JP3350385B2 - Code generation method and coding method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] 1. Field of the Invention [0002] The present invention relates to a method of encoding data, and more particularly, to a method of encoding numerical data represented by a natural number from 1 to N.

[0002]

2. Description of the Related Art Several methods have been proposed for encoding data represented by natural numbers. As one of them, a code for representing a natural number from 1 to N has been developed by Fiala and Greene and is called an SSS code. The SSS code has a feature that a large natural number is described with a long code length and a small natural number is described with a short code length. This feature works effectively when the exact appearance probability of the symbol of the data to be encoded is unknown, but it is known that generally small values are likely to appear and large values are unlikely to appear. The SSS code has three bit length parameters (start, step, and stop). A numerical value from a natural number of 1 to 2 {start (operator を represents a base) is represented by a sign bit having a bit length start. For a numerical value larger than that, the bit length is increased by step, and a code bit of (step + start) bits is allocated. The range of numerical values that can be represented by (step + start) bits is from 2 @ start + 1 to (2 @ (2 * step + start) -2 @ star
t) / (2 @ step-1) (operator * represents multiplication). When a code is to be assigned to a numerical value larger than that, the bit length is increased again by step, and (2 * step + start) bits of the sign bit are assigned. Thus, (2 ＾ (3 * step + sta)
rt) -2 ＾ start) / (2 ＾ step-1). When assigning a code to a larger numerical value, the bit length is further increased step by step, and a code is assigned to the numerical value until the bit length finally becomes stop. Therefore, SSS
The sign is maximum (2 @ (stop + start) -2 @ st
Signs can be assigned to numerical values up to (art) / (2 @ step-1). The SSS code cannot uniquely identify each code only by the code bit. Therefore, to make each code identifiable, (k * step
+ Start) An identification bit indicating the length k is added before the sign bit of the bit. The identification bits are generated by adding k followed by ones followed by ones. However,
When the bit length is stop, the last one of the identification bits can be omitted. As an example of the SSS code, (star
FIG. 7 shows the case where the values of (t, step, stop) are (0, 1, 5) and (1, 2, 5). Similarly, a CBT code has been proposed as a code for representing a natural number. When the encoding target is a natural number from 1 to N, if a fixed length code is used, the code length is k = <log2 (N)>
(<X> represents the minimum integer value not less than x). Generally, it is known that fixed-length codes have redundancy except when N is represented by the power of two. In order to reduce the redundancy, the CBT code uses a variable length code for the numerical value n when 1 ≦ n ≦ 2 ＾ k−N, when n−1 is k−1 bits, when 2 ＾ k−N <n ≦ N, n + 2 ＾ k-N-1 is represented by a bit length of k bits. FIG. 8 shows an example of the CBT code when N = 10.

[0003]

Generally, when encoding natural numbers 1 to N, the SSS code has a problem that the code has redundancy. For example, when a natural number up to N = 37 is encoded by SSS (0, 1, 5) in FIG. 7, numerical values 32 to 37 whose code bit length is “stop” are numerical values SSS (0, 1, 5) code 32 00000 00000 33 00000 0000 34 00000 0010 35 00000 00011 36 00000 00100 37 00000 00101. At this time, it is apparent that a uniquely decodable code is formed if there are at most three code bits. As can be seen from this example, the value of N is just SS
Except when it matches the maximum value that can be encoded with the S code,
SSS codes have redundancy. As a method for reducing the redundancy, a CBT code is applied to the last m numbers whose code bit length is “stop”. In the above example, since 2 ＾ k−N = 2, the numerical value 32
The code bit length of the code for the codes 33 and 33 is represented by 2 bits, and the code bit length of the codes for the numerical values 34 to 37 is represented by 3 bits, so that the code is represented by the following formula. 00000 111, and the code bit length of the numerical values 32 and 33 can be reduced by one bit compared to the fixed length code. Although the use of CBT codes reduces code redundancy, another problem arises. Here, paying attention to the codes of the numerical values 16 to 31, since the numerical codes are 16 to 3100001xxxx (x represents 0 or 1), the code length is 9 bits. Therefore, CBT
When a code is used, the numerical value 3 is obtained from the code length of the numerical values 16 to 31.
The code lengths of 2 to 37 are smaller. When the SSS code is used, it is premised that the smaller the value of the target data is, the higher the probability of appearance is. Therefore, the second method is not optimal from the viewpoint of entropy. SUMMARY OF THE INVENTION It is an object of the present invention to provide a code generator for generating a code having a small redundancy in which the bit length of a small numerical value is not always greater than the bit length of a large numerical value for encoding natural numbers up to an arbitrary N. A method and an encoding method for performing encoding using the code are provided.

