JP2011216953A - Variable length encoding method, variable length encoding device, compression method of image, compression device, driver circuit, and electronic equipment - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a variable length encoding technology which can obtain a high compression rate.SOLUTION: An encoding device 24 performs variable length encoding to a symbol whose value takes a nonnegative integer and as the value becomes larger, an appearance frequency falls. A determination portion 30 determines a range of the value of the symbol. A first encoding portion 32 generates a code term by Golomb-Rice encoding when a symbol value "n" is equal to or less than a predetermined threshold. A second encoding portion 34 generates a code term by Gamma encoding when the symbol value "n" is greater than the threshold.

Description

  The present invention relates to a variable length coding technique.

  Various methods have been proposed for compressing large amounts of data such as image data and audio data. For example, JPEG (Joint Photographic Experts Group), GIF (Graphics Interchange Format), PNG (Portable Network Graphics), etc. are known as methods for compressing image data.

JP 2009-1095 A US Pat. No. 7,362,245

  These algorithms have a problem that in a situation where hardware resources are limited, real-time processing is difficult because of a large amount of time calculation, and hardware cost is high because of a large amount of space calculation. Therefore, it is difficult to realize in applications that require real-time performance and / or cost reduction.

  As a method for compressing digital data, variable-length coding techniques represented by Rice coding and Golomurice coding are also known. In variable-length coding, a symbol having a high appearance frequency is encoded into a word having a short code length, and a symbol having a low appearance frequency is encoded into a word having a long code length, thereby compressing a statistical data amount.

  In Rice encoding, if the parameter (divisor) used at the time of encoding is not appropriate, there is a problem that the code length becomes long and the compression rate decreases.

  The present invention has been made in view of such a problem, and one of exemplary purposes of an aspect thereof is to provide a variable-length coding technique that can obtain a high compression rate.

  An aspect of the present invention relates to a method for variable-length encoding a symbol whose value takes a non-negative integer and whose appearance frequency decreases as the value increases. In this method, Golomb-Rice coding is performed when the symbol value is less than or equal to a predetermined threshold value, and gamma coding is performed when the symbol value is larger than the threshold value.

  Another aspect of the present invention relates to a method for variable-length encoding a symbol whose value takes a positive or negative integer and whose appearance frequency decreases as its absolute value increases. In this method, when the symbol value is 0, it is encoded to “00”, and when the symbol value is +1 or −1, one of them is encoded to “010” and the other is encoded to “011”. When the absolute value of the symbol is not less than 2 and not more than a predetermined threshold value, gamma coding is performed. When the absolute value of the symbol is larger than the threshold value, a code word is generated by removing the separator from the code word obtained by gamma coding.

  Another aspect of the present invention relates to a method for variable-length encoding a symbol whose value takes a non-negative integer and whose appearance frequency decreases as the value increases. In this method, when the value of the symbol is 0, it is encoded as “00”, and when the value of the symbol is 1 or 2, one of them is encoded as “010” and the other is encoded as “011”. When the symbol value is 3 or more and not more than a predetermined threshold value, gamma encoding is performed. When the value of the symbol is larger than the threshold value, a code word obtained by removing the separator from the code word obtained by gamma coding is generated.

  According to these aspects, a high compression rate can be realized.

  Note that any combination of the above-described components, or a conversion of the expression of the present invention between methods, apparatuses, and the like is also effective as an aspect of the present invention.

  According to an aspect of the present invention, a high compression rate can be realized.

It is a block diagram which shows the structure of a display apparatus provided with the variable length coding apparatus which concerns on 1st Embodiment. It is a figure which shows the relationship between the symbol value input into the encoding apparatus of FIG. 1, and the codeword produced | generated. FIGS. 3A and 3B are diagrams illustrating difference processing by the difference calculator. It is a figure which shows the non-negative number process by a non-negative number part. It is a flowchart of the encoding method which concerns on 1st Embodiment. It is a block diagram which shows the structure of the variable-length-coding apparatus which concerns on 2nd Embodiment. It is a figure which shows the relationship between the symbol value input into the encoding apparatus of FIG. 6, and the codeword produced | generated. It is a flowchart of the encoding method which concerns on 2nd Embodiment.

