,2 the output scheme three of coding rule basic coding table, be encoded into
, by the two-dimensional constrains code word of 2 × 2
write array (3,3) place, namely completes two-dimensional constrains array code process one-dimensional data being flow to a page.
Embodiment 2:
Figure 10 gives concrete decode procedure.First data are read to two-dimensional array buffer module from two-dimentional pen recorder.In the present embodiment, this two-dimensional data array of 8 × 8 is as follows:
Then be an elementary cell by this two-dimensional data array with 2 × 2, be divided into size equal 4 × 4 two-dimentional word cell array as follows:
Then the two-dimensional constrains code word of 2 × 2 is read line by line along the diagonal lines of two-dimentional word cell array.Before reading data, each word cell arranging 4 × 4 two-dimentional word cell arrays reads zone bit
, zone bit " 0 " represents two-dimentional word cell coordinate
2 × 2 two-dimensional constrains code words at place can be read, and zone bit " 1 " expression not can read, here
.
First from diagonal angle, the 0th row-coordinate (0,0) place reads the two-dimensional constrains code word of 2 × 2
, the two-dimentional word cell array after reading, as shown in Figure 11 (1), then reads the two-dimensional constrains code word at the 1st row (0,1) place
, due to
belong to
, therefore the word cell coordinate of array is equaled respectively the reading mark position 1 of (0,2) and (1,1), namely has
, the two-dimentional word cell array after now reading is as shown in Figure 11 (2), and figure empty represents that two-dimensional constrains code word is read.Because array diagonal the 1st row still has data not to be read, therefore continue the two-dimensional constrains code word of the word cell (1,0) reading this diagonal lines toward the lower left corner from the upper right corner
, because
belong to
, so by the reading mark position 1 of unit coordinate (2,0) and (1,1), due to above
, therefore only put
, Figure 11 (3) describes and reads two-dimensional constrains code word
after situation.Repeat the process of above-mentioned reading two-dimensional array, until the data of two-dimensional array are all read.Two-dimensional constrains code word after above-mentioned reading, according to reading order, arranges as follows:
，
，
，
，
，
，
，
，
，
In the present embodiment, the 2-D data word of reading according to table 1,2 the decoding table of coding and decoding rule be decoded into one dimension 2 bit data word, namely have:
;
;
;
.Finally by 11,01,00,11,01,11,11,10,11,00 these one dimension 2 bit data word are assembled into customer traffic 00110111111011001011 and export, and get final product two dimensional decodings of completing user data.
Based on table 3,4 the second coding and decoding rule, also can complete coding and decoding work similarly, its specific embodiment is shown in Figure 12 coding examples and Figure 13 decoding example.Although described embodiment disclosed by the invention in detail, should understand do not depart from based on table 1,2 and table 3,4 two kinds of coding and decoding rules, the present invention also has a lot of change at specific embodiment, substitutes and amendment.