[0004]

FIG. 1 shows a basic flow of a code generation method for achieving the above object. 101
Is a predetermined number N1, N2,..., Nm,.
N1 <N2 <.. <Nm <.. <NM <N) are determined, and natural numbers from 1 to N are defined as sections (0, N1),
(N1, N2),..., (NM, N), where the notation “(” and “)” represents an open section,
The notation "[" and "]" indicates a closed section. Here, (0, N1),..., (NM-1, N
M] is set to be the second power. In particular,
An initial code bit length a is set, and a predetermined number Nm is set to (2 ＾ a).
* Set to the value of (2 @ m-1), and set the maximum number NM of the predetermined number to the value of the maximum integer M satisfying (2 @ a) * (3 * 2 @ (M-1) -1) ≤N Therefore set. Reference numeral 102 denotes a step of generating an identification bit for identifying a section including an arbitrary natural number for each section. In particular, the identification bits are in the interval (0, N1), (N1, N2),.
It represents the bit length of a code bit representing a natural number included in each section of (NM-1, NM).
03 is the interval (0, N1), (N1, N2),.
This is a step of allocating fixed-length code bits to natural numbers included in each section of (NM-1, NM).
In particular, fixed bit lengths a, a + 1,...
A code bit of a + M-1 is assigned.
104 denotes a natural number included in the section (NM, N).
This is the step of assigning variable-length code bits. In particular, for the section (NM, N), 2 ＾ k−N code bits with a bit length a + M bits (where k = <log2
(N-NM)>) and a bit length a
+ M + 1 bits are assigned to 2 * N-2 @ k natural numbers. FIG. 2 shows a basic flow of an encoding method for achieving the above object. 20
1 is a step of inputting data n (1 ≦ n ≦ N) to be encoded. 202 is a predetermined number N1, N2,.
Nm, ..., NM (0 <N1 <N2 <... <Nm <...
<NM <N) (0, N1), (N
, N2],..., (NM, N), to which an identification bit for identifying whether the data n belongs is given.
N]. 204
Indicates that, as a result of the determination, the data n is in the interval (0, N1
, (N1, N2),..., (NM-1, NM), a step of adding a fixed-length code bit to the data n.
M, N], a step of adding variable-length code bits to the data n. 206 is a step of outputting the identification bit and the code bit as a code representing the data n. As described above, according to the code generation method of the present invention, by making the code of the section (NM, N) variable length, it is possible to reduce the redundancy that occurs when encoding natural number data. Is set to the value of (2 ＾ a) * (2 ＾ M-1) according to the value of the maximum integer M that satisfies (2 ＾ a) * (3 * 2 ＾ (M−1) −1) ≦ N. By doing so, a code can be generated such that the code length of a small natural value does not always become larger than the code length of a large natural value. , Natural number data can be efficiently encoded using the code generated by.

[0005]

