KR101445663B1 - Method for compressing and restoring Look-Up table values - Google Patents

Abstract

A method for compressing and restoring look-up table values is disclosed. Setting an initial seed vector corresponding to an initial condition for a cose problem that defines a polynomial regression for compressing a plurality of original function values sampled from an original function into a look-up table, Generates a seed vector corresponding to each of the original function values, and restores the corresponding original function value from among the plurality of original function values based on the corresponding seed vector among the generated seed vectors.

DSP, look-up table, polynomial regression

Description

Method for compressing and restoring look-up table values {

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a digital signal processor (DSP), and more particularly to a method of compressing and restoring look-up table values to be stored in a look-up table using an RNP (Recursive Near Polynomial) .

A look-up table (LUT) is widely used in digital signal processing algorithms. This is for an effective representation of the functional dependence between the sets of input and output parameters in the software and hardware implementation of the digital signal processing algorithms.

The functional dependence between one input parameter and one output parameter can be expressed by a one-dimensional look-up table (LUT), and the functional dependence between two input parameters and one output parameter And can be represented by a two-dimensional look-up table (two-dimensional LUT).

Interpolation may be used to obtain a continuous functional dependence from a look-up table representation. The look-up table values may be accessed in random or sequential order by digital signal processing algorithms.

When the look-up table values are accessed in a sequential order, the input parameter values may vary monotonically within the range of valid parameter values. The look-up table can be used to improve the performance of digital signal processing algorithms, but apart from this performance, there may be other constraints on the efficiency of the look-up table. One of these other constraints is the memory size or memory capacity occupied by the look-up table.

Up table may be used in various ways to reduce the size (or capacity) of the look-up table. For example, the look-up table values to be stored in the look- Can reduce the memory footprint. However, additional complex hardware logic or software code may be required to perform these methods.

Polynomial regression may be used to reduce the memory size of the look-up table. In this case, only the coefficients of the polynomial regression equation suitable for the look-up table values to be stored in the look-up table can be stored in the memory. This can reduce the memory size of the look-up table. However, it can be problematic that many multiplications are needed to recover the look-up table values from the coefficients of the polynomial regression equation. This problem may reduce performance in the execution of software to restore the look-up table values from the coefficients of the polynomial regression equation, and the hardware implementation cost to implement it may increase.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide a data compression and restoration method capable of improving performance in execution of software for performing compression and decompression of look-up table values through polynomial regression, And to provide a method.

According to an aspect of the present invention, there is provided a data compression and decompression method for compressing a plurality of original function values (look-up table data) sampled from an original function having one independent variable into a look- A seed vector expansion step of generating a seed vector corresponding to each of the plurality of original function values based on the set initial seed vector, And restoring the corresponding original function value from among the plurality of original function values based on the corresponding seed vector among the seed vectors generated in the seed vector expansion step.

According to an aspect of the present invention, there is provided a method of compressing and restoring data, the method comprising: expressing a polynomial regression of look-up table data as initial conditions of a cosine problem for a differential equation having a polynomial regression; The initial conditions are a condensed representation of the first dimensional function with one independent variable and are called the initial seed vector.

The one-dimensional look-up table data restored through the repetitive iterative numerical solution of the kosh problem is an approximation of the original one-dimensional look-up table data. The process of restoring the original one-dimensional look-up table data according to the present invention is called a one-dimensional recursive near-polynomial (RNP) expansion of the initial seed vector.

The data compression and decompression method may further include a step of generating the initial seed vector based on a residual difference between the corresponding original function value and the restored original function value among the plurality of original function values (original look-up table data) And updating the data. This is to determine an initial seed vector that minimizes the error between the original look-up table data and the look-up table data restored through the one-dimensional RNP extension to the initial seed vector. This process is called one-dimensional RNP compression of the original look-up table data into the initial seed vector.

According to another aspect of the present invention, there is provided a method of compressing and decompressing data, comprising: setting a first seed matrix for compressing function values of a two-dimensional matrix form having two independent variables through polynomial regression; Generating a second seed matrix using a one-dimensional RNP extension based on each of the first arrays of seed matrices, using a one-dimensional RNP extension based on each of the second arrays of generated second seed matrices And restoring the function values in the form of a two-dimensional matrix.

