Chapter 3 Existing Encoding Schemes
4.3 Architecture of Dynamic BI-XNOR Encoding
4.3.1 The Encoder Stage
The encoder structure of dynamic BI-XNOR scheme is shown in Fig.4.3. In this encoding architecture, three control bits C0, C1 and C2 are needed. We divide this architecture into five stages and discuss each stage in detail.
D0(t+1)
In stage 1, D(t+1) and E(t) are compared by the set of XOR gates. If they are identical, there is no self transition between D(t+1) and E(t) and the XOR gate will send 0.
If they are different, there is a self transition and the XOR gate will send 1.
In stage 2, multiplexer 1 calculates the number of self transitions between D(t+1) and E(t) and sends output C0. If the number of self transitions is 0 to 2 or 6 to 8, C0 is set to 0, otherwise C0 is set to 1. Multiplexer 2 calculates the number of self transitions between D(t+1) and E(t) and sends output C1a. If the number of self transitions is 6 to 8, C1a is set to 1, otherwise C1a is set to 0. Multiplexer 3 gathers a statistic for the four MSBs of D(t+1) and sends output C1b. If the number of 1’s is greater than or equal to the number of 0’s (i.e., the number of 1’s is greater than or equal to 2), C1b is set to 0.
Otherwise C1b is set to 1. Multiplexer 4 does the same operations with multiplexer 3 for the four LBSs of D(t+1) and sends output C2. C1b and C2 decides whether D(t+1) should be inverted or not in the set of XOR gates within stage 2.
In stage 3, C1a decides whether D(t+1) should be inverted or not in the set of XOR gates. D(t+1) or [D(t+1)]’ executes XNOR operation with E(t).
In stage 4, the set of 2-to-1 multiplexers controlled by C0 are needed. They select the correct value of E(t+1).
In stage 5, the output E(t) is sent back to the input in the next cycle time. In multiplexer 5, either C1a or C1b is sent as an output C1 because C1a is valid when C0is 0 and C1b is valid when C0is 1.
4.3.2 The Decoder Stage
The decoder structure of dynamic BI-XNOR is shown in Fig.4.4. We divide this architecture into three stages and discuss each stage in detail.
E0(t+1)
In stage 1, E(t+1) execute XNOR operation with E(t) in the set of XNOR gates. C1
indicates whether E(t+1) should be inverted or not in the set of XOR gates.
In stage 2, C1 indicates whether the four MSBs should be inverted or not and C2
indicates whether the four LSBs should be inverted or not in the set of XOR gates. Note that C1 of stage 2 is different from C1 of stage 1. C1 of stage 1 is C1a in the encoder and C1 of stage 2 is C1b in the encoder. They are not both valid in the same cycle time.
In stage 3, the set of 2-to-1 multiplexers controlled by C0 select the valid value of D(t+1). The decoding is completed here.
Chapter 5
Simulation Results
In this chapter, we will make comparisons of self transitions and correlative transitions for dynamic BI-XNOR encoding and other encoding schemes mentioned in chapter 3.
5.1 Simulation Overview
We will analyze an 8×2 data matrix
A11 A21 A31
A41
A51
A61
A71
A81 A12 A22 A32
A42
A52
A62
A72
A82
,
where the first column Ax1 denotes the previous encoded pattern E(t) and the second
5.2 Simulation Results
5.2.1 Self Transitions
Fig.5.1 shows the conditional averaged self transitions after encoding. The x-axis denotes the condition when there are N self transitions between E(t) and D(t+1), the y-axis denotes the average self transitions between E(t) and E(t+1) after encoding.
Fig.5.1 Averaged Conditional Self Transitions after Encoding
Fig.5.2 shows the conditional averaged self transition reduction after encoding.
The x-axis denotes the condition when there are N self transitions between E(t) and D(t+1), the y-axis denotes the averaged self transition reduction between E(t) and E(t+1) after encoding.
Fig.5.2 Averaged Conditional Self Transition Reduction after Encoding
Compared with BITS and hihrTS schemes, our scheme is superior to these two schemes in all conditions regardless of the number of self transitions in x-axis.