Embodiments of the present invention will be described with reference to the drawings. First, the code generation method of the present invention will be described. FIG. 3 is a diagram showing the flow of the embodiment of the code generation method of the present invention. 301 is a step of initializing parameters. The parameters are four, the initial code bit length a, the bit length increment L, the section number m, and the number Nm that defines the range of the section (represented as section Rm) identified by the section number m. The initial code bit length a is a code bit length of a code corresponding to a natural number included in the section (0, N1), and the initial code bit length a is set to an appropriate value based on prediction of the appearance probability of encoded data. Rm is (Nm-1, Nm)
Represents the range. Where N0 = 0 and N (M + 1)
= N. The bit length increment L indicates the increment of the code bit length in each section with respect to the initial code bit length a. That is, the code bit length of each section is a + L. Each parameter is set to L = 0, m = 1, and N0 = 0 as initial values. In this embodiment, the sections R1, R2, R3,.
M is 2 {a, 2 (a + 1), 2}
Codes are generated such that (a + 2),..., 2） (a + M−1). At this time, since Nm represents the maximum number of sections Rm, the value of Nm is the sum of the sizes of the sections R1 to Rm, and Nm is the sum of geometric series of the first term 2 ＾ a and the common ratio 2 Therefore, Nm = (2 ＾ a) * (2 ＾ m−1). 302 is the maximum value N of the natural number and the initial code bit length a
(2 ＾ a) * (3 * 2)
This is a step of comparing the magnitudes of ＾ (m-1) -1).
If N is smaller, steps 303 to 306 are executed to assign fixed-length code bits to natural numbers in the section Rm, and the process returns to 302 to generate a code for the next section. Otherwise, steps 307 to 309 are executed to assign variable length code bits to natural numbers in the section Rm, and the process ends. Here, in the conditional branch of 302, N and (2 ＾
a) The reason for comparing * (3 * 2 ＾ (m−1) −1) will be described. First, the size of the section R (M-1) is 2 ＾
Since (a + M−1), the code bit length of the section R (M−1) is a + M−1 bits. If the size of the last section RM is smaller than 2 ＾ (a + M−1), the code bit length of the section RM can be represented by bits shorter than a + M−1 bits. Therefore, the size of the section RM is the section R
It must be larger than (M-1). FIG.
(A) illustrates a state when codes are generated up to the section R (m-1) on a number line. Nm = (2 ＾ a) *
(2 ＾ m−1), the range of the section Rm is usually (2 ＾ a
* (2 @ (m-1) -1), 2 @ a * (2 @ m-1)]
However, as shown in FIG. 4A, the section (2 ＾ a *
(2 ＾ (m-1) -1), 2 ＾ a * (2 ＾ m-1)], the section (2 ＾ a * (2 ＾ m) from the size 2 ＾ (a + m-1)
−1), N] when the size N−2 ＾ a * (2 ＾ m−1) is smaller, ie, N−2 ＾ a * (2 ＾ m−1).
When <2 ＾ (a + m−1), the range of Rm is as shown in FIG.
(Nm−1, Nm) as shown in FIG.
−1 = 2 ＾ (m−1) −1 and Nm = N. Also, as shown in FIG. 4C, the section (2 ＾ a * (2 ＾
(M-1) -1) When the size of the section (2 ＾ a * (2 ＾ m-1), N] is larger than the size of 2 ＾ a * (2 ＾ m-1)], the value of Rm The range is shown in FIG.
-1, Nm]. Step 303 is a step of calculating Nm in order to determine the range of the section Rm to which fixed-length code bits are allocated. As described above, the value of Nm is Nm = (2
＾ a) * (2 ＾ m−1). 3
Step 04 is a step of setting an identification bit for the section Rm. The identification bit indicates the code length of the code bit in each section. The identification bit may be any bit string that can be uniquely decoded. In the present embodiment, a bit length increment L is encoded and used as an identification bit. That is, the identification bit is configured by setting L bits 0 and then setting bit 1 for indicating the division of the identification bit. Therefore, the identification bits for m = 0, 1, 2,... Are 1, 01, 001,. The code bit length of the section represented by such identification bits is a length obtained by adding the initial code bit length a to the number of bit 0 of the identification bits. Step 305 is a step of setting a sign bit for a natural number in the section Rm. A fixed length code of a + L bits is assigned to 2 ＾ (a + L) natural numbers included in the section Rm. For example, when a natural value to be encoded is n, a bit string in which a value of n−N (m−1) +1 is represented by a + L bits is a natural number n code bits.
