Fibonacci Compression Codes

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Fibonacci Compression Codes
On the Usefulness of

• Shmuel Tomi Klein
• Bar Ilan University, Israel

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Binary character Huffman
Binary word-based Huffman
256-ary word-based Huffman
Tagged Huffman
End tagged Huffman
(s,c) dense codes
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Fibonacci Compression Codes
Compression ratio
Vocabulary representation
Fast decoding
Compressed search
Robustness
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Fibonacci numbers of order
for
for
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Fibonacci numbers of order
1 2 3 5 8 13 21 34
Fibonacci representation
45 0 0 1 0 1 0 0 1 1
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Compression Efficiency
bits
codeword length
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- log p
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ETDC
Fib2
Fib3
0
1
16
256
4096
65536
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Compression Efficiency
bits
average codeword length for Zipf
22
18
14
10
ETDC
Fib2
6
Fib3
1
100
10000
1000000
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Compression Efficiency
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Vocabulary Representation
Many Huffman codes
ETDC
SCDC
fixed sets
Fibm
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Fast Decoding
Bitwise very slow
Partial decoding tables
227
221
226
221
223
1 1 1 0 0 0 1 1
1 1 0 1 1 1 0 1
1 1 1 0 0 0 1 0
1 1 0 1 1 1 0 1
1 1 0 1 1 1 1 1
for to length of text in
bytes
(output, R) Tab Texti , R
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Fast Decoding, cont
Too many tables, one for each prefix
To reduce the number of tables,
use properties of Fibonacci numeration systems
i
i - 1
i 1
S
S
oldSV
PV
SV
oldSL
PL
SL
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Fast Decoding, Results
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Compressed search
Search in Huffman synchronization
problem
TH, ETDC, SCDC, Fibm not suffix
codes
day 1011000111
search for 1111011000111
found in 100001000111-11011000111
burnt offering
Problem codewords starting with 1s
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Compressed search, cont
Solution 1 Eliminate first codeword 111
2 compression loss
Solution 2 Check if occurrence is preceded
by 0111 or 0111111, etc
Solution 3 Define a new codeword for the
the
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Compressed search, cont
Bitwise BM search is slow use
Blocked-BM
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Robustness
Bit-flips 1 or 2 codewords lost
for fixed length, TH, SCDC, Fibm.
No propagation
for TH, SCDC, like var length Huffman all the
suffix may be lost
Insertions Deletions
Fibm are immune because codeword ending is
explicit
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Conclusion
Higher order Fibonacci codes
plausible alternative to dense codes
Tradeoff better compression and robustness
worse on time (decoding and
search)
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Thank you !