The data compression and decompression method is also generalized to a two-dimensional fuzzy table through a cascaded one-dimensional RNP extension.

In a first step, each column array of the first seed matrix is treated as an initial seed vector and expanded using the one-dimensional RNP extension to generate the column arrays of the second seed matrix.

Each row array of the second seed matrix generated in the second step is treated as a new initial seed vector. The new initial seed vector is extended through a one-dimensional RNP extension to recover the two-dimensional look-up table data. In this regard, the first seed matrix is a compressed form of the two-dimensional look-up table data and is called an initial seed matrix. The cascaded calculation process for the original two-dimensional look-up table values is referred to as the RNP extension of the initial seed matrix.

INDUSTRIAL APPLICABILITY The data compression and decompression method according to the present invention has the effect of improving the performance of software for compressing and restoring look-up table values and reducing hardware implementation cost by using RNP equations for polynomial regression.

In order to fully understand the present invention, operational advantages of the present invention, and objects achieved by the practice of the present invention, reference should be made to the accompanying drawings and the accompanying drawings which illustrate preferred embodiments of the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, the present invention will be described in detail with reference to the preferred embodiments of the present invention with reference to the accompanying drawings. Like reference symbols in the drawings denote like elements.

A look-up table (LUT) presentation method according to the present invention is a method for storing and restoring a compressed look-up table value in a sequentially accessed look-up table.

1 shows a one dimensional (one dimensional) lookup table 100 that is accessed sequentially representing an original function F (x). 1, x (i) = h (i) · i, and i represents a sampling index of the original function F (x). h (i) may be a constant, but it may also be a variable value.

The original function F (x) may be sampled at regular intervals or irregular intervals and the original value Q (i) of the sampled original function may be stored in the one-dimensional look-up table 100 It is the original one dimensional LUT value. The sequential access to the one-dimensional look-up table 100 begins at the first element (i = 0) of the one-dimensional look-up table 100 and is incremented by i in the right direction Can proceed.

If the original function F (x) is a smooth function (for example, the original function F (x) can be represented by polynomial regression), the one-dimensional look- The memory capacity required to store the one-dimensional look-up table values may be reduced using RNP compression.

In this case, the polynomial regression for the original function F (x) is as shown in Equation (1).

는 i번째 계수를 나타내는 값으로 실수일 수 있다.Where M is a natural number,

Is a value representing the i-th coefficient and may be a real number.

This polynomial regression is expressed as a solution of the Cauchy problem defined by Equations (1) and (2).

Here, the initial conditions given by Equation (3) are the compressed representations of the original look-up table values, which is called the initial seed vector.

The restoration of the look-up table values (this is referred to as 'initial seed vector extension') is a process of the numerical solution of the above-mentioned cosh problem. For example, the kosh problem can be solved by an iterative Euler method of first order as given by Equations (4) and (5).

Where x = i · Δ and F _i ≡ F (i · Δ). Where DELTA represents the convergence parameter and controls the accuracy of the new hair curl integral. DELTA may be a constant or may be a variable value. DELTA has the same characteristics as h (i) shown in FIG.

The derivative values obtained in i (where i is a natural number) th stage may be referred to as an i th seed vector similar to the initial seed vector in the first zero step. Equations (4) and (5) represent a recursive relationship between the current i-th seed vector and the (i-1) -th seed vector known in the previous step.

In a practical implementation, the iterations given by equations (4) and (5) are not accurate. That is, an approximate value of the polynomial regression for the original function is obtained during the process of restoring the original one-dimensional look-up table values from the initial seed vector by equations (4) and (5).

The quality of the approximation of the polynomial regression for the original function is determined by the value of the convergence parameter DELTA, i.e., the value of the numerical arithmetic used for calculating equations (4) and (5) It depends on bit precision. This method of compressing the original primary look-up table values is called RNP (recursive near-polynomial) compression.

The first dimension RNP equation expressed by equations (4) and (5) is linear with respect to the seed vector.

That is, the i-th seed vector generated through the RNP extension of the initial seed vector obtained by adding the first initial seed vector and the second initial seed vector is the i-th seed generated through the RNP extension of the first initial seed vector, And the i th seed vector generated through the RNP extension of the second initial seed vector.