  The present invention will be described below based on preferred embodiments with reference to the drawings. The same or equivalent components, members, and processes shown in the drawings are denoted by the same reference numerals, and repeated descriptions are omitted as appropriate. The embodiments do not limit the invention but are exemplifications, and all features and combinations thereof described in the embodiments are not necessarily essential to the invention.

(First embodiment)
FIG. 1 is a block diagram illustrating a configuration of a display device including the variable length coding device according to the first embodiment. The display device 2 includes a display panel 4 and a display driver 6. The display driver 6 is a functional IC integrated on one semiconductor substrate, receives a predetermined number of image data (frame data) D _IMG every second, and drives the display panel 4 based on the image data D _IMG .

For example, the capacity of 8-bit RGB image data D _IMG of 1024 × 768 pixels is
1024 × 768 × 3 × 8 = 18,874,368 bits≈2.4 Mbytes. As the resolution of the display increases, the capacity for holding the image data _DIMG increases more and more. For this reason, if the image data _{DIMG is} to be stored without compression, the display driver 6 occupies most of the area of the memory for storing the image data.

In order to solve this problem, the display driver 6 includes an image compression device 8, a memory 10, and a decoder 12. The image compression device 8 compresses the image data _DIMG in real time and stores it in the memory 10. The decoder 12 reads the compressed image, decodes it, and outputs it to the display panel 4.

  Next, the configuration of the image compression device 8 will be described. The image compression device 8 includes a difference calculator 20, a non-negative number unit 22, and an encoding device 24.

The difference calculator 20 calculates a difference between pixel values of a certain pixel constituting the image data D _IMG and a pixel adjacent thereto. Although the case where the pixel values are R, G, and B values will be described here, the difference between the U, V, and Y values may be calculated. Specifically, the difference ΔR = R _i −R _i−1 and ΔG = G _i −G _{i− for} each of the R value, the G value, and the B value of an i−1 pixel adjacent to an i th pixel. ₁ , ΔB = B _i −B _i−1 is calculated. In the following, R, G, B or U, V, Y are collectively rewritten as X. That is, the difference data is ΔX = X _i −X _i−1 . As will be described later, the difference calculator 20 outputs not the difference data ΔX itself but a value ΔX ′ obtained by converting the difference data ΔX itself.

  The non-negative number converting unit 22 converts the difference data ΔX ′ into non-negative numbers and outputs the result to the encoding device 24. The encoding device 24 encodes the non-negative difference ΔXs.

  The encoding device 24 provides a high compression rate for data (symbols) whose value takes a non-negative integer and whose appearance frequency decreases as the value increases. In many image data, adjacent pixels often have the same color and brightness, and therefore, the difference between adjacent pixel values has a high probability of being close to zero. Therefore, by using the difference ΔXs between adjacent pixel values as an input symbol of the encoding device 24, a high compression rate can be obtained.

  Hereinafter, the encoding device 24 according to the embodiment will be described. The encoding device 24 takes a symbol value (hereinafter referred to as a symbol value n) equal to or less than a predetermined threshold value α and performs symbol encoding on the symbol.

  The encoding device 24 includes a determination unit 30, a first encoding unit 32, and a second encoding unit 34. The determination unit 30 compares the value of the symbol with a predetermined threshold value α. The first encoding unit 32 performs Golomb-Rice encoding when the value of the symbol is equal to or less than the threshold value α. The second encoding unit 34 performs gamma encoding when the value of the symbol is greater than the threshold value α.

  FIG. 2 is a diagram showing the relationship between the symbol value n input to the encoding device 24 of FIG. 1 and the generated codeword. FIG. 2 shows a state in which Golomb-Rice coding is performed when the symbol value n is a threshold value α = 13 or less, and gamma coding is performed when n> 13.

In Golombrice coding, symbols are encoded into an upper bit group (variable code length portion) UB and a lower bit group (fixed code length portion) LB. The upper bit group UB is a thermometer code indicating a quotient q obtained by dividing a symbol value by a fixed parameter m (= 2 ^k ). FIG. 1 shows a case where k = 1 and m = 2. The low-order bit group LB is a k-bit binary code indicating the division remainder r. A 1-bit separator (for example, “0”) is inserted between the upper bit group UB and the lower bit group LB. In FIG. 1, this separator is added to the least significant bit LSB of the upper bit group UB.

