KR20030096504A - method and apparatus for multi-symbol data compression using a binary arithmetic coder - Google Patents

Abstract

PURPOSE: A method and an apparatus for compressing multiple code data using binary arithmetic coding are provided to improve compression and release speed by using binary arithmetic coding, and increase a compression rate by coding bits with conditional probability to binary code. CONSTITUTION: Multiple code data is transformed into binary type data(S110). An MSB(most significant bit) is coded by using probability having a null condition(S120). A second bit is coded by using conditional probability having considered a value of the MSB(S130). A kth bit is coded by using conditional probability having considered all values of a superior position(S140).

Description

Method and apparatus for multi-symbol data compression using a binary arithmetic coder}

The present invention relates to a method and apparatus for providing multiple coded data compression using a binary arithmetic coder (BAC), and more particularly to a method of using a binary arithmetic code in multiple coded data compression used for image data processing. And to an apparatus.

There are two main ways to compress data. That is, one is lossy compression and the other is lossless compression. A representative example of lossless compression is JPEG, and a representative example of lossless compression is LZW (GIF file). In the case of lossy compression, only the data with the most information is used and the rest is discarded. However, in the case of lossless compression, the data before compression and the data after compression must be the same. Lossy compression has a high compression rate, but since a large amount of information is lost, a lossless compression method is used for perfect data recovery.

On the other hand, in the case of lossless compression, a compression method is created by accessing the entropy of data. The techniques widely used in the conventional compression method are Huffman coding or arithmetic coding. Of these, in Huffman coding, the probability of a symbol must be a power of 1/2 to be close to entropy, whereas in arithmetic coding, entropy is reached without such a restriction. Therefore, since the arithmetic coding is very excellent in compression efficiency, arithmetic coding is adopted in many algorithms.

The most commonly used form of arithmetic coding is the arithmetic coding of multiple symbols published by Witten. This is a method of dividing the interval between 0 and 1 into several symbol intervals, and assigning the probability of generating a symbol to each interval. Each interval is calculated in a recursive manner and one number in that interval is transmitted.

Arithmetic coding requires the probability of occurrence of symbols, and various methods are used for this. That is, the fixed or adaptive model is used to handle multiple symbols. Of these, the adaptive method used by Witten calculates the probability using the frequency of symbol occurrence. In other words, the initial probability is assumed to be a uniform distribution, and each time a symbol occurs, the probability of the symbol is calculated by recording the frequency of occurrence of each symbol and dividing it by the total number of events. In addition, when each symbol occurs, the start point and the end point of the interval must be calculated, and multiplication is used in the calculation.

However, when the division and multiplication operations are to be repeatedly performed as described above, there is a problem in that the calculation is complicated and the compression takes a long time.

The present invention has been made to solve such a problem, and an object thereof is to provide a new method and apparatus capable of compressing multiple code data in a short time.

Another object of the present invention is to provide a multi-code data compression method and apparatus thereof having a high compression rate.

1 is a flowchart illustrating an encoding method according to an embodiment of the present invention.

2 is a tree showing a node used to encode each bit in the encoding method according to the embodiment of the present invention.

3 is a table comparing compression / decompression times according to an encoding method and a conventional encoding method according to an embodiment of the present invention.

4 is a table comparing compression rates according to an encoding method and a conventional encoding method according to an embodiment of the present invention.

In order to achieve the above object, the present invention compresses multiple code data using a binary arithmetic coder (BAC), but encodes each bit using the concept of conditional entropy. The BAC uses only subtraction and bit shifts to calculate the probability intervals, and uses a state machine based on the Bayesian estimation principle to calculate the adaptive probability distributions. Since it is not necessary to perform a division operation, the calculation is simple. Since each bit to be encoded is encoded using conditional probabilities in consideration of all upper values, the compression ratio can be increased compared to the case of independent encoding.

That is, the multi-code data compression method according to the present invention includes converting each code constituting the multi-code data into binary form, and encoding the converted binary code by using arithmetic coding. Is done.

Here, in the encoding step, a binary arithmetic encoder may be used, and in the encoding step, the converted binary code is sequentially encoded, but the bit (s) encoded first for the bits after the first coded bit. It is preferable to encode using conditional probabilities with the condition.