Compared with EXODUS encoding, our scheme has similar performance with EXODUS when there are 3, 4 and 5 self transitions in x-axis. However, our scheme has better result than EXODUS in other conditions (i.e., when there are 0, 1, 2, 6, 7 and 8 self transitions in x-axis). Compared with BI encoding, our scheme has similar performance with BI encoding when there are 0, 1, 2, 6, 7 and 8 self transitions in x-axis since our scheme has the same encoding rule in these conditions. But our scheme has better result than it when there are 3, 4 and 5 self transitions in x-axis.
Table 5.1 shows the number of averaged conditional self transitions for each encoding
Table 5.1 No. of Averaged Conditional Self Transitions
Self Transitions
before Encoding Probability
Un-encoded BI BITS hihrTS EXODUS BI-XNOR
0 0.39% 0 0 2.91 3.5 2.5 0
1 3.13% 1 1 2.91 3.625 2.5 1
2 10.94% 2 2 2.91 3.75 2.5 2
3 21.88% 3 3 2.91 3.875 2.5 2.5
4 27.34% 4 4 2.91 4 2.5 2.5
5 21.88% 5 3 2.91 4.125 2.5 2.5
6 10.94% 6 2 2.91 4.25 2.5 2
7 3.13% 7 1 2.91 4.375 2.5 1
8 0.39% 8 0 2.91 4.5 2.5 0
Self Transitions after Encoding
Observing BITS, hihrTS and EXODUS encoding schemes, these three schemes make the self transitions become worse than that of un-encoded data when there are 0, 1 and 2 self transitions in x-axis. HihrTS encoding even also has worse result when there are 3 self transitions in x-axis. The averaged self transitions are equal to the weighted average of conditional self transitions in Table 5.1.
Since our scheme has the least self transitions and the most reduction of self transitions in all conditions, the averaged self transitions of our scheme will also be the least of all. Fig.5.3 shows the comparison of averaged self transitions of all encoding schemes. Fig.5.4 shows the percentage reduction of the averaged self transitions. Table 5.2 shows the number of averaged self transitions in each encoding scheme.
Fig.5.3 Averaged Self Transitions after Encoding
Table 5.2 No. of Averaged Self Transitions for Each Encoding Scheme
Encoding Scheme Unencode
d BI BITS hihrTS EXODUS BI-XNOR
Self Transitions 4 2.91 2.91 4 2.5 2.28
Percentage of Reduction 0% 27.3% 27.3% 0% 37.5% 43%
HihrTS encoding scheme has not any improvement in the reduction of averaged self transitions. It is because this scheme use the first bit as the encoding hint. Since we use all possible test patterns here, hihrTS encoding may loose its superiority in this simulation.
5.2.2 Correlative Transitions
Fig.5.5 shows the averaged conditional correlative transitions after encoding. The x-axis denotes the condition when there are N self transitions between E(t) and D(t+1), the y-axis denotes the averaged self transitions between E(t) and E(t+1) after encoding.
Fig.5.5 Averaged Conditional Correlative Transitions after Encoding
Fig.5.6 shows the averaged conditional correlative transition reduction after encoding. The x-axis denotes the condition when there are N self transitions between E(t) and D(t+1), the y-axis denotes the averaged correlative transition reduction between E(t) and E(t+1) after encoding.
Fig.5.6 Averaged Conditional Correlative Transition Reduction after Encoding
Compared with BITS and hihrTS schemes, our scheme is superior or similar to these two schemes in all conditions regardless of the number of self transitions in x-axis. Compared with BI encoding, our scheme has similar performance with BI encoding when there are 0, 1, 2, 6, 7 and 8 self transitions in x-axis because our scheme has the same encoding rule in these conditions. But our scheme has better
Table 5.3 No. of Averaged Conditional Correlative Transitions
Self Transitions
before Encoding Probability
Un-encoded BI BITS hihrTS EXODUS BI-XNOR
0 0.39% 0 0 0 0 0.063 0
1 3.13% 0 0 0.198 0.375 0.125 0
2 10.94% 0.125 0.125 0.340 0.661 0.170 0.125
3 21.88% 0.375 0.375 0.425 0.857 0.196 0.251
4 27.34% 0.750 0.750 0.453 0.964 0.205 0.266
5 21.88% 1.250 0.375 0.425 0.982 0.196 0.251
6 10.94% 1.875 0.125 0.340 0.911 0.170 0.125
7 3.13% 2.625 0 0.198 0.75 0.125 0
8 0.39% 3.500 0 0 0.5 0.063 0
Correlative Transitions after Encoding
Observing BITS, hihrTS and EXODUS encoding schemes, BITS encoding makes the correlative transitions become worse than that of un-encoded data when there are 1, 2 and 3 self transitions in x-axis. HihrTS encoding makes the correlative transitions become worse when there are 1, 2, 3 and 4 self transitions in x-axis. EXODUS encoding makes the correlative transitions become worse when there are 0, 1 and 2 self transitions in x-axis. The averaged correlative transitions are equal to the weighted average of conditional correlative transitions in Table 5.3.
