JP3051501B2 - Data compression method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention compresses and encodes an input character string such as character information using a universal algorithm.
Lud on over data compression method. In recent years, various types of data such as character codes, vector information, and images have been handled by computers, and the amount of data handled has rapidly increased. When dealing with large amounts of data, compressing the amount of data by eliminating redundant parts in the data,
It will be possible to reduce storage capacity and transmit faster.

[0002] Universal encoding has been proposed as a method capable of compressing such various data by one method. Here, the field of the present invention is not limited to character code compression, and can be applied to various types of data. In the following, one word unit of data is called a character, following the name used in information theory, Data in which arbitrary words are connected is called a character string.

[0003] As a typical method of the universal code,
There is a Ziv-Lempel code (for details,
For example, see Munakata "Ziv-Lempel Data Compression Method", Information Processing, Vol. 26, No. 1, 1985). Jibulempel code has (1) universal type and (2) incremental decomposition type (Incr
two algorithms have been proposed.

Further, as an improvement of the universal algorithm, LZSS codes (TC Bell, “Better OPM / L Tex
t Compression ”, IEEE Trans. on Commun., Vol.COM-3
4, No. 12, Dec. 1986), and QIC-122, a standard compression method for 1/4 inch cartridge magnetic tape.
There is a sign. As an improvement of the incremental decomposition type algorithm, there is a LZW (Lempel-Ziv-Welch) code (TA W
elch, “A Technique for High-Performance Data Comp
ression ", Computer, June 1984).

[0005] These improved codes are used for file compression of an auxiliary storage device and data transmission through personal computer communication.

[0006]

2. Description of the Related Art First, a conventional universal algorithm and a QIC-122 code which is one of the improvements will be described. [Universal type algorithm] The universal type algorithm is a data compression method that requires a large amount of calculation but can obtain a high compression rate.

That is, in the universal type algorithm, a character string to be coded is divided into a sequence that matches the maximum length from an arbitrary position of the coded character string, that is, a so-called subsequence, and the input character string is divided. Encode as a copy of the past substring that matches the maximum length. FIG. 9 shows an encoding method of the universal type Jeho Lempel code. In FIG. 9, a P-buffer 12 having a function as a dictionary stores character strings that have already been input, and a Q-buffer 10 serving as a character input unit.
Is a character string to be encoded. The pattern matching unit 14 compares the character string in the Q buffer 10 with the series in the P buffer 12 and searches the P buffer 12 for a matching character substring of the maximum length. And
In order to specify the substring that matches the maximum length searched in the P buffer 12, the information is coded as the start position (start address) coincidence length (length) of the maximum length matching sequence in the P buffer in FIG. If there is no matching series, the raw data is output together with the unmatched symbols.

Next, the coded character string in the Q buffer 10 is transferred to the P buffer 12, and a new coded character string is registered. Hereinafter, the same operation is repeated to decompose the input character string into subsequences and encode them. As described above, in the Zibo Lempel code, a current character string is encoded as a copy from an encoded past character string. In the case of using the Zivurempel code, the character code document information can be compressed to about 1/2.

[QIC-122 code] QIC (Quauter Inch Cartrrige S), a group of manufacturers centering on 3M
tandard Inc.) as a standard compression method for 1/4 inch cartridge magnetic tape. QIC-
In the algorithm of 122 codes, 20 buffers are used as the P buffer.
A mode having a 48-byte history and representing the character string to be encoded in the Q buffer as a copy of the character string in the P buffer;
It has two modes of encoding raw data one byte at a time. When the maximum length matching character string in the P buffer is two or more characters, the encoding is performed in the copy mode, and otherwise, the encoding is performed in the raw data mode.

FIG. 11 shows a QI expressed in the BNF meta language.
3 shows a codeword format of the C-122 code. Also BN
The meta symbols used in the F meta language have the meanings shown in FIG. The codeword format of the QIC-122 code of FIG. 11 will be described in detail as follows. (1) A compressed stream (Compressed Stream) is composed of a compressed string (Compressed String) and an end marker.

(2) The compressed string is represented by an ASCII raw byte following the identification bit 0 for raw data, and a compressed byte following the identification bit 1 for compressed data. (3) An ASCII raw byte is represented by one byte of 8 bits. (4) A compressed byte is a set of an offset (start position) and a length (match length).