  The encoding device 24 performs gamma encoding when the code length of the code word is larger than the threshold value α = 13. A code word of gamma coding is also composed of an upper bit group UB that is a thermometer code, a separator (0), and a lower bit group LB that is a binary code, like a code word by Golombrice coding. In gamma coding, every time the lower bit group LB overflows (carry), the number of digits is incremented by one. When the lower bit group LB overflows, the value of the upper bit group UB increases by one.

  When image data is compressed at a certain compression rate by the encoding method according to the present embodiment, the boundary (threshold value α) between Golombrice encoding and gamma encoding is PSNR (Peak Signal-to- -Noise Ratio) is affected. As a result of examining the PSNR by changing the threshold value α when the input symbol is represented by β = 8 bits from 0 to 255, the PSNR shows the best value when the threshold value α is 13. I understood.

  This threshold value α = 13 is the maximum value that can be taken by a symbol in the range where the code length of a code word encoded by Golomb-Rice encoding is a predetermined value (8 in this case) or less. It should be noted that this predetermined value is equal to the number of bits β of the symbol to be encoded.

  That is, in order to perform efficient encoding, it can be said that the predetermined value is preferably equal to or approximately the same as the bit length β of the input symbol (for example, β ± 1).

Next, the difference calculation process in the difference calculator 20 will be described.
FIGS. 3A and 3B are diagrams illustrating difference processing by the difference calculator 20.
FIG. 3A shows processing when the current value (X _i ) is smaller than the previous value (adjacent pixel) (X _i-1 ). Specifically, the case of X _i = 10 and X _i-1 = 235 is shown. In this case, the maximum value vmax (255 in the case of 8 bits) that can be taken by the data X is added to the current data X _i , and a difference ΔX _i ′ between the value X _i ′ and the previous data X _i−1 is calculated.

At the time of reproduction (decoding), X _i = X _i−1 + ΔX is calculated, and when the maximum value 255 is exceeded, 256 is subtracted, whereby the original value X _i can be reproduced. As a result, the difference ΔX = 0 to 255 can be shifted to a range ΔX ′ = − 128 to 127 centered on zero, and the absolute value thereof can be reduced, so that the compression rate in the subsequent stage can be increased. it can.

FIG. 3B shows processing when the current value (X _i ) is greater than the previous value (adjacent pixel) (X _i-1 ). Specifically, the case of X _i = 235 and X _i-1 = 10 is shown. In this case, the maximum value vmax (255 in the case of 8 bits) that the data X can take is subtracted from the current data X _i , and the difference ΔX _i ′ between this value X _i ′ and the previous data X _i−1 is calculated.

At the time of reproduction (decoding), X _i = X _i-1 + ΔX is calculated, and when the minimum value is less than 0, 256 is subtracted, whereby the original value X _i can be reproduced. Thereby, the difference ΔX = −255 to 0 can be shifted to a range ΔX ′ = − 128 to 127 centered on zero, and the absolute value thereof can be reduced, so that the compression rate at the subsequent stage is increased. Can do.

  As shown in FIGS. 3A and 3B, according to the difference calculator 20, the difference −255 to 255 can be expressed as −128 to 127, so that the necessary number of bits is reduced by 1 bit. It becomes possible.

  Next, non-negative number processing in the non-negative number converting unit 22 will be described. The difference data of pixel values input to the non-negative number unit 22 has positive and negative integers, and the appearance frequency tends to decrease as the absolute value increases around zero.

  FIG. 4 is a diagram illustrating the non-negative number processing by the non-negative number unit 22.

  When a sign bit is added to the most significant bit (MSB) (leftmost column), −1 having a high appearance frequency is converted to 101b (= 5), so that the compression rate by the encoding process in the subsequent stage decreases. Even when 2's complement expression is used (second column from the left), -1 is converted to 111b (= 7), and the compression rate is reduced.

  When a sign bit is added to the LSB (third column from the left), it is somewhat improved, but there is still room for improvement because 001b, which is expected to have a high compression rate in the subsequent stage, is not used.