The result of multiplying the i-th seed vector generated through the RNP extension of the first initial seed vector by a predetermined constant is obtained by multiplying the i-th seed vector generated through the RNP extension to the value obtained by multiplying the first initial seed vector by the predetermined constant. Th seed vector

This linear property can be summarized as Equations (6) and (7). S (0) represents an initial seed vector.

는 i번째 스텝(즉, i번째 시드 벡터)에서 초기 시드 벡터의 RNP 확장의 결과이다. C는 소정의 상수이고, S₁(0)는 제1 초기 시드 벡터이고, S₂(0)는 제2 초기 시드 벡터이다. 상술한 이러한 선형적 성질로 인하여 수많은 요소들 (elememts)을 포함할 수 있는 전체 LUT에 대한 효과적인 제어가 가능하다.

Is the result of the RNP extension of the initial seed vector at the ith step (i. C is a predetermined constant, S ₁ (0) is a first initial seed vector, and S ₂ (0) is a second initial seed vector. This linear nature described above allows effective control over the entire LUT, which may include a number of elememts.

If the convergence parameter (e.g., h (i) or?) Is a power of two, a binary operation of bit shift may be used to calculate the following equation (4) to RNP equations of the form < RTI ID = 0.0 > RNP < / RTI > can be implemented without using expensive multiplication operations.

The lower the number of multiplication operations, the greater the performance of software for restoring the original first look-up table values from the initial seed vector, and the hardware implementation cost may be reduced.

The method of calculating the initial seed vector for effectively approximating the original first look-up table values minimizes the residual error between the original first look-up table value and the look-up table value obtained through the RNP extension .

This is called RNP compression to the initial seed vector of the original one-dimensional look-up table value.

The error can be defined by equation (8).

는 i번째 스텝에 대한 상기 초기 시드 벡터의 RNP 확장 결과(즉, 상기 i번째 스텝에서 상기 오리지널 함수에 대한 근사)이고,

는

에서 오리지널 함수 값이다.Where S (0) is the initial seed vector,

Is an RNP extension result (i.e., an approximation to the original function in the i-th step) of the initial seed vector for the i-th step,

The

Is the original function value.

The residual error function according to Equation (8) has an initial seed vector as an argument. The optimal initial seed vector can be obtained by minimizing the error function value by a standard New Hair method such as the Newton method.

Fig. 2 shows one-dimensional look-up table values Q (i), i = 0 to (k-1) to be stored in an initial seed vector S (0) according to an embodiment of the present invention, Is a natural number). Referring to FIGS. 1 and 2, an initial seed vector is first set. The initial seed vector S (i, i = 0) defines a polynomial regression equation for compressing the original one-dimensional look-up table values sampled from the original function F (x) Which corresponds to the initial condition for.

The initial seed vector S (i, i = 0) contains a number of elements for the cose problem that define the polynomial regression. For example, S (i, i = 0)) = [S ₀ (0) to S _M (0)]. Where M can be a natural number. The corresponding element among the plurality of elements (S ₀ (0) to S _M (0)) may correspond to a corresponding coefficient among the coefficients of the polynomial regression equation (S210).

Based on the initial seed vector (S (i, i = 0 ) = [S 0 (0) ~ S M (0)]), the original one-dimensional look-corresponding to up table values (Q (i)) seed vector may produce the (S (i, i> 0 ) = [S 0 (i) ~ S M (i)]).

And the seed vector (S (including a i, i = 1 ~ (k -1)) is also a number of factors. For example, it can be _{S (i) = [S 0} (i) ~ S M (i)]. Where i = 0 to (k-1).

The original first-dimensional look-seed vectors (S (i, i> 0 ) = [S 0 (i) ~ S M (i)]) corresponding to the up table values (Q (i)) is Equation (9) and It is generated based on the initial seed vector (S (0) = [S 0 (0) ~ S M (0)]) using the equation (10). The calculation process of the seed vector S (i, i = 1 to (k-1)) is referred to as extension of the initial seed vector (S220).

S ₀ (i) = S ₀ (0)

S _j (i) = S _j (i-1) + S _{j -1} (i-1 ⁾

In Equation (9) and Equation (10), i = 0 to (k-1), j denotes the jth element of the seed vector S (i), and j = 1 to M. Where M can be a natural number.