(5) The offset (start position) is represented by 7 bits in the case of the identification bit 1. The identification bit 0 is represented by 11 bits. (6) The end marker is 1100000000000, and the offset is 0. (7) The bit b is 0 or 1. (8) The length (match length) is represented by a variable length code as shown in FIG.

FIG. 13 shows a specific example of the encoding of the QIC-122 code. FIG. 13 shows the character string “ABAAAAAAACAB”.
The case where "A" is input is taken as an example. For the first three characters "ABA", a bit sequence of ASCII raw bytes is output because the number of matching characters in the P buffer is one or less. The five "A" characters from the fourth character to the eighth character match the character "A" immediately before in the P buffer, so the compressed byte identification bit 7-bit offset identification bit Offset = 1 Length = 5 bytes The series "1 1 000 0001 110
Output as "0".

Here, the offset value indicating the start position of the substring having the maximum length match indicates the number of the latest registered position (address) in the P buffer going back. Since the ninth character "C" is not in the P buffer, it outputs an ASCII raw byte. The 10th to 12th characters "ABA" are P
Since the three characters have already been registered as the three characters from the head of the buffer, a bit sequence “1 1000100101” consisting of compressed byte identification bits, 7-bit offset identification bits, offset = 9 length = 3 bytes is output.

[0015] Since all the input characters have been encoded as described above, "1 100000" is output as end data, and the processing is terminated.

[Data compression method proposed by the present inventor]
However, in a conventional data compression method using a universal code using a Zibou Lempel code, a QIC-122 code, or the like, a character string having the maximum length to be copied is set to a “match start position” and a “match length”. When the number of encoded character strings held in the P buffer increases, the match start position is represented by a long bit number because the match start position is represented by the address of the memory constituting the P buffer. In such a case, there is a problem that redundancy remains between the encoded character strings and a high compression ratio cannot be obtained.

Accordingly, the present inventors have developed a data compression system using a universal code which can obtain a high compression rate by encoding with reduced redundancy between encoded character strings by taking in correlation between characters. is suggesting. FIG.
FIG. 4 shows the principle of the encoding process proposed by the present inventors. . In FIG. 14, assuming that a character string “acba...” To be coded from now on is stored in the Q buffer 10, the character string “b” includes the immediately preceding character “b” which is one character immediately before being coded. After the character "b", a search is performed to determine whether a character string matching the character string in the Q buffer 10 exists in the P buffer 12. It is assumed that, for example, character strings S1, S2, S3, and S4 can be searched as character strings that satisfy this condition.

Since the appearance numbers of the character strings S1 to S4 are registered in the P buffer 12 from the right, the character string S1: the first character string S2: the second character string S3: the third character string S4: the fourth The appearance order is set, and the appearance numbers 1, 2, 3, and 4 are sequentially assigned.

Next, a character string S4 that matches the input character string with the maximum length is searched from the character strings S1 to S4.
Is represented by the appearance number 4 and is output as a code word paired with the matching length. On the other hand, for a character string in which the preceding character "b" is continuous, such as the character string S2, the continuous character string S2
Is encoded by assigning an appearance number to either the start point or the end point. Also, the start and end points of the continuous character string S are 2
One occurrence number may be allocated and encoded as a code word of a set of two occurrence numbers and a matching length.

FIG. 15 is a flow chart showing an embodiment of a universal encoding algorithm using the appearance numbers of FIG. 14 using the QIC-122 code as an example. FIG.
First, in step S1, the contents of the P buffer are emptied, and the Q buffer is filled with input data to be encoded. Next, in step S2, the longest character string S in the P buffer that matches the character string from the position of the immediately preceding character in the Q buffer is searched. Subsequently, it is determined whether or not the longest character string S retrieved in step S3 has three or more characters.

If the longest character string S is one or two characters, the flow advances to step S4 to enter the raw data mode.
Output 1 byte of raw data consisting of II code. That is,
The codeword of the data format of FIG. 17A is output. on the other hand,
If the longest character string S is three or more characters, the process proceeds to step S5 to set the copy mode, and sets a flag bit 1 indicating that the data is compressed data, and codes a set of the order of appearance and the matching length of the longest character string. Become That is, a code word in the data format shown in FIG.

