hardware implementation of data compression ... - INFN Bologna

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22 Data compression techniques 2.1 Applications of data compression An early example of data compression is the Morse code, developed by Samuel Morse in the mid-19th century. Letters sent by telegraph are encoded with dots and dashes. Morse noticed that certain letters occurred more often than others. In order to reduce the average time required to send a message, he assigned shorter sequences to letters that occur more frequently such as a (· −)ande (·) and longer sequences to letters that occur less frequently such as q (− −·−)orj (· −−−). What is being used to provide compression in the Morse code is the statistical structure of the message to compress, i.e. the message contains letters with a probability to occurr higher than others. So far most compression techniques exploit the input statistical structure to provide compression, but this is not the only kind of structure that exists in the data. There are many other kinds of structures in data of differents types that can be exploited for compression. Let us take speech as an example. When we speak, the physical construction of our voice box dictates the kinds of sounds that we can produce, that is the mechanics of speech production impose a structure on speech. Therefore, instead of transmitting the sampled speech itself we could send information about the conformation of the voice box, which could be used by the receiver to synthesize the speech. An adequate amount of information about the conformation of the voice box can be represented much more compactly than the sampled values of the speech. This compression approach is being used currently in a number of applications, including transmission of speech over mobile radios and the synthetic voice in toys that speak. Data compression can also take advantage of some redundant structure of the input signal, that is a structure containing more information than needed. For example if a sound has to be transmitted for being heard by a human being, all frequencies below 20 Hz and above 20 KHz can be eliminated (thus providing compression) since these frequencies
2.2 — Remarks on information theory cannnot be perceived by humans. 2.2 Remarks on information theory Without going into details we just want to recall Shannon’s theorem [8]. He defines the information contents of a message in the following way: given a message which is made up of N characters in total containing n different symbols, the information contents measured in bits of the message is the following: n I = N (−pilog(pi)) (2.1) i=1 where pi is the occurrence probability of symbol i. What is regarded as a symbol depends on the application: it might be an ASCII code, 16 or 32 bit words, words in a text and so on. A practical illustration of the Shannon theorem is the following: let us assume to measure a charge or any other physical quantity using an 8-bit digitizer. Very often measured quantities will be distributed approximately exponentially. Let us assume that the mean value of the statistical distribution is one tenth of the dynamic range, i.e. 25.6. Each value between 0 and 255 is regarded as a symbol. Applying the −(i+0.5) e 25.6 Shannon’s formula with n = 256 and pi = we obtain a mean 25.6 information content I/N of 6.11 bits per measured value which is almost 25% less than the 8 bits we need saving the data as a sequence of bytes. Even if we had increased the dynamic range by a factor of 4 using a 10-bit ADC, it turns out that the mean information contents expressed as the number of bits per measurement would have been virtually the same and hence the possible compression gain even higher (39%). This might be surprising but considering that an exponential distribution delivers a value beyond ten times the mean only every e10 = 22026 samples, it is clear that even using a quite long code for such measurements cannot have an appreciable influence on the compression 23
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Page 5 and 6: Contents Introduction ix 1 The ALIC
Page 7 and 8: CONTENTS 4 2D compression algorithm
Page 9 and 10: Introduction This thesis work has b
Page 13 and 14: Chapter 1 The ALICE experiment ALIC
Page 15 and 16: 1.1 — The Inner Tracking System 1
Page 17 and 18: 1.1 — The Inner Tracking System t
Page 19 and 20: 1.1 — The Inner Tracking System P
Page 21 and 22: 1.2 — Design of the drift layers
Page 23 and 24: 1.3 — The SDDs (Silicon Drift Det
Page 25 and 26: PASCAL AMBRA 1.4 — SDD readout sy
Page 27 and 28: data_in[0] data_in[1] data_in[2] da
Page 29 and 30: 1.4 — SDD readout system 1.4.2 Ev
Page 31 and 32: 1.4 — SDD readout system with a c
Page 33: Chapter 2 Data compression techniqu
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Page 39 and 40: 2.4 — Lossless compression techni
Page 45 and 46: Original sequence Sequence after di
Page 47 and 48: 2.5 — Lossy compression technique
Page 63 and 64: 2.6 — Implementation of compressi
Page 65 and 66: Symlets sym2 sym3 sym4 sym8 Wavelet
Page 67 and 68: Chapter 3 1D compression algorithm
Page 69 and 70: 3.2 — 1D compression algorithm Fi
Page 71 and 72: 3.3 — 1D algorithm performances s
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Page 75 and 76: 3.4 — CARLOS v1 Figure 3.6: CARLO
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Page 81 and 82: 3.5 — CARLOS v2 have a 100% compa
Page 83 and 84: 3.5 — CARLOS v2 3.5.1 The firstch
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3.5 — CARLOS v2 data and when loa
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3.5 — CARLOS v2 which of the 8 qu
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- indat6 : input 32-bit bus; - inda
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3.5 — CARLOS v2 - femux is a mult
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3.5 — CARLOS v2 total optical fib
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3.5 — CARLOS v2 Figure 3.11: Desi
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3.5 — CARLOS v2 that CARLOS will
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3.6 — CARLOS v2 design flow Figur
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3.7 — Tests performed on CARLOS v
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Chapter 4 2D compression algorithm
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4.1 — 2D compression algorithm Fi
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4.2 — CARLOS v3 vs. the previous
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4.3 — The final readout architect
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4.5 — CARLOS v3 building blocks -
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4.5 — CARLOS v3 building blocks T
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4.5 — CARLOS v3 building blocks F
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4.5 — CARLOS v3 building blocks c
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4.5 — CARLOS v3 building blocks o
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4.5 — CARLOS v3 building blocks u
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4.5 — CARLOS v3 building blocks a
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4.5 — CARLOS v3 building blocks p
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4.7 — CARLOS layout features post
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Chapter 5 Wavelet based compression
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levels used: 5.1 — Wavelet based
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5.2 — Multiresolution algorithm o
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5.3 — Choice of the architecture
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5.3 — Choice of the architecture
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Dettaglio 1 1 D1 2 Downsample Hi_De
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2 Upsample Dettaglio 1 1 D1 Hi_Rec
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5.4 — Multiresolution algorithm p
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5.5 — Hardware implementation ter
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5.5 — Hardware implementation Fig
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5.5 — Hardware implementation com
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5.5 — Hardware implementation Haa
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Conclusions The main goal of this t
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Bibliography [1] ALICE Collaboratio
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BIBLIOGRAPHY [19] D. Cavagnino, P.
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