1/2 ^{k (j)} corresponds to the convergence parameter (?) In Equation (4), and is selected in the form of a power of 2 to improve the performance of the multiplication operation.

FIG. 3 is a flow chart showing the seed vector expansion step (S220) shown in FIG. 3, elements (S _j (i), j = 1 to M (i)) of the ith seed vector S (i) corresponding to the ith original one-dimensional look- ) Based on the elements S _j (i-1), j = 1 to M of the (i-1) th seed vector S (i-1) and the initial seed vector S (0) (S310).

The seed vector S (i), i = 1 to (k-1) may be sequentially generated from the initial seed vector S (0) according to Equation (10). The original one-dimensional look-up table value Q (i) can be recovered from the seed vector S (i), i = 1 to (k-1) generated by equation (11) (S230).

Q (i) = S _M (i)

According to Equation (11), the original one-dimensional look-up table value Q (i) is calculated by multiplying the corresponding seed vector S (i) among the generated seed vectors S (S _M (i)) among the elements of (i).

The original one-dimensional look-up table values Q (i), i = 0 to (k-1) are generated by the elements S (i, _{i = 0) = [S 0} (0) ~ S M (0)]) may be compressed to form, by the equation (9) to equation (11) the original first-dimensional look-of-an approximation to the up table value again Can be restored.

FIG. 4 is a flow chart for compressing and restoring original two-dimensional look-up table values according to an embodiment of the present invention. FIG. 5 is a flowchart illustrating a method of compressing and restoring original 2-dimensional look-up table values stored in a first seed matrix form according to an embodiment of the present invention. Up table values of the < / RTI > 4 and 5, a method for compressing and restoring original two-dimensional look-up table values in accordance with the present invention employs the application of a cascaded one-dimensional RNP expansion process.

First, a first seed matrix is set. The first seed matrix is a function of the function values in the form of a two-dimensional matrix sampled from an original function F (x, y) having two arguments (arguments, x and y) Values). Each first array (e.g., a column array) of the first seed matrix may be a first initial seed vector for a first stage of the RNP extension (S410).

A second seed matrix is generated (S420). The second seed matrix may be generated using a first dimensional RNP extension based on each of the first arrays of the first seed matrix (e.g., column arrays). This is called the first one-dimensional RNP step.

For example, when the first initial seed vector is [R1, R2, R3, R4, and R5], the corresponding first array (e.g., column array, [T ₁₁ ~T _1B ]) of the second seed matrix Dimensional RNP extensions.

The original two-dimensional look-up table values may be reconstructed using a first dimension RNP extension for each of the second arrays of generated second seed matrices (e.g., row arrays) (S430). This is called the second one-dimensional RNP step.

For example, the second oxide corresponding row array (row array, Ca4 = [T 14 ~ T P4]) of the matrix as shown in FIG. 5, the second by setting the initial seed vector, corresponding to the original 2-D look that Up data values (for example, Ca4 ') may be restored using the one-dimensional RNP extension described above.

The original second-dimensional look-up table values can be recovered from a P x Q first seed matrix using the cascaded one-dimensional RNP equation, so that an original A-B look-up table value Can be compressed into a P x Q first seed matrix. Where P, Q, A, and B are natural numbers. The original second dimensional look-up table values may be generated line by line from top to bottom, and from left to right.

The original second-dimensional look-up table values restored by the cascaded RNP expansion process described above can be approximated by a two-dimensional polynomial regression according to equation (12).

The accuracy of the approximation can be expressed as? In Equation 4 or 1/2 ^{k (j)} in Equation 10 Can be controlled by the convergence parameter.

는 P×Q 제1 시드 매트릭스를 나타낸다.Where x and y are independent variables of the two-dimensional polynomial regression function F (x, y)

Represents a P x Q first seed matrix.

The error function for the original two-dimensional look-up table values may be expressed as Equation (13).

는 (i, j)좌표의 2차원 룩-업 테이블 요소를 얻기 위한 제1 시드 매트릭스의 RNP확장의 결과이다.

는 (i,j) 좌표를 가진 2차원 룩-업 테이블에 대응하는 오리지널 제2 차원 룩-업 테이블 값이다.Where S (0) is the first seed matrix,

Is the result of the RNP extension of the first seed matrix to obtain a two-dimensional look-up table element of (i, j) coordinates.