In step S6, the encoded character string or character in the Q buffer is transferred to the P buffer, and the same number of new characters are input to the Q buffer. QIC-12
In the two-code algorithm, the P buffer is fixed at 2048 bytes, and the oldest characters corresponding to the number of characters transferred to the P buffer are discarded from the P buffer. Hereinafter, similar processing is repeated.

FIG. 16 is a diagram for explaining a format using the QIC-122 codeword encoded in the duplication mode of FIG. 15. In FIG. 16, the offset is a 3-bit fixed-length representation indicating the appearance number as compared with FIG. ing. In this case, the order of appearance can be encoded up to the seventh. Here, the appearance number 0 is E
Used for ND mark. Since the matching length represents a character string of three or more characters including the immediately preceding character, the matching length = | S | -2 is used. Furthermore, although the appearance numbers are counted from the right, they may be counted from the left.

As described above, when the appearance number is used instead of the conventional 7-bit or 11-bit offset indicating the start position, the offset indicating the appearance number can be represented by a small number of bits of 3 bits. Thus, the compression ratio can be improved.

[0025]

However, in the data compression system using the universal code which takes in the correlation between characters proposed by the inventors of the present invention, the appearance number in the P buffer is represented by a fixed length. If the number of occurrences of the subsequence that has the maximum match length with respect to the number of occurrences of the preceding character is small, unnecessary bits may be taken extra or, conversely, if the maximum number of occurrences is exceeded. May not be able to represent all occurrence numbers of the maximum matching length subsequence, and there is a problem that the compression code is wasted.

The present invention has been made in view of such a problem. Even if the number of appearances is undecided, data compression using a universal code which efficiently expresses bits and further improves a compression ratio is performed. The aim is to provide a scheme.

[0027]

FIG. 1 is a diagram illustrating the principle of the present invention. First, the present invention stores an encoded character string already proposed by the present inventors in the dictionary 12 and starts the dictionary 12 starting from the same first character as the immediately preceding character 18 for the input character string of the character input unit 10. , The number n of occurrences of the matching substrings S1, S2, S3, and S4 of the encoded character string stored in the substring S4 is searched, and the substring S4 that matches the maximum length is searched. The present invention is directed to a data compression method using a universal code including an encoding unit 14 that encodes a set of an appearance order n in which the character immediately preceding the maximum length matching subsequence S4 appears and a matching length L.

According to the present invention, there is provided a data compression system using a universal code in which the correlation between characters is taken in as described above to reduce the redundancy between encoded character strings.
It is characterized in that the appearance number i is variable-length coded according to the number of bits based on the number of appearances n. Also, the encoding unit 14 performs variable length encoding by bit fraction compensation,
Where “l” representing the smallest integer equal to or greater than log ₂ n
og ₂ n ”, p is the number of bits, and n
If n ^* is represented by (p-1) bits excluding the most significant bit of, and i ^* is represented by (p-1) bits excluding the most significant bit of the occurrence number i to be encoded, If i ^* > n ^* , i ^* is a variable length code. If i ^* ≦ n ^* , a variable length code is obtained by adding the most significant bit of the occurrence number i after i ^* .

Further, as variable-length encoding by Phasing in Binary Codes, the encoding unit 14 uses “log ₂ ” representing a minimum integer equal to or greater than log ₂ n when the number of appearances is n.
The number of bits given by "n" is p, and the number represented by (p-1) bits excluding the most significant bit of the number of occurrences n is n ^*
And then, further except for the most significant bit of the occurrence number i to be encoded (p-1) if those expressed in bits and i ^*, the i ^* a variable length code if i ^* <2 and ^P -n-1 if i ^* ≧ 2 a ^P -n-1, and variable-length code i ^* to the value obtained by adding (2 ^P -n-1) represented by p bits.

Furthermore, the encoding unit 14 regards n substrings that match the input character string following the immediately preceding character 18 as appearing with equal probability, and encodes the appearance order i in multi-level arithmetic. . Further, the encoding unit 14 converts the input character string into １ ／
Encode to the QIC-122 code which is a standard compression method for inch cartridge magnetic tape.

[0031]

As described above, according to the present invention, the immediately preceding character (P
Search for all the matching substrings in the encoded character set whose first character is the latest character in the buffer), and search for n
When encoding as a copy of a subsequence that matches the maximum length in the matching subsequence, the present invention uses what is conventionally coded with the set of the start position of the maximum matching length subsequence and the matching length. ,
The subsequence having the maximum matching length is represented by a set of the occurrence number i and the matching length in the P buffer and coded, and further, the occurrence number i is coded as a variable length instead of a fixed length.

