# Patent

## Title
Encoding and decoding data arrays

## Abstract

Some embodiments of the invention provide a method of performing a Discrete Cosine Transform (“DCT”) encoding or decoding coefficients of a data array by (1) multiplying the coefficients by a scalar value before the encoding or decoding, and then (2) dividing the encoded or decoded coefficients by the scalar value. When used in conjunction with fixed-point arithmetic, this method increases the precision of the encoded and decoded results. In addition, some embodiments provide a method of performing a two-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). This method splits a pre-multiplication operation of the iDCT into two or more separate stages. When used in conjunction with fixed-point arithmetic, this splitting increases the precision of the decoded results of the iDCT.

## Background
RELATED APPLICATIONS
This patent application claims the benefit under title 35, United States Code, Section 119(e) to the U.S. Provisional Patent Application entitled “Method and Apparatus for Coding and Decoding,” having serial No. 60/396,156 filed on Jul. 14, 2002.


FIELD OF THE INVENTION
The present invention is directed towards encoding and decoding data arrays using separate pre-multiplication stages.
BACKGROUND OF THE INVENTION
Moving Picture Experts Group (MPEG) video compression is currently used in many video products such as digital television set-top boxes, DSS, HDTV decoders, DVD players, video conferencing, Internet video, and other applications. These products benefit from MPEG video compression since compressed video requires less storage space for video information and less bandwidth for the transmission of the video information.
An MPEG video is a sequence of video frames comprised of intra coded I-frames and/or inter coded P and B-frames, as is well known in the art. Each video frame is typically divided into sub-sections of macro blocks (16×16 pixels in a data array). A macro block typically includes sub-sections of four luminance blocks and two chrominance blocks (8×8 data arrays). A luminance block specifies brightness information (e.g., luminance image coefficients) about the pixels in the block, while the two chrominance blocks specify Cr and Cb color information (e.g., Cr and Cb image coefficients) about the pixels in the macro block.
MPEG video encoding and decoding processes typically use discrete cosine transform (“DCT”) and inverse DCT (“iDCT”) to encode and decode coefficients of a block (i.e., data array). A DCT operation takes image values defined in a spatial domain and transforms them into a frequency domain. The DCT operation transforms the inputted image values into a linear combination of weighted basis functions. These basis functions are the frequency components of the inputted image values. As such, when a DCT operation is applied to a block of image values, it yields a block of weighted values corresponding to how much of each basis function is present in the original image to be encoded.
For most images, most of the image information lies at low frequencies which appear in the upper-left corner of the DCT-encoded block. The lower-right values of the DCT-encoded block represent higher frequencies, and are often small enough to be neglected with little visible distortion. The top left corner value in the DCT-encoded block is the DC (zero-frequency) component and lower and rightmore entries represent larger vertical and horizontal spatial frequencies.
The DCT operation is a separable transform in that the matrix that defines this transformation is decomposable into two matrices, one that corresponds to a column transform and another that corresponds to a row transform. Thus it can be implemented as two one-dimensional (1D) transforms. In other words, a two-dimensional (2D) DCT is just a 1D DCT applied twice, once in the column direction and once in the row direction. In the case of a 1D 8-point DCT, the first coefficient (the DC coefficient) represents the average value of the image values and the eighth coefficient represents the highest frequencies found in the image. An iDCT operation is used to convert the frequency coefficients back into the image information.
DCT encoding of a block is a two-dimensional (2D) transformation operation that can be expressed by the following formula:



  
    
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In the formula above, a column dimension of the block is represented by x values and a row dimension of the block is represented by y values, so that f(x,y) is the image information at position [x,y] of the block. As such, F(u,v) is the 2D encoded image information at position [u,v] of the 2D encoded block.

A DCT decoder performs an inverse DCT transformation on a DCT encoded block to reconstruct the block. DCT decoding of a block is also a two-dimensional (2D) transformation operation, which can be expressed by the following formula:




  
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In the formula above, the columns of the 2D encoded block are represented by u values and the rows of the 2D encoded block are represented by v values, so that F(u,v) is the encoded image data at position [u,v] of the block. As such, f(x,y) is the image data at position [x,y] of the block.