  The rightmost column of FIG. 4 shows the non-negative number processing according to the embodiment. The non-negative number unit 22 adds 1 to the value when the symbol value of the difference data is negative. If positive, do not add. Subsequently, a sign bit is added to the least significant bit. In FIG. 4, 0 is assigned positively and 1 is assigned negatively as a sign bit. In this case, since the non-negative value increases as the absolute value of the input difference value decreases, that is, as the appearance frequency decreases, centering on 0, the encoding device 24 in the subsequent stage increases the compression rate. Can be obtained. At the time of non-negative integer conversion, positive sign may be assigned to 1 and negative sign may be assigned 0 as a sign bit.

  FIG. 5 is a flowchart of the encoding method according to the first embodiment. This flowchart shows a preferable process when the encoding device 24 is configured by a digital signal processing circuit, but it goes without saying that the same process can be performed according to other flows.

  Steps S <b> 100 to S <b> 114 show a difference calculation process by the difference calculator 20. In step S104, the difference temp (= ΔX) is calculated. In the subsequent step S106, when temp (= ΔX) is equal to or larger than the maximum integer (127) equal to or smaller than (vmax / 2) (Y in S106), the difference diff (= ΔX ′) = ΔX− (vmax + 1) is obtained. (S114).

  When temp (= ΔX) is smaller than the maximum integer (127) equal to or less than (vmax / 2) (N in S106), the process proceeds to step S108. In step S108, when the value temp is smaller than the minimum integer (−127) equal to or larger than (−vmax / 2) (Y in S108), the difference diff (= ΔX ′) = (vmax + 1) + temp is obtained (S112).

  When −127 ≦ temp <127 (N in S108), diff = temp, that is, ΔX ′ = ΔX is obtained (S110).

Steps S120 to S124 show the non-negative number processing by the non-negative number unit 22.
When the difference ΔX ′ is positive (N in S120), it is converted to sdiff (= ΔXs) = diff × 2 (S122). (× 2) indicates a 1-bit shift to the upper side, and indicates that a sign bit 0 indicating positive is added to the LSB.

  When the difference ΔX ′ is negative (Y in S120), the difference ΔX ′ is converted into sdiff (= ΔXs) = (| diff | −1) × 2 + 1 (S124). (× 2) indicates a 1-bit shift to the upper side, and +1 indicates addition of a sign bit 1 indicating negative.

Steps S <b> 130 to S <b> 138 show encoding processing by the encoding device 24.
When the difference input sdiff (= ΔXs) is less than a certain threshold value n = m × l (N in S130), the first encoding unit 32 performs Golombrice encoding in steps S132 and S134. The threshold value n is α + 1.

  When the difference input sdiff is greater than or equal to the threshold value n (Y in S130), the second encoding unit 34 performs gamma encoding according to steps S136 and S138.

  According to the first embodiment, image data can be suitably compressed.

(Second Embodiment)
FIG. 6 is a block diagram showing the configuration of the variable length coding apparatus 40 according to the second embodiment. The encoding device 40 can be used in place of the encoding device 24 in the image compression device 8 of FIG.

The encoding device 40 provides a high compression rate for data (symbols) whose value takes a non-negative integer and whose appearance frequency decreases as the value increases.
The encoding device 40 includes a first encoding unit 42, a second encoding unit 44, a third encoding unit 46, and a determination unit 48.

  The determination unit 48 selects the first encoding unit 42 to the third encoding unit 46 that should perform encoding according to the symbol value n. Specifically, the first encoding unit 42 is selected when n is 0 to 2, the second encoding unit 44 is selected when n is 3 ≦ n <α, and the third encoding is performed when n ≧ α. Select the part.

  The first encoding unit 42 outputs the code word 00 when n = 0. The second encoding unit 44 encodes one of n = 1 and 2 into the code word “010” and the other into the code word “011”. n = 1 may be assigned to “010” and n = 2 may be assigned to “011”, or vice versa.

  The second encoding unit 44 performs gamma encoding when the symbol value n is 3 ≦ n <α. The gamma coding has already been described.

  When the symbol value n is greater than or equal to a predetermined threshold value α, the separator 0 between the upper bit group UB and the lower bit group LB of the code word obtained by gamma encoding is omitted. The third encoding unit 46 performs encoding at this time.

  FIG. 7 is a diagram showing the relationship between the symbol value n input to the encoding device 40 of FIG. 6 and the generated codeword.

  As modifications of the encoding device 40 of FIG. 7, there are the following modifications. The encoding device 40a according to the modified example receives differential data that is not converted to a non-negative number and performs variable-length encoding on the difference data.