Fig.5.7 shows the comparison of averaged correlative transitions of all encoding schemes. Fig.5.8 shows the percentage reduction of averaged correlative transitions.
Table 5.4 shows the number of averaged correlative transitions in each encoding scheme.
Fig.5.7 Averaged Correlative Transitions after Encoding
Though our scheme is inferior to EXODUS encoding in averaged correlative transitions, our scheme assures that the conditional correlative transitions will never become worse. Because EXODUS encoding makes the correlative transitions become worse when there are 0, 1 and 2 self transitions in x-axis.
5.3 Experiment with Sample Patterns
To evaluate the efficiency of our encoding, we perform experiments with random data streams, different types of audio input, image files and image files with DCT transformation.
5.3.1 Random Data Streams
We simulate all schemes with random data streams. Each data stream has 100,000 patterns and the bus width is eight bits. The experimental result is shown in Table 5.5.
It is roundly matching our simulation result in Table 5.2 and Table 5.4. This proves our simulation method by an 8×2 matrix is correct.
Table 5.5 Experimental Result of Random Data Streams
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 400,100 290,782 290,846 399,404 249,930 225,954 Percentage of Reduction - 27.3% 27.3% 0.2% 37.5% 44.0%
CorrelativeTransitions 87,870 39,955 39,833 87,501 18,683 22,459 Percentage of Reduction - 54.5% 54.7% 0.4% 78.7% 74.4%
5.3.2 Audio Files
We experiment with five different types of audio files including classic music, pop music, normal speech, noisy speech and song. All of them have the length of 10 seconds. The input signals are from WAVE files and the sample rate is 44100 points per second. Each point has two fractional numbers within 1 and -1. One is for left channel and the other is for right channel. We use 16-bit two’s complement to represent each data sample of left or right channel, the first bit is the sign bit and the other 15 bits represent the magnitude. Then we divide each 16-bit pattern into two 8-bit patterns and individually encode each channel with an 8-bit wide bus. Fig.5.9 shows an example of voice input. Complement Notation (c) Transmission with an 8-bit Wide Bus
the experimental result. Fig.5.13 is the waveform of a noisy speech file and Table 5.9 is the experimental result. Fig.5.14 is the waveform of a song file and Table 5.10 is the experimental result.