306 is a step of updating the parameters. In order to generate a code for the next section, the value of the section number m is increased by 1, and accordingly, the value of the bit length increment L is also increased by 1. Now, by executing the processing of 302 to 306, the generation of the code for one section ends. 3
After executing the process of step 06, the process returns to the conditional branch of step 302 again.
Here, as a result of the numerical comparison, N is (2 ＾ a) * (3 * 2 ＾).
If the value is equal to or more than the value of (m-1) -1), a code for the last section is generated, and the process is terminated. The last section (Nm,
N] to generate a code for
At step 7, an identification bit is set. The identification bit here is L
Bits 0 are set, but unlike 304, bit 1 indicating the delimitation of the identification bit is not required. Because the section (Nm, N] is the last section, there is no possibility that bit 0 continues as an identification bit any more.
Although code bits are allocated, a CBT code is used as a variable length code in this embodiment. 308 is a step of obtaining the code length of the CBT code. The size of the section RM is 2 ＾
(A + L) or more and less than 2 ＾ (a + L + 1), C
The code length of the BT code is a + L and a + L + 1. Therefore, the coding of the section RM is performed with the code length k = a + L. 309 is a step of setting a code bit for a natural number in the section RM based on the CBT code. Section RM
Is N−N (m−1), so that N (m−1) ≦ n
When ≦ N (m−1) + 2 ＾ k−N, n is encoded with a + L bits, and when N (m−1) + 2 ＾ k−N <n ≦ N, n is encoded with a + L + 1 bits. FIG. 9 shows reference numerals created based on this embodiment. Here, a = 0, 2
And N = 37. Next, an encoding method for encoding natural number data using a code created by the code generation method described above will be described. FIG. 5 is a diagram showing a flow of an embodiment of the encoding method of the present invention. Reference numeral 501 denotes a step of inputting data n to be encoded. n is limited to the range of 1 to N. Reference numeral 502 denotes a step of examining a section Rm to which n belongs from the value of the data n, and determining an identification bit I (m) of the section Rm and a parameter for encoding. The coding parameters are the code bit length L (m) and the head data N (m) of the section Rm, and represent the sum of the initial code bit length and the increment of the code bit, and the minimum data of the data belonging to each section. In the present embodiment, the identification bits and the encoding parameters are referred to by the table shown in FIG. That is, since the identification bit and the encoding parameter take the same value with respect to the data included in the section Rm, the item of the section Rm to which n belongs from the input data n should be referred to. In step 503, it is determined whether or not the data n belongs to the last section (NM, N), and in this embodiment, the logical sum of all the bits constituting the identification bit I (m) is obtained. As is clear from the code generation process,
Since all the sections other than the last section (NM, N) include bit 1 to indicate the end of the identification bit, the logical sum thereof is 1, but constitutes the identification bit of the section (NM, N). Since all the bits are 0, the logical sum is 0. Therefore, when the obtained logical sum is 0, the data n is in the section (N
M, N], and when it is 1, it belongs to other sections. 5
04 is false in the judgment result of 503 (that is, the logical sum is 1)
Is a step of adding a sign bit C (n) to the data n. The sign bit C (n) at this time
Is L (m). In this embodiment, n−N
When the value of (m) is obtained, since the value takes a value of 0 to 2 ＾ L (m) −1, the value of n−N (m) is
(M) Encode with a binary string of bits. 505 is 503
Is true (that is, the logical sum is 0), a sign bit C (n) is added to the data n. When the value of nN (m) is obtained in the same manner as in step 504, the value takes a value of 0 to NN (m).
Apply the CBT code to the value of -N (m). That is, the constant k = 2 ＾ (L (m) +1) − (NN−m (m) +
1), when n−N (m) <k, n−N (m)
Is encoded by a binary sequence of L (m) bits, and n−N
When (m) ≧ k, the value of n−N (m) + k is represented by L (m) +
Encode with a 1-bit binary sequence. 506 is a step of combining the identification bit I (m) and the code bit C (n) as a code representing the data n, and outputting the code.