Conventionally, 2D DCT and 2D iDCT processes contain a pre-multiply stage that multiplies each coefficient of the block to be transformed by a pre-multiplication value. The pre-multiplication value is usually less than one. As such, the pre-multiplication operation results in the loss of precision, when it is used with fixed point arithmetic that rounds or truncates the multiplication results.
SUMMARY OF THE INVENTION
Some embodiments of the invention provide a method of performing a Discrete Cosine Transform (“DCT”) encoding or decoding coefficients of a data array by (1) multiplying the coefficients by a scalar value before the encoding or decoding, and then (2) dividing the encoded or decoded coefficients by the scalar value. When used in conjunction with fixed-point arithmetic, this method increases the precision of the encoded and decoded results.
In addition, some embodiments provide a method of performing a two-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). This method splits a pre-multiplication operation of the iDCT into two or more separate stages. When used in conjunction with fixed-point arithmetic, this splitting increases the precision of the decoded results of the iDCT.



BRIEF DESCRIPTION OF THE DRAWINGS
The novel features of the invention are set forth in the appended claims. However, for purpose of explanation, several embodiments of the invention are set forth in the following figures.
FIG. 1 illustrates a process that performs a 2D iDCT operation.
FIG. 2 illustrates a process that performs a 2D DCT operation.
FIG. 3 illustrates a process that receives a DCT-encoded data stream, generates a DCT-encoded block, and decodes the block using only one transpose operation.
FIG. 4 illustrates a process that DCT encodes a data array and outputs the DCT-encoded data array using only one transpose operation.



DETAILED DESCRIPTION OF THE INVENTION
In the following description, numerous details are set forth for purpose of explanation. However, one of ordinary skill in the art will realize that the invention may be practiced without the use of these specific details. In other instances, well-known structures and devices are shown in block diagram form in order not to obscure the description of the invention with unnecessary detail.
Some embodiments of the invention provide a method of performing a Discrete Cosine Transform (“DCT”) encoding or decoding of coefficients of a data array by (1) multiplying the coefficients by a scalar value before the encoding or decoding, and then (2) dividing the encoded or decoded coefficients by the scalar value. When used in conjunction with fixed-point arithmetic, this method increases the precision of the encoded and decoded results.
In addition, some embodiments provide a method of performing a two-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). This method splits a pre-multiplication operation of the iDCT into two or more separate stages. When used in conjunction with fixed-point arithmetic, this splitting increases the precision of the decoded results of the iDCT.
Several embodiments are described below by reference to FIGS. 1 to 4. These embodiments are part of an MPEG encoder or decoder that encodes or decodes video frames by using 2D DCT and IDCT operations on 8-by-8 image blocks (i.e., data arrays). One of ordinary skill, however, will realize that other embodiments might use other compression techniques (e.g., H.263 compression). Alternatively, other embodiments might use other types of transformations (such as those used in MPEG 4 part 10). Also, other embodiments might apply their transform operations on different size blocks, such as 4×4, 8×4, or any n×m set of pixels, where n and m are integers.
DCT decoding is a separable two-dimensional (2D) transform operation. The separable nature of the iDCT decoding can be exploited by (1) performing a first 1D iDCT process in the column direction of the 2D encoded block to produce a 1D encoded block and then a second 1D iDCT process in the row direction of the encoded block to produce the block. Alternatively, the first 1D iDCT operation can be performed in the row direction of the 2D encoded block and the second 1D iDCT operation can be performed in the column direction of the encoded block.
The scaled-version of the Chen method can be used to perform two 1D iDCT operations. This scaled-version is described in the paper “2D Inverse Discrete Cosine Transform,” which can be found on the internet, incorporated herein by reference. The Chen algorithm is an efficient implementation of the iDCT operation that requires a fewer number of computations than a straightforward implementation of the iDCT.
FIG. 1 illustrates a process 100 that performs a 2D iDCT operation. This process decodes a data array of coefficients that were encoded using a DCT operation. As shown in FIG. 1, the process 100 initially multiplies (at 105) each coefficient in the data array by a scalar value S. In some embodiments, the scalar value is 16. These embodiments perform the multiplication by shifting up each coefficient in the data array by four bits. Some of these embodiments shift up each coefficient by four bits since (1) in these embodiments, each coefficient in the data array can be represented by a 12 bit value, and (2) these embodiments perform 16×16 fixed point multiplication. A 16×16 fixed point multiplication multiplies two 16 bit values to obtain a 32 bit value, which it then converts into a 16 bit value by truncating the lowest 16 bits and rounding the 17th bit (which after the truncation will be the 1st bit) based on the truncated 16 bits.
After 105, the process performs (at 110) a first pre-multiplication operation for a first 1D iDCT operation. In some embodiments, the first pre-multiplication operation entails multiplying each coefficient of the data array that remains after 105 by a value of a following pre-multiplication array (A):