Claims (7)
1., for a two-dimentional run length constraint coding/decoding device for elongated code check, it is characterized in that comprising encoder, described scrambler comprises:
One-dimensional data stream buffering and grouping module, this module, while buffer accepts one-dimensional data stream, is one group according to 2 bits and is divided into several one-dimensional data words;
2 × 2 code word generation modules, this module is according to coding and decoding rule list, several one-dimensional data words that one-dimensional data stream buffering and grouping module divide being generated corresponding 2 × 2 two-dimensional constrains code words, being input to according to successively producing order 2 × 2 word cell buffer zones that 2 × 2 code words write two-dimentional word cell array module;
Two dimension word cell array structure module, two-dimensional array is divided into the two-dimentional word cell array that several two-dimentional word cells being 2 × 2 by size form by this module, and each two-dimentional word cell write zone bit of juxtaposition two dimension word cell array is for writing;
2 × 2 code words write two-dimentional word cell array module, 2 × 2 two-dimensional constrains codeword sequences in 2 × 2 code word generation modules read from the buffer zone of this module according to sequencing by this module, and capable along two-dimentional word cell array diagonal, line by line 2 × 2 two-dimensional constrains code words are written in two-dimentional word cell array;
Four modules of above-mentioned scrambler connect successively, write two-dimentional word cell array module two-dimensional data array is exported to 2-D data pen recorder finally by 2 × 2 code words wherein;
Described demoder comprises:
Two-dimensional array buffer module, it is the two-dimensional data array of 2N × 2M that this module is mainly used in temporarily depositing the size read from 2-D data pen recorder;
Two dimension word cell page constructing module, it is the two-dimentional word cell array of the N × M of minimum reading unit that this module is mainly used in the 2N × 2M two-dimensional data array in two-dimensional array buffer module to be divided into by 2 × 2, and it is readable mark that each word cell of juxtaposition two dimension word cell array reads zone bit;
Two dimension word cell read module, this module is mainly used in reading 2 × 2 suitable two-dimensional constrains code words from two-dimentional word cell array, and temporarily deposits 2 × 2 produced two-dimensional constrains codeword sequences;
2 × 2 code words are to one-dimensional data mapping block, this module is mainly used in reading 2 × 2 two-dimensional constrains codeword sequences from two-dimentional word cell read module, according to coding and decoding rule list, 2 × 2 two-dimensional constrains code words are decoded into according to precedence the one-dimensional data word that size equals 2 bits;
One-dimensional data stream Knockdown block, the 2 bit one-dimensional data words that this module is mainly used in 2 × 2 code words produce to one-dimensional data mapping block are assembled into one-dimensional data stream according to the sequencing produced;
Five modules of above-mentioned demoder connect successively, export finally by one-dimensional data stream Knockdown block wherein.
2., for a two-dimentional run length constraint coding/decoding method for elongated code check, it is characterized in that realizing cataloged procedure by scrambler, comprise the following steps successively:
S101) the binary one-dimensional data stream of input is one group by every 2 bits and is divided into some one dimension 2 bit data word equably by one-dimensional data stream buffering and grouping module, and the data buffer this 2 bit data word being input to 2 × 2 code word generation modules is kept in;
S102) 2 × 2 code word generation modules read one dimension 2 bit data word one by one from data buffer, and one dimension 2 bit data word is changed into 2 × 2 two-dimensional constrains code words by the output scheme choosing encoding and decoding rule list;
S103) two-dimentional word cell array structure module is according to the storage size of 2-D data pen recorder, by size be 2N × 2M a two-dimensional data array with 2 × 2 word cell be one group, be divided into the two-dimentional word cell array comprising 2 × 2 identical two-dimentional word cells of N × M size, each 2 × 2 two-dimentional word cell writes of juxtaposition are masked as true, and wherein N and M is positive integer;
S104) 2 × 2 code words write two-dimentional word cell array module: 2 × 2 two-dimensional constrains code words obtained by step S102, the two-dimentional word cell of obtain with step S103 2 × 2 is benchmark, successively two-dimensional constrains code word write size is equaled in the two-dimentional word cell of 2 × 2 along two-dimentional word cell array diagonal direction from the upper right corner to the lower left corner, carry out selective filling according to the direct neighbor two dimension word cell of encoding and decoding rule list to the right of the two-dimentional word cell of current write and below simultaneously; If the two-dimentional word cell of this diagonal lines is all written into, enter next step, if all two-dimensional constrains code words have been filled complete, directly terminate cataloged procedure;
S105) judged whether that next diagonal lines not yet writes, if having, gone to step S104; If all 2 × 2 two-dimentional word cells of this two-dimentional word cell page have write full two-dimensional constrains code word, then enter next step;
S106) judge whether uncoded one-dimensional data word in addition, if having, go to step S102; Otherwise end cataloged procedure.