Fig.5.10 Waveform of a Classic Musical File
Table 5.6 Experimental Result of Classical Music
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 7,039,529 5,124,745 4,132,657 5,531,791 4,978,785 3,308,088 Percentage of Reduction - 27.2% 41.3% 21.4% 29.3% 53.0%
CorrelativeTransitions 885,246 402,248 586,994 1,009,538 614,085 269,986 Percentage of Reduction - 54.6% 33.7% -14.0% 30.6% 69.5%
Fig.5.11 Waveform of a Pop Music File
Table 5.7 Experimental Result of Pop Music
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 6,765,271 4,930,279 3,938,904 5,284,240 5,030,128 3,189,566 Percentage of Reduction - 27.1% 41.8% 21.9% 25.6% 52.9%
CorrelativeTransitions 832,480 379,215 555,660 962,606 588,521 257,796 Percentage of Reduction - 54.4% 33.3% -15.6% 29.3% 69.0%
Fig.5.12 Waveform of a Normal Speech File
Table 5.8 Experimental Result of Normal Speech
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 6,878,350 5,119,560 3,271,491 4,567,920 5,216,049 2,912,749 Percentage of Reduction - 25.6% 52.4% 33.6% 24.2% 57.7%
CorrelativeTransitions 412,745 192,404 422,230 828,932 791,055 204,986 Percentage of Reduction - 53.4% -2.3% -100.8% -91.7% 50.3%
Fig.5.13 Waveform of a Noisy Speech File
Table 5.9 Experimental Result of Noisy Speech
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 7,034,513 5,126,147 4,144,264 5,544,866 4,913,900 3,315,180 Percentage of Reduction - 27.1% 41.1% 21.2% 30.1% 52.9%
CorrelativeTransitions 888,533 404,188 590,707 1,016,636 596,681 275,707 Percentage of Reduction - 54.5% 33.5% -14.4% 32.8% 69.0%
Fig.5.14 Waveform of a Song File
Table 5.10 Experimental Result of a Song File
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 7,049,922 5,124,058 4,690,920 6,172,301 4,553,272 3,599,330 Percentage of Reduction - 27.3% 33.5% 12.4% 35.4% 48.9%
CorrelativeTransitions 1,203,822 545,492 693,539 1,172,629 457,195 330,969 Percentage of Reduction - 54.7% 42.4% 2.6% 62.0% 72.5%
From the above experiments, we summarize them in Table 5.11 and Table 5.12.
For the audio inputs, our scheme has a better improvement than other schemes in both self and correlative transitions.
Table 5.11 Averaged Self Transition Reduction of Audio Files
Unencoded BI BITS hihrTS EXODUS BI-XNOR
Classic Music 7,039,529 5,124,745 4,132,657 5,531,791 4,978,785 3,308,088 Pop Music 6,765,271 4,930,279 3,938,904 5,284,240 5,030,128 3,189,566 Normal Speech 6,878,350 5,119,560 3,271,491 4,567,920 5,216,049 2,912,749 Noisy Speech 7,034,513 5,126,147 4,144,264 5,544,866 4,913,900 3,315,180 Song 7,049,922 5,124,058 4,690,920 6,172,301 4,553,272 3,599,330 Average 6,953,517 5,084,958 4,035,647 5,420,224 4,938,427 3,264,983
Reduction - 26.9% 42.0% 22.1% 29.0% 53.0%
Table 5.12 Averaged Correlative Transition Reduction of Audio Files
Unencoded BI BITS hihrTS EXODUS BI-XNOR
Classic Music 885,246 402,248 586,994 1,009,538 614,085 269,986 Pop Music 832,480 379,215 555,660 962,606 588,521 257,796 Normal Speech 412,745 192,404 422,230 828,932 791,055 204,986 Noisy Speech 888,533 404,188 590,707 1,016,636 596,681 275,707 Song 1,203,822 545,492 693,539 1,172,629 457,195 330,969 Average 844,565 384,709 569,826 998,068 609,507 267,889
Reduction - 54.4% 32.5% -18.2% 27.8% 68.3%
5.3.3 Gray Image Files
We perform experiments with three gray image files. The input signals are from RAW files. All gray image files have the resolution of 256×256. Fig.5.15 is the first sample image file. This image is read as a 256×256 matrix, each element of this matrix is an integer ranging from 0 to 255. We use an unsigned 8-bit integer to represent each element. Then we transmit this image file and compare all encoding schemes. Table 5.13 is the experimental result of gray image 1. Fig.5.16 is the second sample image file and Table 5.14 is its experimental result. Fig.5.17 is the third sample image file and Table 5.15 is its experimental result.