  
    
      
        
          
            
              
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Next, the process performs (at 115) a first 1D iDCT operation. In some embodiments, the process performs the first 1D iDCT operation according to the scaled-version of the Chen method, which is described in the above-referenced paper. The first 1D iDCT operation is either along the row direction or the column direction. In the embodiments described below, the first 1D iDCT operation is along the column direction.
After 115, the process performs (at 120) a second pre-multiplication operation for a second 1D iDCT operation. In some embodiments, the second pre-multiplication operation entails multiplying each coefficient of the data array that remains after 105 by a value of the pre-multiplication array (A).
Next, the process performs (at 125) a second 1D iDCT operation. Like the first 1D iDCT operation, the process performs the second 1D iDCT operation according to the scaled-version of the Chen method, which is described in the above-referenced paper. The second 1D iDCT operation can also be either along the row direction or the column direction. In the embodiments described below, the second 1D iDCT operation is along the row direction.
From 125, the process transitions to 130. At 130, the process divides by four each coefficient in the data array that remains after 125. This division is part of the iDCT pre-multiplication operation, which the process 100 divides into three stages 110, 120, and 130. By splitting the pre-multiplication operation into separate stages, the process maintains larger coefficient values that result in less precision loss when fixed-point multiplication is used.
After 130, the process divides (at 135) each coefficient by the scalar value S that it used as the multiplier at 105. When the scalar value is 16, the division at 135 entails shifting down each coefficient by four bits. Although 130 and 135 are illustrated as two separate operations in FIG. 1, one of ordinary skill will realize that both operations can be performed simultaneously. For instance, when the scalar value is 16, the process can perform 130 and 135 by shifting down each coefficient by six bits.
Like iDCT decoding, DCT encoding is a separable two-dimensional (2D) transform operation. The separable nature of the DCT encoding operation can be exploited by (1) performing a first one-dimensional (1D) DCT operation in the column direction of the image block to produce a 1D encoded block, and then (2) performing a second 1D DCT operation in the row direction of the 1D encoded block to produce a 2D encoded block. Alternatively, the first 1D DCT operation can be performed in the row direction of the block and the second 1D DCT operation performed in the column direction of the block.
The scaled-version of the Chen method can be used to perform the two 1D DCT operations. This scaled-version is described in the paper “2D Discrete Cosine Transform,” which can be found on the internet, incorporated herein by reference. The Chen algorithm is an efficient implementation of the DCT operation that requires a fewer number of computations than a straightforward implementation of the DCT. While a straightforward implementation of the DCT requires a number of computations that is proportional to N^2 (where N=8 for an 8-point DCT), the Chen algorithm exploits symmetry and periodicity inherent in the DCT calculation to reduce the number of computations to an amount proportional to N log(N).
FIG. 2 illustrates a process 200 that performs a 2D DCT operation. This process encodes a data array of coefficients. As shown in FIG. 2, the process 200 initially multiplies (at 205) each coefficient in the data array by a scalar value S. Some embodiments use a scalar value of 16, and hence perform the multiplication by shifting up each coefficient in the data array by four bits. Some of these embodiments shift each coefficient of by four bits for the reason described above for some embodiments of FIG. 1.
After 205, the process performs (at 210) a first 1D DCT operation. In some embodiments, the process performs the first 1D DCT operation according to the scaled-version of the Chen method, which is described in the second paper referenced above. The first 1D DCT operation is either along the row direction or the column direction. In the embodiments described below, the first 1D DCT operation is along the column direction.
After 210, the process performs (at 215) a second 1D DCT operation. Like the first 1D DCT operation, the process performs the second 1D DCT operation according to the scaled-version of the Chen method, which is described in the second paper referenced above. The second 1D DCT operation can also be either along the row direction or the column direction. In the embodiments described below, the second 1D DCT operation is along the row direction.
Next, at 220, the process performs a post multiply operation, according to the scaled-version of the Chen method. After 220, the process divides (at 225) each coefficient by the scalar value S that it used as the multiplier at 205. When the scalar value is 16, the division at 225 entails shifting down each coefficient by four bits. Although 220 and 225 are illustrated as two separate operations in FIG. 2, one of ordinary skill will realize that both operations can be performed simultaneously.