In addition, the multiple code data compression device, that is, the encoder according to the present invention includes a storage device and a processing device connected to the storage device, and the storage device stores a program for controlling the processing device. The processing device operates in conjunction with the program, converts each code constituting the multi-code data into binary form, and encodes the converted binary form code using arithmetic coding.

In addition, the present invention provides a method for recovering multiple coded data compressed by the above method and an apparatus therefor.

Embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

1 is a simplified flowchart of an encoding method according to an embodiment of the present invention. First, in order to encode multiple code data using binary arithmetic coding, a code must be converted into a binary form (S110). For example, if there are M signs to be processed, each sign can be represented by N bits of binary number. Where 2 ^N-1 M <2 ^N.

Each bit is then coded using binary arithmetic coding with its own probability state (S120-S140). That is, there are N independent contexts for probability estimation.

For example, if the number of alphabets A of random variable X is 4, then random variable X can be represented by two random variables B ₀ and B ₁ , and each of random variables B ₀ and B ₁ is 0, 1 Has a sign. P (x) = Pr {X = x} = Pr {B ₀ = b ₀ , B ₁ = b ₁ }, b _i IN {0, 1} Can be.

Here, the expected code length when encoding X using the coder proposed by Witten is slightly larger than or equal to entropy H (X). At this time, H (X) is defined as follows.

p (x) log ₂ p (x)

The probability distribution of the random variable X can be expressed as a joint probability distribution of two random variables B ₀ and B ₁ . The joint entropy H (B ₀ , B ₁ ) of a pair of discrete random variables B ₀ , B ₁ with a joint distribution p (b ₀ , b ₁ ) is defined as follows.

p (b ₀ , b ₁ ) log ₂ p (b ₀ , b ₁ )

= H (B ₀ ) + H (B ₁ vert B ₀ )

H (B ₀ ) + H (B ₁ )

Where H (B ₁ vert B ₀ ) is conditional entropy, and the equal sign is established when two arbitrary variables B ₀ and B ₁ are independent of each other. However, it is difficult to guarantee that two arbitrary variables are independent of each other. Therefore, if two arbitrary variables B ₀ and B ₁ are encoded independently (independent encoding for binary representation), the expected length of the code is longer than the code length of the multiple code arithmetic coding of the random variable X.

A binary arithmetic coder (BAC) may be used for coding a code represented by a binary number. Binary arithmetic encoders include Q-coders, QM-coders, MQ-coders, and the like. The BAC only needs subtraction and bit shifting to calculate the probability interval. In addition, a state machine based on the Bayesian estimation principle is used to calculate the adaptive probability distribution. This state machine eliminates the need for division operations when computing sign probabilities. Therefore, BAC is easier to implement than Witten's multiple code arithmetic coder.

On the other hand, the present invention introduces the concept of conditional entropy in order to improve the compression ratio of multiple code arithmetic coding for binary representation. First, the most significant bit (MSB) is encoded using a probability p (B _N-1 ) having a null condition (S120). The second bit is encoded using the conditional probability p (B _N-2 vert B _N-1 ) considering the value of the MSB as a condition (S130). In the same manner, the k th bit is encoded with a conditional probability p (B _k vert B _N-1 , B _N-2 ,..., B _{k + 1} ) (S140).

This situation may be expressed in the form of a binary tree shown in FIG. 2.

In other words, the MSB uses the root node 210 which is a null condition. The condition for encoding the second bit b _N-2 is one of two descendants 220_1 and 220_2 according to the value of the MSB. Kth bit of the binary representation of arbitrary variable X (b _Nk ; 0 In order to encode k <N), the present invention uses one of the descendants 240_1, ..., 240_m of k-1 of the root node as a condition according to a previously encoded value of Nk-1 bits.

The method according to the invention is distinguished from an independent coding method for binary representations in that it uses a conditional probability distribution. That is, the independent coding method for binary representations only deals with independent probability distributions, that is, p (B _N-1 ), p (B _N-2 ), ..., p (B ₀ ), In the method according to the embodiment, all nodes of the tree as shown in FIG.

According to Equation 2, in this method, a shorter encoding length may be obtained than in the case of independent encoding of binary representations.