Fig.5.15 Gray Image File 1
Table 5.13 Experimental Result of Gray Image File 1
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 174,721 144,795 197,200 258,165 160,138 140,769 Percentage of Reduction - 17.1% -12.9% -47.8% 8.3% 19.4%
CorrelativeTransitions 44,165 32,626 26,406 60,585 8,083 12,737 Percentage of Reduction - 26.1% 40.2% -37.2% 81.7% 71.2%
Fig.5.16 Gray Image File 2
Table 5.14 Experimental Result of Gray Image File 2
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 211,112 164,844 202,728 276,158 168,098 156,068 Percentage of Reduction - 21.9% 4.0% -30.8% 20.4% 26.1%
CorrelativeTransitions 54,615 35,384 24,342 66,680 7,965 14,275 Percentage of Reduction - 35.2% 55.4% -22.1% 85.4% 73.9%
Table 5.15 Experimental Result of Gray Image File 3
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 155,861 132,757 189,373 223,724 152,637 131,067 Percentage of Reduction - 14.8% -21.5% -43.5% 2.1% 15.9%
CorrelativeTransitions 39,101 29,645 26,669 47,672 13,644 13,198 Percentage of Reduction - 24.2% 31.8% -21.9% 65.1% 66.2%
We summarize these three experimental results in Table 5.16 and Table 5.17. For the gray image files, our scheme has a better improvement than other schemes in self transitions. In the reduction of correlative transitions, our scheme is inferior to EXODUS by 8% but superior to other three schemes.
Table 5.16 Averaged Self Transition Reduction of Gray Image Files
Unencoded BI BITS hihrTS EXODUS BI-XNOR
Gray Image 1 174,721 144,795 197,200 258,165 160,138 140,769 Gray Image 2 211,112 164,844 202,728 276,158 168,098 156,068 Gray Image 3 155,861 132,757 189,373 223,724 152,637 131,067 Average 108,339 88,479 117,860 151,609 96,175 85,581
Reduction - 18.3% -8.8% -39.9% 11.2% 21.0%
Table 5.17 Averaged Correlative Transition Reduction of Gray Image Files
Unencoded BI BITS hihrTS EXODUS BI-XNOR
Gray Image 1 44,165 32,626 26,406 60,585 8,083 12,737 Gray Image 2 54,615 35,384 24,342 66,680 7,965 14,275 Gray Image 3 39,101 29,645 26,669 47,672 13,644 13,198
Average 27,576 19,531 15,483 34,987 5,938 8,042
Reduction - 29.2% 43.9% -26.9% 78.5% 70.8%
5.3.4 Color Image Files
We perform the experiment with three color image files. The input signals are from JPEG files. All color image files have the resolution of 256×256. Fig.5.18 is the color image file 1. This image is read as a 256×256×3 matrix, each element of this matrix is an integer ranging from 0 to 255. The 256×256×1 denotes red (R) elements, the 256×256×2 denotes green (G) elements and the 256×256×3 denotes blue (B) elements of the image. We use an unsigned 8-bit integer to represent each element and transmit R, G and B elements of this image file in order and compare all encoding schemes. Table 5.18 is the experimental result. Fig.5.19 is the color image file 2 and Table 5.19 is the experimental result. Fig.5.19 is the color image file 3 and Table 5.19 is the experimental result.
Fig.5.18 Color Image File 1
Table 5.18 Experimental Result of Color Image File 1
Fig.5.19 Color Image File 2
Table 5.19 Experimental Result of Color Image File 2
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 555,496 458,354 607,542 797,543 485,404 452,955 Percentage of Reduction - 17.5% -9.4% -43.6% 12.6% 18.5%
Correlative Transitions 140,901 105,181 79,021 186,689 25,359 39,743 Percentage of Reduction - 25.4% 43.9% -32.5% 82.0% 71.8%
Fig.5.20 Color Image File 3
Table 5.20 Experimental Result of Color Image File 3
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 439,664 379,122 600,933 717,710 451,243 398,815 Percentage of Reduction - 13.8% -36.7% -63.2% -2.6% 9.3%
Correlative Transitions 111,997 91,017 87,190 153,378 30,326 36,839 Percentage of Reduction - 18.7% 22.1% -36.9% 72.9% 67.1%
We summarize these three experimental results in Table 5.21 and Table 5.22. In the reduction of self transitions, our scheme is inferior to BI by 1.4% but superior to other three schemes. In the reduction of correlative transitions, our scheme is inferior to EXODUS by 8.5% but superior to other three schemes.