When 2D DCT encoding and decoding processes are separated into two 1D DCT operations or two 1D iDCT operations, transpose operations are typically performed between the 1D operations. Conventionally, two transpose operations are used in each of the encoding and decoding processes. One approach uses only one transpose operation in each of the encoding and decoding processes, as disclosed in U.S. patent application Ser. No. 10/427,889 filed Apr. 30, 2003, entitled “Video Encoding and Decoding,” which is incorporated herein by reference.
FIG. 3 illustrates a process 300 that receives a DCT-encoded data stream, generates a DCT-encoded block, and decodes the block using only one transpose operation. The operations of the process 300 are similar to the operations of the process 100 of FIG. 1. Hence, similar numbers are used to described similar operations in these figures.
The process 300 starts when it receives a data stream of encoded values. The process 300 parses out and derasterizes (at 305) the values of the data stream and stores the values in a data array according to a transposed zig-zag scan order. The transposed zig-zag scan order is identical to a conventional zig-zag scan order except that it has been flipped symmetrically about the diagonal line that connects the top-left and the bottom-right corners of the data array. The process then performs (at 310) an inverse quantization process on the data array. For an MPEG encoding, the inverse quantization entails multiplying each value of the data array by a value of a transposed quantization matrix. The transposed quantization matrix is a transposed version of the quantization matrix used by conventional MPEG inverse quantizers.
The process 300 then multiplies (at 105) each coefficient in the data array by a scalar value S. The process performs (at 110) a first pre-multiplication operation for a first 1D iDCT operation. Next, the process performs (at 115) a first 1D iDCT operation. The first 1D iDCT operation is either along the row direction or the column direction. In the embodiments described below, the first 1D iDCT operation is along the column direction.
The process next performs (at 315) a transpose operation on the coefficients of the data array that exists after 115. A transpose operation interchanges the row and columns of an array. In other words, a transpose AT of an array A is an array that is symmetrically related to the array A, such that row i in AT is column j in A, and column j in AT is row i in A.
The process then performs (at 120) a second pre-multiplication operation for a second 1D iDCT operation. Next, the process performs (at 125) a second 1D iDCT operation. The second 1D iDCT operation can also be either along the row direction or the column direction. In the embodiments described below, the second 1D iDCT operation is along the row direction. The process then divides (at 130) by four each coefficient in the data array that remains after 125. The process then divides (at 135) each coefficient by the scalar value S that it used as the multiplier at 105. The process then ends.
FIG. 4 illustrates a process 400 that DCT encodes a data array of coefficients and outputs the DCT-encoded data array using only one transpose operation. The operations of the process 400 are similar to the operations of the process 200 of FIG. 2. Hence, similar numbers are used to described similar operations in these figures.
As shown in FIG. 4, the process 400 initially multiplies (at 205) each coefficient in the data array by a scalar value S. The process then performs (at 210) a first 1D DCT operation. The first 1D DCT operation is either along the row direction or the column direction. In the embodiments described below, the first 1D DCT operation is along the column direction.
The process next performs (at 405) a transpose operation on the coefficients of the data array that exists after 210. The process performs (at 215) a second 1D DCT operation. The second 1D DCT operation can also be either along the row direction or the column direction. In the embodiments described below, the second 1D DCT operation is along the row direction. Next, at 220, the process performs a post multiply operation, according to the scaled-version of the Chen method. After 220, the process divides (at 225) each coefficient by the scalar value S that it used as the multiplier at 205.
The process then performs (at 407) a quantization operation. For an MPEG encoding, the quantization entails multiplying each value of the data array (that exists after 225) by a value of a transposed quantization matrix. The process then rasterizes (at 410) the coefficients of the data array remaining after 407 in a transposed zig-zag scan order to produce a data stream. The process then ends.
While the invention has been described with reference to numerous specific details, one of ordinary skill in the art will recognize that the invention can be embodied in other specific forms without departing from the spirit of the invention. Several embodiments described above relate to MPEG compression. One of ordinary skill in the art, however, will realize that the invention can relate to other types of compression, such as H.263 compression. However, if other compression techniques are used, some of the aspects of the above-described processes might have to be modified.

