compression no. 1 seattle pacific university data compression kevin bolding electrical engineering...

Compression No. 1Seattle Pacific University

Data Compression

Kevin BoldingElectrical Engineering

Seattle Pacific University


Compression

• Reducing the size of a message by removing redundant data

• Compression relies on some understanding of the structure of a message

• Only works on structured messages; random messages cannot be effectively compressed

• Because wireless systems (especially mobile phones) have limited capacity, compression is critical

• For example, an average compression rate of 50% doubles system capacity


Lossless compression

• Lossless compression transmits enough information to recreate the original with no defects• Huffman coding

• Calculate statistics for the occurrence rates of various symbols

• Assign short codes to common signals, long codes to uncommon symbols


Huffman Encoding• Example: Alphabet of {A,B,C,D,E,F,G}

• We could pick A=000, B=001, C=010, etc.• Encoding of the string: BACADAEAFABBAAAGAH is 54 bits:

001000010000011000100000101000001001000000000110000111

• What if we know that some symbols occur more frequently (A, followed by B in this example)?• A=0; B=100; C=1010; D=1011; E=1100; F=1101; G=1110; H=1111• Encoding of the previous string is only 42 bits:

100010100101101100011010100100000111001111


General Lossless Compression

• If source type is known (i.e. English text), a pre-defined dictionary/index can be used

• If source type is not known, the algorithm can create a dictionary with statistics on the fly

• Dictionary must be transmitted with the message

• ZIP file compression works this way


Lossy Compression• If the only purpose of the message is to be

interpreted by a human, we can remove data not perceived by human senses

• Music – Limits on hearing• Cannot hear frequencies above 20kHz• Cannot detect frequencies with low amplitudes in

the presence of frequencies with high amplitudes

• Voice – Purpose is communication, not fidelity• Intelligibility matters most• Pleasing sound also matters

• Images and Video• Models of how humans see can help…


Voice Compression

• Tremendous opportunity for compression

• We know the model for voice production

• We know the model for reception

• We probably know the rules of speech (language-specific)

• Language has tremendous redundancy

• Speech is time-limited, with communication as its primary purpose; it is not generally saved and studied in more detail later


Voice Compression Techniques

• Companding• Use non-linear encoding to decrease dynamic range• Reduces the number of bits needed per sample

• Linear Predictive Coding• Use a model of the human vocal tract• Send parameters that reflect operations on the

components of the vocal tract• Codebooks

• Form a book of “codes” that correspond to types of sounds commonly used in speed

• Send the number for each code rather than the sound itself


Nonlinear coding• Linear coding samples using

a linear scale• Large amplitude Cross

many levels during waveform (good)

0123456789

101112131415

• Nonlinear encoding

• More levels concentrated near the center level

• Wider spacing at edges

• Compresses dynamic range

0

1

23456789

10111213

14

15

• Small amplitude Cross few levels during waveform (bad)


Companding

• A form of non-linear encoding commonly used with telephone systems

• Before quantitizing, reshape the signal by increasing the amplitude of low-amplitude signals

• In US and Japan, mu-law is used; in Europe, A-law is used

Original (top) and companded (bottom) waveforms.


Linear Predictive Coding

• The human vocal tract can be modeled by:

• A buzzer with varying pitch and volume (the vocal cords)

• A tube with resonances at certain frequencies (the vocal tract)• Resonant frequencies are called formants

• A filter (lips, tongue, etc.)

• LPC Encoding

• Estimate the frequency and intensity of the original buzz

• Find the closest match to overall tone by selecting formants

• Remove these from signal left-over is residue

• Transmit the buzz frequency and intensity, the formants selected, and the residue


Codebooks

• Since speech is chosen from a limited number of basic sounds, it may be described as only these basic sounds

• Make a codebook including examples of all types of speech sounds

• Encoding: Find best matching sound and send the code for that

• Decoding: Look up code and produce sound• Drawbacks:

• Codebook may reflect “standard” speech, not the speaker in particular

• Codebook may be excessively large


Codebook Excited Linear Predictive Coders

• CELP coders use two steps

• Encode the speech using an LPC. This gives codes for the frequency, intensity and formants, plus a residue.

• Encode the residue using codebook techniques. Normally, two codebooks are used:

• Fixed codebook of common residue signals.• Adaptive codebook that includes recently used

residue signals. This reduces the data rate for repetitive signals.

compression no. 1 seattle pacific university data compression kevin bolding electrical engineering...

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