Up table value corresponding to a two-dimensional look-up table having coordinates (i, j).

The first seed matrix that minimizes the error between the original second-dimensional look-up table value and the restored 2-dimensional look-up table through the RNP extension of the first seed matrix is determined through Equation (13). The first seed matrix thus determined may be set as an initial seed matrix for compressing the two-dimensional look-up table values.

6 is a block diagram of a digital signal processor 600 capable of compressing and restoring look-up table values according to an embodiment of the invention. Referring to FIG. 6, the digital signal processor 600 includes a seed vector storage unit 610, and an RNP calculation unit 620.

The seed vector storage unit 610 stores the initial seed vector (or the first seed matrix for the second dimensional look-up table). The seed vector storage 610 may be implemented in a non-volatile memory (e.g., flash EEPROM, or ROM), or a volatile memory (e.g., DRAM).

The RNP calculator 620 expands the initial seed vector using the one-dimensional RNP equation and restores the original look-up table function values. The RNP calculation unit 620 includes a seed vector expansion unit 620 and a look-up table value restoration unit 624.

The seed vector extension 620 may generate a seed vector corresponding to each of the original function values based on the set initial seed vector S (0).

The look-up table value restoration unit 640 can restore the original function value corresponding to the original function values based on a corresponding seed vector among the generated seed vectors.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS A brief description of each drawing is provided to more fully understand the drawings recited in the description of the invention.

Figure 1 shows a one-dimensional look-up table that is accessed sequentially representing an original function.

FIG. 2 is a flowchart illustrating a method of restoring 1-dimensional look-up table values to be stored as an initial seed vector according to an embodiment of the present invention.

FIG. 3 is a flowchart showing the seed vector expansion step shown in FIG. 2. FIG.

4 is a flowchart for compressing and restoring original two-dimensional lookup table values according to an embodiment of the present invention.

FIG. 5 illustrates a method of restoring original two-dimensional lookup table values stored in a first seed matrix form according to an embodiment of the present invention

6 is a block diagram of a digital signal processor capable of compressing and restoring lookup table values in accordance with an embodiment of the present invention.

Claims (8)

An initial seed vector corresponding to an initial condition for a Cauchi problem defining a polynomial regression for compressing a plurality of original function values sampled from the original function into a look-up table ; A seed vector expansion step of generating a seed vector corresponding to each of the plurality of original function values based on the set initial seed vector; And And restoring a corresponding original function value from the plurality of original function values based on a corresponding seed vector among the seed vectors generated in the seed vector expansion step. 2. The method of claim 1, wherein the one- And updating the initial seed vector based on a residual difference between a corresponding original function value and the restored original function value among the plurality of original function values. 2. The method of claim 1, (i-1) th seed vector corresponding to the i-th original function value, based on the elements of the (i-1) -th seed vector corresponding to the i-th original function value A one-dimensional data compression and reconstruction method for generating elements of a seed vector. 4. The method of claim 3, (J is a natural number) element among the elements included in the i-th seed vector, based on the j-th element and the (j-1) -th element among the elements included in the (i- Dimensional data compression and decompression method. The one-dimensional data compression and decompression method of claim 4, wherein the corresponding original function value among the plurality of original function values is restored using a first-order Euler method. Setting a first seed matrix for compressing function values in the form of a two-dimensional matrix having two independent variables through polynomial regression; Generating a second seed matrix using a one-dimensional recursive near polynomial (RNP) extension based on each of the first arrays of the first seed matrix; And And reconstructing the two-dimensional matrix-form function values using the one-dimensional RNP extension based on each of the second arrays of the generated second seed matrix. 7. The method of claim 6, wherein generating the second seed matrix comprises: Setting each of the first arrays to a first initial seed vector; And Generating the second seed matrix based on the first dimensional RNP extension for each of the first initial seed vectors. 8. The method of claim 7, wherein restoring the function values in the form of a two-dimensional matrix comprises: Setting each of the second arrays of the generated second seed matrix to a second initial seed vector; And And restoring the function values in the form of a two-dimensional matrix based on the first dimension RNP extensions for each of the second initial seed vectors.

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