Now let's analyze the number of contexts. Only N contexts are needed to encode a multi-signed random variable X using an independent coding method for binary representations. This is because the N bits are assumed to be independent of each other. According to the present invention, all the values of the previous Nk-1 bits must be known to encode the kth bit. Therefore, the encoding of the k th bit has a context of 2 ^Nk-1 . That is, the total number of contexts required to encode the arbitrary variable X represented by N bits of binary is as follows.

2 ^i-1 = 2 ^N -1

If the number of alphabets is not a power of 2, the total number of contexts is reduced to some extent. In BAC, the context count represents the amount of memory required to store the context state.

Experimental Example

Experiments were performed to compare the compression rate and computation time of the present invention with other methods. Six gradation images with different characteristics were used in the experiment, and each image consisted of 8 bits per pixel, 512 * 512 pixels. The results of compression and decompression using three different methods are shown in the tables of FIGS. 3 and 4. 3 and 4 are tables comparing compression / decompression time and compression ratio according to an encoding method according to an embodiment of the present invention and a conventional encoding method, respectively.

First, it is assumed that the value of each pixel is multi-symbol and compressed using Witten's adaptive method. Thus 256 symbols were processed. Secondly, each pixel was converted into an 8-bit binary number, and each bit was compressed using independent encoding of a binary representation. Finally, after converting each pixel value into a binary number, each bit is compressed using the coder of the present invention, which is a binary arithmetic coder with conditional probability as described above. At this time, QM coder was used as a binary arithmetic coder.

Computation time and compression rates were compared using a Windows 2000 operating system on a Pentium III (1.0 GHz) computer with 512 MB of memory.

The time taken to compress / decompress using each method is shown in FIG. 3. Since the QM coder does not use multiplication and division to estimate the probability distribution and calculate the probability interval, it is faster to calculate than the multi-symbol arithmetic coder as in Witten's coder.

In FIG. 4, the independent coding method for the binary representation shows a slightly lower compression rate. This means that the eight bits are not independent of each other. As a result of compressing the image according to the method of the present invention, it can be seen that the compression ratio is higher than that of other methods. The difference in compression ratio in the coder of Witten and the method of the present invention seems to be due to the difference between probability estimation and calculating the interval.

In conclusion, the experimental results shown in FIGS. 3 and 4 show that the method of the present invention significantly improves the compression rate and the calculation speed of the multi-symbol data compression.

Meanwhile, in the above-described embodiment, the QM coder is used to encode a binary code, but this is merely presented as an example and other types of binary arithmetic coders may be used.

The present invention has been described in detail with reference to preferred embodiments, but the scope of the present invention is not limited thereto, and should be interpreted by the following claims. In addition, it will be understood by those skilled in the art that various modifications or changes may be made without departing from the spirit of the present invention.

As described above, according to the present invention, the compression and decompression speed can be improved by using binary arithmetic coding, and the compression rate can be increased by performing encoding using conditional probability on the binary code.

Claims (9)

In a method for compressing multiple code data using a computer, Converting each code constituting the multi-code data into binary form; And encoding the transformed binary code using arithmetic coding. The method of claim 1, In the encoding step, a binary coded data compression method using a binary arithmetic coder (BAC). The method of claim 1, In the encoding step, the encoded binary code is sequentially encoded, and the code after the first coded bit is encoded using conditional probabilities subject to the coded bit (s). . 4. A method for recovering multiple coded data compressed by the method of any one of claims 1 to 3 using a computer. An apparatus capable of compressing multiple code data using a computer, Memory, A processing device connected with the storage device, The storage device stores a program for controlling the processing device, The processing device operates in conjunction with the program, Convert each code constituting the multi-code data into binary form, A multi-code data compression apparatus for encoding a converted binary code using arithmetic coding. The method of claim 5, And a multi-code data compression device encoding the converted binary code using BAC. The method of claim 5, And encoding the converted binary code sequentially, and encoding the bit after the first coded bit using conditional probabilities subject to the coded bit (s). Memory, A processing device connected with the storage device, The storage device stores a program for controlling the processing device, The processing device operates in conjunction with the program, 4. A multiple code data decompression device for decompressing multiple code data compressed by the method of any one of claims 1 to 3. A recording medium having recorded thereon a program that can be read and executed using a computer, The program is run on the computer, Convert each code constituting the multi-code data into binary form, A recording medium readable and executable by a computer that encodes the converted binary code using arithmetic coding.