  In this modification, the first encoding unit 42a outputs the code word 00 when the symbol value n = 0. The second encoding unit 44a outputs the code word “010” when n = + 1 or −1, and outputs “011” when the other. n = + 1 may be assigned to “010” and n = −1 may be assigned to “011”, or vice versa.

  The second encoding unit 44a performs gamma encoding when the absolute value n of the symbol is 2 ≦ n <α. When the absolute value n of the symbol is larger than the threshold value α, the third encoding unit 46a generates a code word in which the separator 0 is omitted from the code word obtained by gamma encoding.

  FIG. 8 is a flowchart of the encoding method according to the second embodiment. This flowchart shows a modification in which differential data that is not converted to a non-negative number is variable-length encoded.

  Steps S100 to S114 related to the difference calculation processing are the same as those in the flowchart of FIG.

  Steps S202 to S212 correspond to non-negative integer conversion and encoding processing. First, the parameter l is calculated using the difference data diff (S202). Subsequently, a code s is generated (S204). If l is 1 or less (Y in S206), the code word is 0. l. s (S214). The process of step S214 corresponds to the encoding by the first encoding unit 42 in FIG.

If l is greater than 1 (N in S206), the process proceeds to step S208. When the parameter l is equal to the largest integer (9 when vmax = 255) equal to or less than log ₂ (vmax / 2 + 1) (N in S208), the third encoding unit 46 generates a codeword by the process of step S210. Is done. The code word obtained in step S210 is obtained by omitting the separator from the gamma-coded code word.

  When the parameter l is other than that (Y in S208), that is, when 2 ≦ l ≦ 8, the second encoding unit 44 is selected and performs gamma encoding (S212).

  The present invention has been described based on the embodiments. This embodiment is an exemplification, and it will be understood by those skilled in the art that various modifications can be made to combinations of the respective constituent elements and processing processes, and such modifications are within the scope of the present invention. is there. Hereinafter, such modifications will be described.

  In the embodiment, the display device has been described as an example. However, the application of the encoding technique according to the present invention is not limited thereto. For example, it is effective for applications that require real-time image compression in electronic devices that handle image data such as digital cameras and digital video cameras.

  In Golombrice coding or gamma coding, the code words “1” and “0” may be bit-inverted.

  Although the present invention has been described based on the embodiments, the embodiments merely show the principle and application of the present invention, and the embodiments depart from the idea of the present invention defined in the claims. Many modifications and changes in the arrangement are allowed within the range not to be performed.

DESCRIPTION OF SYMBOLS 2 ... Display apparatus, 4 ... Display panel, 6 ... Display driver, 8 ... Image compression apparatus, 10 ... Memory, 12 ... Decoder, 20 ... Difference calculator, 22 ... Non-negative number unit, 24 ... Encoding apparatus, 30 ... Determining unit, 32 ... first encoding unit, 34 ... second encoding unit, 40 ... encoding device, 42 ... first encoding unit, 44 ... second encoding unit, 46 ... third encoding unit, 48 ... determination unit.

Claims (21)

