Images.Audio.Cryptography - Steganography.

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MultiMedia Compression

} Movies

Statistic codeGiving a presentation in a different length to each item according to its probability.

Dictionary codeA collection of strings.The compressed file contains pointers to those strings.

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Codes' type

Static codeTwo passes on data.One for gathering information and one for executing the compression.

Adaptive codeOne pass on data for both gathering information and compression's executing.Faster than static.If file isn't uniform, can be sometimes better since it can "forget".

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Another division for types

Lossless CodeNo loss of data

Lossy CodeSome data may lost. Very common in use for audio, images, video etc.

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Yet another division for types

Fixed length code can be easily broken into codewords.How can we split a variable length code?

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Uniquely Decipherable

A - 0B - 10C - 11D - 1

110 can be “CA” or “DB” or “DDA”.

No codeword is the prefix of any other codeword.Example:

A - 000B - 001C - 0100D - 0101E - 011F - 10G - 11

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The prefix property

10011010000000111

F C G E A B

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Tree of Prefix code

10

11100100

011010001000

01010100

A prefix code is complete if it fits a complete binary tree.A prefix code is complete if an insertion of another codeword will make it a not Uniquely Decipherable code.These two definitions are equivalents.

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A complete prefix code

Divide the set of symbols into two equal or almost equal subsets based on the probability of occurrence of characters in each subset.One set is assigned 0.The other set is assigned 1.Repeat the procedure until all subsets have a single element.Each element's code is the concatenation of the sets' bits.

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Shannon-Fano coding

A - 5%, B - 15%, C - 20%, D - 25%, E - 35%.

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An example

15%

5%25%

20%

35%

5%20%

25% 15%

35%

25% 15% 35%5% 20%

20%5%

1

1

1

1

0

00

0

111 A(5%)

01 B(15%)

110 C(20%)

10 D(25%)

00 E(35%)

This tree will give a better compression:Shannon-Fano tree:3*0.05+2*0.15+3*0.20+2*0.25+2*0.35=2.25This better tree:3*0.05+3*0.15+2*0.20+2*0.25+2*0.35=2.2

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Shannon-Fano is not optimal

15%

5%25%

20%

35%

5%

20%25%

15% 35%

25%

15%

35%5% 15%20%

5%

1

1

1

1

0

00

0