3. decoding method according to claim 2, is characterized in that realizing decode procedure by demoder, comprises the following steps successively:
S201) two-dimensional data array read from 2-D data pen recorder is temporarily left in 2-D data buffer module;
S202) two-dimentional word cell page constructing module reads size is the two-dimensional data array of 2N × 2M, this two-dimensional data array is evenly divided for minimum reading unit with 2 × 2, formation is contained in the two-dimentional word cell array of 2 × 2 identical two-dimentional word cells of N × M size, it is that readable mark is true that each two-dimentional word cell of juxtaposition two dimension word cell array reads zone bit, and wherein N and M is positive integer;
S203) two-dimentional word cell read module with 2 × 2 two-dimentional word cells of this two-dimentional word cell array for benchmark, according to encoder encodes order, along the diagonal lines of two-dimentional word cell array, reading mark selectivity successively according to each two-dimentional word cell from the upper right corner to the lower left corner reads the two-dimensional constrains code word in two-dimentional word cell array, if the two-dimensional constrains code word of this row is all read, enter next step, if the two-dimensional constrains code word of current two-dimentional word cell array has read complete, then go to step S205;
S204) the not yet decoding of next diagonal lines has been judged whether, if go to step S203; If the two-dimensional constrains code word of all diagonal lines of this two-dimentional word cell page is all read, enter next step;
S205) 2 × 2 code words are to the one-dimensional data mapping block decoding table corresponding according to selected encoding and decoding table, 2 × 2 two-dimensional constrains code words read from two-dimentional word cell read module are decoded into corresponding one dimension 2 bit data word according to generation order, after completing, enter next step;
S206) one dimension 2 bit data word obtained is assembled according to corresponding decoding precedence by one-dimensional data stream Knockdown block, and obtain corresponding one dimension binary data stream, decoding completes.
4. decoding method according to claim 2, is characterized in that, the method that the right of step S104 to the two-dimentional word cell of current write 2 × 2 two-dimentional word cell adjacent with below carries out selective filling is:
If the two-dimensional constrains code word a) being written to current 2 × 2 two-dimentional word cells does not belong to diagonal matrix or sub-diagonal matrix, then judge and the right of direct neighbor of current 2 × 2 two-dimentional word cells, the two-dimentional word cell in below write mark true and false; If true, be the two-dimensional constrains code word of diagonal matrix or sub-diagonal matrix at the two-dimentional word cell position Filling power corresponding with this zone bit; If false or undefined, then do not fill two-dimensional constrains code word;
After completing above-mentioned ablation process, the two-dimentional word cell write of putting current 2 × 2 two-dimentional word cells and filling two-dimensional constrains code word is masked as vacation, again can not be allowed write two-dimensional constrains code word after representing these positions;
If the two-dimensional constrains code word b) being written to current 2 × 2 two-dimentional word cells belongs to diagonal matrix or sub-diagonal matrix, after current two-dimentional word cell position writes this two-dimensional constrains code word, it is false for being write traffic sign placement.
5. decoding method according to claim 3, is characterized in that, the method for the two-dimensional constrains code word that step S203 selectivity reads in two-dimentional word cell page is:
If a) the two-dimentional word cell of current reading reads zone bit is true, then read the two-dimensional constrains code word in this two-dimentional word cell, the reading of this two-dimentional word cell of juxtaposition is masked as vacation, is not allowed to read namely; If the two-dimensional constrains code word of current reading does not belong to diagonal matrix or sub-diagonal matrix, the adjacent right of current reading word cell position is set in the lump, the two-dimentional word cell of below reads and be masked as vacation, namely do not allow to read;
If b) the two-dimentional word cell of current reading reads zone bit is false, then proceed to the data in the next one two dimension word cell reading this two-dimentional word cell place diagonal lines.
6. the decoding method according to any one of claim 2 ~ 5, is characterized in that, described encoding and decoding rule list sees the following form 1 and 2:
The coding schedule of the first coding and decoding rule of table 1
The decoding table of the first coding and decoding rule of table 2
7. the decoding method according to any one of claim 2 ~ 5, is characterized in that, described encoding and decoding rule list sees the following form 3 and 4:
The coding schedule of table 3 the second coding and decoding rule
The decoding table of table 4 the second coding and decoding rule
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