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Shmuel Tomi Klein Bar Ilan University, Israel. On the Usefulness of. Fibonacci Compression Codes. Binary character Huffman. Binary word-based Huffman. 256-ary word-based Huffman. Tagged Huffman. End tagged Huffman. ( s , c ) dense codes. Fibonacci Compression Codes. Compression ratio.

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shmuel tomi klein bar ilan university israel
Shmuel Tomi Klein

Bar Ilan University, Israel

On the Usefulness of

Fibonacci Compression Codes
slide2

Binary character Huffman

Binary word-based Huffman

256-ary word-based Huffman

Tagged Huffman

End tagged Huffman

(s,c) dense codes

slide3

Fibonacci Compression Codes

Compression ratio

Vocabulary representation

Fast decoding

Compressed search

Robustness

slide5

Fibonacci numbers of order

1 2 3 5 8 13 21 34

Fibonacci representation:

45 = 0 0 1 0 1 0 0 1 1

slide7

Compression Efficiency

bits

codeword length

20

- log p

10

ETDC

Fib2

Fib3

0

1

16

256

4096

65536

slide8

Compression Efficiency

bits

average codeword length for Zipf

22

18

14

10

ETDC

Fib2

6

Fib3

1

100

10000

1000000

slide10

Vocabulary Representation

Many Huffman codes

ETDC

SCDC

fixed sets

Fibm

slide11

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 [ Text[i] , R ]

slide13

Fast Decoding, con’t

Too many tables, one for each prefix

To reduce the number of tables,

use properties of Fibonacci numeration systems

i - 1

i

i + 1

S

S

oldSV

PV

SV

oldSL

PL

SL

slide16

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

slide17

Compressed search, con’t

Solution 1: Eliminate first codeword111

2% compression loss

Solution 2: Check if occurrence is preceded by

0111 or 0111111, etc

Solution 3: Define a new codeword for “the the”

slide18

Compressed search, con’t

Bitwise BM search is slow use Blocked-BM

slide19

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

slide20

Conclusion

Higher order Fibonacci codes:

plausible alternative to dense codes

Tradeoff: better compression and robustness

worse on time (decoding and search)