Table 5.21 Averaged Self Transition Reduction of Color Image Files
Unencoded BI BITS hihrTS EXODUS BI-XNOR
Color Image 1 497,581 411,391 593,922 766,689 490,460 414,331 Color Image 2 555,496 458,354 607,542 797,543 485,404 452,955 Color Image 3 439,664 379,122 600,933 717,710 451,243 398,815 Average 298,548 249,773 360,479 456,388 285,421 253,220
Reduction - 16.3% -20.7% -52.9% 4.4% 15.2%
Table 5.22 Averaged Correlative Transition Reduction of Color Image Files
Unencoded BI BITS hihrTS EXODUS BI-XNOR
Color Image 1 127,228 94,341 77,325 177,376 28,071 40,223 Color Image 2 140,901 105,181 79,021 186,689 25,359 39,743 Color Image 3 111,997 91,017 87,190 153,378 30,326 36,839 Average 76,025 58,108 48,707 103,489 16,751 23,361
Reduction - 23.6% 35.9% -36.1% 78.0% 69.3%
integer and use 8-bit two’s complement to represent each parameter. We shift all parameters to eight bits and use zigzag scan to transmit all elements in 8-bit wide bus.
The DCT transformation makes the appearance of zero become more frequent. Table 5.23, Table 5.24 and Table 5.25 are the experimental results.
Table 5.23 Experimental Result of DCT-transformed Image File 1
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 54,518 16,378 10,542 16,872 254,254 12,368 Percentage of Reduction - 70.0% 80.7% 69.1% -366.4% 77.3%
CorrelativeTransitions 1,542 1,122 1,044 1,203 60,451 693 Percentage of Reduction - 27.2% 32.3% 22.0% -3820.3% 55.1%
Table 5.24 Experimental Result of DCT-transformed Image File 2
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 129,114 30,446 19,605 34,993 245,507 25,523 Percentage of Reduction - 76.4% 84.8% 72.9% -90.1% 80.2%
CorrelativeTransitions 2,879 2,230 1,484 1,725 56,341 1,580 Percentage of Reduction - 22.5% 48.5% 40.1% -1857.0% 45.1%
Table 5.25 Experimental Result of DCT-transformed Image File 3
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR Self Transitions 52,857 16,825 11,085 17,349 254,703 12,473 Percentage of Reduction - 68.2% 79.0% 67.2% -381.9% 76.4%
CorrelativeTransitions 1,736 1,285 1,140 1,354 57,496 806 Percentage of Reduction - 26.0% 34.3% 22.0% -3212.0% 53.6%
We summarize the experimental results in Table 5.26 and Table 5.27. In the
reduction of self transitions, our scheme is inferior to BITS by 4.2% but superior to other three schemes. In the reduction of correlative transitions, our scheme is superior to all the other schemes.
Table 5.26 Averaged Self Transition Reduction of DCT-transformed Image Files
Unencoded BI BITS hihrTS EXODUS BI-XNOR
Image 1 54,518 16,378 10,542 16,872 254,254 12,368 Image 2 129,114 30,446 19,605 34,993 245,507 25,523 Image 3 52,857 16,825 11,085 17,349 254,703 12,473 Average 47,298 12,730 8,246 13,843 150,893 10,073
Reduction - 73.1% 82.6% 70.7% -219.0% 78.7%
Table 5.27 Averaged Correlative Transition Reduction of DCT-transformed Image Files
Unencoded BI BITS hihrTS EXODUS BI-XNOR
Image 1 1,542 1,122 1,044 1,203 60,451 693
Image 2 2,879 2,230 1,484 1,725 56,341 1,580
Image 3 1,736 1,285 1,140 1,354 57,496 806
Average 1,231 927 734 856 34,858 616
Reduction - 24.7% 40.4% 30.5% -2730.7% 50.0%
We find EXODUX encoding is very bad for the transmission of image files with DCT transformation. This is because the DCT transformation makes the appearance of zero become more frequent. When the data stream is from 00000000 to 00000000, all
The comparison of self transitions is shown in Table 5.28. The experimental result shows our scheme has the best performance in the types of random data, audios and gray image files. For the color image files, our scheme is inferior to BI by 1.4% but better than other three schemes. For DCT-transformed image files, our scheme is inferior to BITS by 4.2% but better than other three schemes.