For this reason, the conventional start position (start address)
, The number of occurrence numbers i of the subsequence is much smaller,
Since the appearance number i can be represented by a small number of bits and the appearance order is represented by a variable-length bit number, the code representation can be represented by a small number of bits without waste, and a high compression rate can be obtained.

[0033]

FIG. 2 is a block diagram showing an embodiment of the present invention. In FIG. 2, reference numeral 16 denotes a buffer memory, which is allocated to a Q buffer 10 as a character string input unit for storing a character string to be encoded and a P buffer 12 functioning as a dictionary in which encoded character strings are registered. Can be

Reference numeral 14 denotes a pattern matching unit as an encoding unit using a CPU, which searches the P buffer 12 for a partial sequence that matches the maximum length of the character string in the Q buffer 10 according to the universal encoding algorithm, and matches the maximum length. As a copy of the subsequence, a codeword consisting of a set of the start position and the matching length is output. That is, the pattern matching unit 14
Assuming that the number of occurrences of the immediately preceding character in the P buffer 12 is n and the occurrence number is i, the encoding process shown in the encoding flowchart of FIG. 3 is performed.

The flowchart of FIG. 3 is basically the same as the scheme already proposed by the present inventors shown in FIG.
The difference is that the number n of occurrences of the immediately preceding character in the P buffer is determined in step S2, and the longest matching character string S is determined in step S5.
Is represented by the number of bits based on the number n of occurrences and is subjected to variable-length encoding. FIG. 4 is a flowchart showing a universal decoding algorithm for restoring a codeword obtained by the data compression method of the present invention.

In the decoding process of FIG. 4, step S3
To determine the duplication mode from the flag bit 1 and step S
5, the number n of occurrences of the immediately preceding character in the P-buffer is obtained in the same manner as in step S2 of FIG.
Is decoded, and in step S6, the longest character string S is restored from the occurrence number and the matching length of the character string immediately before in the P buffer.

Next, a description will be given of a specific embodiment of variable-length encoding of an appearance number performed in the encoding processing of the present invention. (1) Variable Fixed Length Coding Assuming that the number of occurrences of the immediately preceding character in the P buffer is n, the occurrence number is encoded by expressing the occurrence number i with “log ₂ n” bits. Here, “log ₂ n” represents a minimum integer equal to or greater than log ₂ n.

For example, when encoding a certain input character string, P
Assuming that the number n of appearance characters obtained by the search in the buffer is n = 12, the appearance number i of the longest character string S at this time is
Is a variable-length code represented by “log ₂ n” = “log ₂ 12” = 4 bits. This is called variable fixed length coding. (2) Variable Fixed-Length Coding by Bit Fraction Compensation In the variable fixed-length coding of the above (1), if the occurrence number i up to the maximum value i = n corresponding to the number n of occurrences is represented by “log ₂ n” bits A bit loss of “log ₂ n” −log ₂ n bits occurs. Bit fraction compensation is a technique for improving the coding efficiency by reducing the loss of the fraction of bits and expressing the appearance number i (for example, “Ziv-Le”
Improvement of mpel code and performance evaluation by simulation
(II) ", IEICE Technical Report C84-135, pp.1-8,
1984).

In this bit fraction compensation, when the maximum appearance number corresponding to the appearance number n is i = n, the bit number p is p = “log ₂ n”, and the most significant bit of the appearance number i is excluded. What is represented by (p-1) bits is i ^* . Similarly, a value represented by (p-1) bits excluding the most significant bit of the maximum appearance number n is n ^*
And

[0040] Under such conditions, the variable-length code words of the appearance number i by bit fraction compensation is, when i ^* ≦ n ^*, expressed in i ^*, when i ^*> n ^*, i ^* of This is indicated by adding the most significant bit to the end. FIG. 5 shows an example in which the appearance numbers i = 0 to 11 of the appearance number n = 12 are represented by bit fraction compensation.

[0041] In FIG. 5, p = a "log ₂ n" = "log ₂ 12" = 4 bits p-1 = 3 bits, i ^* ≦ 3 when bit, expressed in i ^*, i ^*
When> 3 bits, i ^* is followed by the most significant bit.