A variable length encoding method for a symbol whose value takes a non-negative integer and whose appearance frequency decreases as the value increases,
A method comprising performing Golomb-Rice coding when a symbol value is equal to or less than a predetermined threshold value, and performing gamma coding when the symbol value is larger than the threshold value.   The method according to claim 1, wherein the threshold value is a maximum value that can be taken by the symbol in a range in which a code length of a codeword encoded by Golomb-Rice encoding is equal to or less than a predetermined value.   The method of claim 2, wherein the predetermined value is β when the symbol is β bits. Prior to encoding, the method further comprises a step of making a symbol whose value takes a positive or negative integer and whose appearance frequency decreases around zero as a non-negative number,
The non-negative number step is
When the value of the symbol is negative, adding 1 to the value;
Adding a sign bit to the least significant bit;
The method according to claim 1, comprising: A method of compressing image data,
Calculating a difference between pixel values of adjacent pixels;
Non-negative the difference;
Performing Golomb-Rice coding when the value of a symbol that is a non-negative integer is less than or equal to a predetermined threshold, and performing gamma coding when greater than the threshold;
A method comprising the steps of:   6. The method according to claim 5, wherein the threshold value is a maximum value that can be taken by the symbol in a range where a code length of a codeword encoded by Golomb-Rice encoding is not more than a predetermined value.   The method of claim 6, wherein the predetermined value is β when the symbol is β bits. An apparatus for variable-length encoding a symbol whose value takes a non-negative integer and whose appearance frequency decreases as the value increases,
A determination unit that compares the value of the symbol with a predetermined threshold;
A first encoding unit that performs Golomu-Rice encoding when the value of the symbol is less than or equal to the threshold value;
A second encoding unit that performs gamma encoding when the value of the symbol is greater than the threshold;
An encoding device comprising:   9. The encoding apparatus according to claim 8, wherein the threshold value is a maximum value that can be taken by the symbol in a range where a code length of a code word encoded by Golomb-Rice encoding is a predetermined value or less.   The encoding apparatus according to claim 9, wherein when the symbol is β bits, the predetermined value is β. A compression device for image data,
A difference calculator that calculates a difference between pixel values of adjacent pixels;
A non-negative number unit for converting the difference into a non-negative number;
The encoding device according to any one of claims 8 to 10, which encodes the non-negative number difference,
A compression apparatus comprising: A variable length encoding method for a symbol whose value takes a non-negative integer and whose appearance frequency decreases as the value increases,
When the value of the symbol is 0, it is encoded to “00”,
When the value of the symbol is 1 or 2, one of them is encoded as “010” and the other as “011”.
When the value of the symbol is 3 or more and a predetermined threshold value or less, gamma encoding is performed,
When the value of the symbol is larger than the threshold value, a code word obtained by removing a separator from a code word obtained by gamma coding is generated. A method of compressing image data,
Calculating a difference between pixel values of adjacent pixels;
Non-negative the difference;
The method of claim 12, wherein the non-negative numbered difference is encoded;
A compression method comprising: A variable length encoding method for a symbol whose value takes a positive or negative integer and whose appearance frequency decreases as its absolute value increases,
When the value of the symbol is 0, it is encoded to “00”,
When the value of the symbol is +1 or −1, one of them is encoded as “010” and the other as “011”,
When the absolute value of the symbol is 2 or more and a predetermined threshold value or less, gamma encoding is performed,
When the absolute value of the symbol is larger than the threshold value, a code word obtained by removing a separator from a code word obtained by gamma coding is generated. A method of compressing image data,
Calculating a difference between pixel values of adjacent pixels;
The method of claim 14, wherein the difference is encoded;
A compression method comprising: An apparatus for variable-length encoding a symbol whose value takes a non-negative integer and whose appearance frequency decreases as the value increases,
A first encoding unit that encodes “00” when the value of the symbol is 0, and encodes one of the symbols to “010” and the other to “011” when the value of the symbol is 1 or 2; ,
A second encoding unit that performs gamma encoding when the value of the symbol is 3 or more and a predetermined threshold value or less;
A third encoding unit that generates a codeword obtained by removing a separator from a codeword obtained by gamma encoding when the value of the symbol is greater than the threshold;
An encoding device comprising: A compression device for image data,
A difference calculator that calculates a difference between pixel values of adjacent pixels;
A non-negative number unit for converting the difference into a non-negative number;
The encoding device according to claim 16, which encodes the non-negative number difference,
A compression apparatus comprising: An apparatus for variable-length coding a symbol whose value takes a positive or negative integer and whose appearance frequency decreases as its absolute value increases,
A first encoding unit that encodes “00” when the value of the symbol is 0, and encodes one of them as “010” and the other as “011” when the value of the symbol is +1 or −1. When,
A second encoding unit that performs gamma encoding when the absolute value of the symbol is not less than 2 and not more than a predetermined threshold;
A third encoding unit that generates a code word obtained by removing a separator from a code word obtained by gamma encoding when the absolute value of the symbol is larger than the threshold;
An encoding device comprising: A compression device for image data,
A difference calculator that calculates a difference between pixel values of adjacent pixels;
The encoding device according to claim 18, which encodes the difference;
A compression apparatus comprising: A driver circuit that receives image data and drives a display panel,
The compression device according to any one of claims 11, 17 and 19, which compresses the image data;
Memory to hold the compressed image;
A decoder for decoding the image held in the memory;
A driver circuit comprising: A display panel;
The driver circuit according to claim 20, which drives the display panel;
An electronic device comprising:

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