## Claims

1. A method comprising:
decoding an encoded video stream that has been encoded according to a two-dimensional (2D) transform encoding operation that is separable into two one-dimensional (1D) transform operations, the encoded video stream comprising a plurality of encoded values for a plurality of encoded video images, said decoding comprising:
parsing encoded values out of the data stream and creating a two-dimensional data array that stores the encoded values in a particular scan order, wherein the values in the created data array are encoded in both dimensions of the array;

multiplying each value in the data array by a scalar value, wherein the data array is an array of data values from a video image;
performing a first 1D inverse transform to the data array resulting from the multiplying;
transposing the data array resulting from the first 1D inverse transform;

performing a second 1D inverse transform to the data array resulting from the transposing; and
dividing by the scalar value each value in the data array resulting from the second 1D inverse transform to produce a data array comprising decoded values, the data array comprising decoded values being produced without a second transposing step.

2. The method of claim 1, wherein the particular scan order is a transposed zig-zag scan order.

3. The method of claim 1, wherein each of the plurality of the video images comprises one or more macroblocks.

4. The method of claim 3, wherein each macroblock comprises sub-sections of luminance and chrominance blocks.

5. The method of claim 3, wherein each macroblock is a block of 16 by 16 pixels.

6. The method of claim 1, wherein the data array is an 8 by 8 pixel image block.

7. The method of claim 1, wherein the data array is an n by m pixel image block, wherein n and m are integers.

8. A method comprising:
encoding a video image stored as a data array of coefficients, said encoding based on a two-dimensional (2D) transform operation that is separable into two one-dimensional (1D) transform operations, said encoding comprising:
multiplying each coefficient in the data array by a scalar value;
performing a first 1D transform on the data array resulting from the multiplying;
transposing the data array resulting from the first 1D transform;
performing a second 1D transform on the data array resulting from the transposing;
dividing by the scalar value each coefficient in the data array resulting from the second 1D transform; and
without performing another transposing step, generating a data stream based on the coefficients from the data array resulting from the dividing, wherein the data stream comprises an encoding of said video image.

9. The method of claim 8 further comprising, after performing the second 1D transform and before the dividing, performing a post-multiplication of the each coefficient in the data array resulting from the second 1D transform.

10. The method of claim 8, wherein the video image comprises one or more macroblocks.

11. The method of claim 10, wherein each macroblock comprises sub-sections of luminance and chrominance blocks.

12. The method of claim 10, wherein each macroblock is a block of 16 by 16 pixels.

13. The method of claim 8, wherein the data array is an 8 by 8 pixel image block.

14. The method of claim 8, wherein the data array is an n by m pixel image block, wherein n and m are integers.