That is, reference numbers (appearance numbers) i = 0 to 11
In the four-bit binary notation, four reference numbers i = 4 to 7 satisfying the above conditions are represented by lower three bits i ^* excluding the upper one bit. On the other hand, the reference numbers i = 0 to 3 and i = 8 to 11 satisfying the above conditions are distinguished by attaching the lower 3 bits i ^* excluding the upper 1 bit to the upper 1 bit in binary notation. [Phasing in Binary Codes] This PBC variable-length encoding is performed, for example, in “Text Compression”, Prentice-Hall I
nc. 1990, pp. 293-294.

In PBC variable length coding, i <2 ^P -n-
When 1, expressed by i ^*, when i ≧ 2 ^P -n-1, was added to the occurrence number i (2 ^P -n-1) value (i + 2 ^P -n
-1) is represented by p bits. FIG. 6 shows a specific example of PBC encoding for the occurrence numbers (reference numbers) i = 0 to 11 when the number of appearances n = 12.

In FIG. 6, the above condition is satisfied when reference numbers i = 0 to 3, and in this case, p
= The binary display code of i = 0 to 3 expressed by 4 bits is expressed by PBC with 3 bits excluding the most significant bit. The above condition is satisfied when reference numbers i = 4 to 11, and in this case, i = i expressed by p = 4 bits.
= 4 to 11 binary representations and 4 binary representations "100" are represented by 4 bits in PBC representation. (4) Multi-Level Arithmetic Coding The variable-length coding of (2) and (3) is represented by p bits and p-1 bits by the occurrence number i. Can be reduced, but there is still redundancy in the appearance number sequence as a whole.

Therefore, in order to further reduce the bit loss, the occurrence number (symbol) i is multi-value arithmetically encoded by assuming that n character strings appear with equal probability (multi-value arithmetic code). For example, see the document “Arithmet
ic Coding for Data Compression ”, Communication o
f the ACM, June 1987, Vol. 30, No. 6, pp. 520-540).

FIGS. 7 (a) and 7 (b) show schematic flows of encoding and decoding of multi-level arithmetic encoding used for encoding a plurality of symbols. FIG. 7 (a) multi-level arithmetic coding associates a data string with a point on a number line of [0, 1].
The [0, 1] section is sequentially subdivided according to the cumulative appearance probabilities obtained from the appearance probabilities of the symbols that have appeared for each symbol.

FIG. 8 shows the processing contents of the multi-level arithmetic coding. Assuming that the first appearance number n is n = 4 and the appearance number i of the longest character string is i = 2, Upper limit =
The section corresponding to i = 2 in the section divided into four while the lower limit of ten = 0 is selected. Next, the same number of occurrences of the second time is n = 2, and the occurrence number i of the smallest character string in this case is
Is the i = 1st, the section in the four sub-areas is further selected.

Thereafter, the subdivision of the selected section proceeds similarly, and when the section based on the final character string is selected Nth time,
A combination with an arbitrary point value (a value indicating the upper or lower limit of the section) in the selected section is output as a code word.
Further, in the algorithm of FIG. 7A, a code word cannot be obtained until encoding of the entire symbol sequence is completed, and decoding cannot be performed unless the entire code word is obtained. In value arithmetic coding, a codeword can be obtained in bit units by performing calculations using a fixed-length register having a finite number of digits.

That is, in the first encoding shown in FIG. 8, for example, the upper limit is "001" and the lower limit is "010", and both the most significant bits are "0". "0" is output. The same applies to the second and subsequent times. Furthermore, when using multi-valued arithmetic coding, the number of occurrences of the “match length” of the character string is counted for each match length, and the occurrence probability of the match length estimated from the count value is calculated together with the occurrence number and the multi-value arithmetic. It may be encoded.

In the above embodiment, the QIC-122 code is used as an example, but the present invention is not limited to this, and the present invention can be applied to any appropriate universal code such as a Zibo Lempel code.

[0051]

As described above, according to the present invention, when the coded character string is a copy of the coded character string, and the start position of the copy is represented by a set of "appearance order" and "match length", Since the “appearance order” is represented by a variable-length bit number, the code representation can be represented by a shorter bit number without waste, and a high compression rate can be obtained.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating the principle of the present invention.

FIG. 2 is a configuration diagram of an embodiment of the present invention.

FIG. 3 is a flowchart showing a QIC-122 encoding algorithm using the present invention.