[0006]

As described above, according to the code generation method of any one of claims 1 to 7, for a natural number data having an arbitrary size represented by 1 to N, the code length of a small number is always larger than that of a larger number. The coding can be performed so as to be equal to or shorter than the code length and to minimize the code redundancy. This makes it possible to generate an efficient code for natural number data for which it is known that the exact probability distribution is unknown but that a smaller numerical value has a higher probability of occurrence.
According to the encoding method of the eighth aspect, natural number data can be efficiently encoded using the code generated by the above code generation method.

[Brief description of the drawings]

FIG. 1 is a diagram showing a basic flow of a code generation method according to the present invention.

FIG. 2 is a diagram showing a basic flow of the encoding method of the present invention.

FIG. 3 is a diagram showing a flow of an embodiment of a code generation method of the present invention.

FIG. 4 is a diagram for explaining division of natural number data.

FIG. 5 is a diagram showing a flow of an embodiment of the encoding method of the present invention.

FIG. 6 is a diagram showing an example of a table in step 502 in FIG. 5;

FIG. 7 is a view showing an example of an SSS code.

FIG. 8 is a view showing a code example using a CBT code.

FIG. 9 is a view showing a code example according to the code generation method of the present invention.

[Explanation of symbols]

 101 natural number

Claims (8)

(57) [Claims] 1. A code generation method for generating a code corresponding to a natural number from 1 to N, wherein a predetermined number of N1, N2,
.., Nm, .., NM (0 <N1 <N2 <.. <Nm
<NM <N), and 1 to N according to the predetermined number.
Of the interval (0, N1), (N1, N2),.
(NM, N), a second step of generating an identification bit for identifying an interval including an arbitrary natural number with respect to the interval,
N1], (N1, N2),..., (NM-1, NM), a third step of allocating a fixed-length code bit to a natural number included in each section;
N], a fourth step of allocating variable-length code bits to natural numbers included in the section [N]. 2. The section (0, N1), (N1, N1
2. The code generation method according to claim 1, wherein the size of [2],..., (NM-1, NM) is the second power. 3. The first step sets an initial code bit length a and sets the predetermined number Nm to (2 ＾ a) * (2 ＾ m
-1), and the predetermined maximum number NM is set to (2 ＾
The code generation method according to claim 2, wherein a) is set according to a value of a maximum integer M that satisfies a) * (3 * 2 ^ (M-1) -1) ≤N. 4. The method according to claim 2, wherein in the second step, the identification bit is assigned to the interval (0, N1), (N1, N2),.
2. The code generation method according to claim 1, wherein the code length represents a bit length of the code bit representing a natural number included in each section of (NM-1, NM). 5. The section (0, N1), (N1, N1
2],..., (NM−1, NM) are the first bits of a number equal to the difference between the bit length of the sign bit representing a natural number included in each section and the initial sign bit length a. Bit, followed by one second bit, and the identification bit for the section (NM, N) is obtained by converting the second bit of the identification bit of the section (NM-1, NM) to the first bit. 5. The code generation method according to claim 4, wherein the code generation method comprises a replacement. 6. In the third step, the sections (0, N1], (N1, N2),..., (NM-1, N
M], the bit length a, a + 1,..., A + M
3. The code generation method according to claim 2, wherein the fixed-length code bits of -1 are assigned. 7. In the fourth step, for the section (NM, N), 2 ＾ k−N code bits having a bit length a + M bits (where k = <log2 (N−N
M)>), and the bit length a + M + 1
3. The code generation method according to claim 2, wherein the code bits are assigned to 2 * N-2 @ k natural numbers. 8. An encoding method for encoding data associated with natural numbers from 1 to N, a fifth step of inputting data n (1 ≦ n ≦ N) to be encoded, and a predetermined number N1. , N2,..., Nm,.
The sections (0, N1), (N1, N2),... Divided by <N1 <N2 <... <Nm <.
A sixth step of assigning an identification bit for identifying which of (NM, N] the data n belongs to; and a seventh step of determining whether the data n belongs to the section (NM, N). And the data n is in the interval (0, N1],
(N1, N2],..., (NM-1, NM), an eighth step of adding a code bit having a fixed length in each section to the data n; NM, N], a ninth step of adding a code bit having a variable length in the section to the data n;
An encoding method, comprising: a tenth step of outputting the identification bit and the code bit as a code representing the data n.