Table 5.28 Performance Comparison of Self Transition Reduction
BI BITS hihrTS EXODUS BI-XNOR
Random Data 27.3% 27.3% 0% 37.5% 44.0%
Audio 26.9% 42.0% 22.1% 29.0% 53.0%
Gray Image 18.7% -8.8% -39.9% 11.2% 21.0%
Color Image 16.3% -20.7% -52.9% 4.4% 15.2%
Image with DCT 73.1% 82.6% 70.7% -219.0% 78.7%
The comparison of correlative transitions is shown in Table 5.29. The experimental result shows our scheme has the best performance in the types of audios and DCT-transformed image files. For the random data streams, gray image files and color image files, our scheme is inferior to EXODUS but better than other three schemes. But EXODUS is useless for the transmission of DCT-transformed image files.
Table 5.29 Performance Comparison of Correlative Transition Reduction
BI BITS hihrTS EXODUS BI-XNOR
Random Data 54.5% 54.7% 0.4% 78.7% 74.4%
Audio 54.4% 32.5% -18.2% 27.8% 68.3%
Gray Image 29.2% 43.9% -26.9% 78.5% 70.8%
Color Image 23.6% 35.9% -36.1% 78.0% 69.3%
Image with DCT 24.7% 40.4% 30.5% -2730.7% 50.0%
Chapter 6
Implementation Results
In this chapter, we implement our structure and all mentioned schemes in VHDL, then compare the area and power consumption of the encoder/decoder. Next, we analyze the dynamic power consumption of each encoding scheme when the data patterns are transmitted.
6.1 Implementation Results of Encoder/Decoder
From the encoder and decoder circuits of BI, BITS, hihr-TS, EXODUS and BI-XNOR methods, we implement them in VHDL. Table 6.1 is the implementation results of encoder/decoder for each encoding scheme. The process is 0.18µm UMC technology. The clock frequency is set to be 100MHz.
Table 6.1 Implementation Results of Encoder/Decoder for Each Scheme
Encoder Decoder
2 2
6.2 Dynamic Power Estimation
From equation (2.3), the power dissipation resulted from bus transitions P is bus
2 2 2
(1 ) (2 )
2
S C VS dd + C VC C dd +C VS dd
γ γ where γ is the number of the averaged self S
transitions per bus cycle and γ is the number of averaged correlative transitions per C bus cycle. To estimate whole power consumption, we should also consider the power consumption of encoder/decoder for each encoding scheme. So we obtain the following total power dissipation:
2 2 2
(1 ) (2 )
2
t enc dec S S dd C C dd S dd
P = P + P +γ C V + γ C V + C V (6.1)
Since our VHDL simulation is based on the clock frequency of 100MHz, 100 mega data patterns are transmitted in one second. From the experimental results in chapter 5.3, we can estimate the value of γ and S γ in the frequency of 100MHz. C For general I/O buses, the driving voltage is 3.3V. Table 6.2 [6] shows the value of Cs and Cc in various IC processes. We assume the power consumption of each transition is independent and the length of bus wire is 3cm (standard LQFP 216pin). According to equation (6.1), we could estimate the dynamic power consumption for each encoding scheme when the data patterns are transmitted.
Table 6.2 Self Capacitance and Coupling Capacitance in Various IC Processes
Process
Cs Cc Cs Cc Cs Cc Cs Cc
10.96 40.76 10.5 44.75 9.97 49.35 15.75 46.82 0.05µm
0.18µm 0.10µm
0.25µm
(10 F/ m)−18 μ
In the following sections, we estimate the dynamic power consumption of the bus when different types of sample patterns are transmitted.
6.2.1 Random Data Streams
In the experiment in chapter 5.3.1 and the experimental result in Table 5.5, 100,000 random data patterns are transmitted. According to the same ratio, the self and correlative transitions are normalized and shown in Table 6.3 when the clock frequency is 100MHz. Table 6.4 is the power consumption of each encoding scheme.
Table 6.3 Bus Transitions of Random Data when The Frequency is 100MHz
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR
Encoding Scheme Unencoded BI BITS hihrTS EXODUS BI-XNOR