FIG. 4 is a flowchart illustrating a decoding algorithm of a codeword encoded according to the present invention;

FIG. 5 is a diagram illustrating a specific example of variable-length encoding by bit fraction compensation according to the present invention;

FIG. 6 is a diagram illustrating a specific example of PBC encoding according to the present invention;

FIG. 7 is an explanatory diagram showing the ineffectiveness of multi-level arithmetic coding and a decoding algorithm according to the present invention;

FIG. 8 is an explanatory diagram showing processing contents of multi-value calculation encoding according to the present invention;

FIG. 9 is an explanatory diagram of an encoding method of a universal type Jeho Lempel code.

FIG. 10 is a diagram illustrating the data format of a universal codeword.

FIG. 11 is an explanatory diagram of a format of a QIC122 code.

FIG. 12 is an explanatory diagram of the BNF meta-language used in FIG.

FIG. 13 is an explanatory diagram showing a specific example of encoding using a QIC-122 code;

FIG. 14 is a diagram illustrating the principle of encoding processing proposed by the present inventors.

FIG. 15 shows QIC-122 proposed by the present inventors.
Flowchart showing the encoding algorithm

16 is an explanatory diagram of a code word format in the duplication mode of FIG. 15;

17 is an explanatory diagram of the data format of the code word in FIG.

[Explanation of symbols]

 10: Character input unit (Q buffer) 12: Dictionary (P buffer) 14: Encoding unit (pattern matching unit) 16: Buffer memory 18: Previous character

────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Hirotaka Chiba 1015 Kamiodanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture Inside Fujitsu Limited (56) References JP-A-3-70214 (JP, A) JP-A-3-78322 (JP, A) JP-A-3-209922 (JP, A) JP-A-4-256192 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) G06F 5/00 H03M 7 / 40

Claims (6)

(57) [Claims] An encoded character string is stored in a dictionary, and a character input is performed from among the encoded character strings stored in the dictionary.
Starts with the same character as the character immediately before the character string input from the
Search for a matching substring that matches the input string
The number of occurrences of the matching substring is detected, and the maximum length matches with the input character string from among the matching substrings.
Search for the largest matching subsequence to indicate the order in which the character immediately preceding the maximum length matching subsequence appears.
The occurrence number, the maximum matching substring and the input character string,
And the occurrence number according to the number of bits based on the number of occurrences.
Features and to Lud over data compression method that variable-length coding Te. Wherein at the data compression method of claim 1, wherein said variable-length coding, the occurrence number i represents the smallest integer more than log ₂ n "log ₂ n" bit variable length features and to Lud over data compression method to be represented by the symbol. 3. In data compression method of claim 1, wherein said variable-length coding, log when the number of occurrences is n
_The number of bits given by “log ₂ n” representing the smallest integer of ₂ n or more is represented by p, and the number represented by (p−1) bits excluding the most significant bit of the number of occurrences n is represented by n ^* . appearance except for the most significant bits of the number i (p-1) if those in bits set to i ^*, i ^*> if n ^* a i ^* a variable-length code, i ^* ≦ n a ^* long to if, i ^* the occurrence number i features and to Lud <br/> over data compression method to be variable-length codes obtained by adding the most significant bit of after. 4. In the data compression method of claim 1, wherein said variable-length coding, log when the number of occurrences is n
_The number of bits given by “log ₂ n” representing the smallest integer of ₂ n or more is represented by p, and the number represented by (p−1) bits excluding the most significant bit of the number of occurrences n is represented by n ^* . When i ^* is represented by (p−1) bits excluding the most significant bit of the occurrence number i, if i ^* <2 ^P− n−1, i ^* is a variable length code, and i ^* ≧ if 2P-n-1, i ^* the characteristics and to Lud over data compression how to be a variable length code represents a value obtained by adding 2 ^P -n-1 with p-bit
Law . 5. In data compression method of claim 1, wherein said variable-length coding assumes that n partial string that matches the input character string following the immediately preceding character appear with equal probability, the appearance features and to Lud over to the multilevel arithmetic coding order i data compression
How . 6. In claim 1 data compression method of claim 5, wherein said variable-length encoding, the input string is a standard compression scheme of 1/4 inch cartridge magnetic tape QIC- 12
Features and to Lud over data compression method to be encoded in code words of the two code.