This document discusses arithmetic coding, a lossless data compression technique. It begins with an overview of source coding and commonly used compression algorithms like Huffman coding and run-length encoding. It then describes problems with Huffman coding like less efficiency and flexibility. Arithmetic coding is presented as an alternative with better compression ratios and adaptiveness. The document proceeds to explain the encoding and decoding process of arithmetic coding through assigning probabilities to symbols and mapping them to ranges within 0 to 1. It provides examples and figures to illustrate the technique. In summary, arithmetic coding achieves better compression than Huffman coding by producing a single codeword rather than multiple codewords.

1. MU-MIT
Arithmetic Coding
GROUP MEMBERS
1.Gidey Leul
6/18/2017
1ECE /MIT/2009

2. CONTENTS
1. What is Source Coding general concept?
2. What are Commonly Used Data compression algorithms?
3. Problems of Huffman and the need of Arithmetic coding , general comparison?
4. Arithmetic Encoding.
5. Arithmetic Decoding.
6/18/2017
2ECE /MIT/2009

3. 1.GENERAL CONCEPT OF
SOURCE CODING
Source Coding : encoding information using fewer bits than the original
representation.
Importance of Data Compression is :
A technique to reduce the quantity of data .
preserve quality of themultimedia data.
Allows more bytes to be packed than uncompressed.
Saving storage ,saving Bandwidth .
Reduce file transfer time . quick encode & send .
i.e,mp4->mp3.
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4. CONTND….
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5. CONTND…..
Compression
can be either:
I. LOSSY or
II. lossles
FIGURE 1.2 Comparision Loosy vs lossless
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6. CONTND…..
Figure 1.3 Quality comparison for lossy system
o What is Lossy Compression?
 after compression ,file cannot recover.
 reduce image size .
 redundant information lost.
 i.e -mp3,JPEG,wav
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7. Contnd… Reserved original , word press.
text
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8. 2.COMMONLY USED COMPRESSING
ALGORITHMS
• i.Huffman Coding
• assign short codewords to those input blocks with high probabilities and long
codewords to those with low probabilities.
6/18/2017 8ECE /MIT/2009

9. CONTND…..
ii. Run Length Encoding
Algorithm:
 Run length encoding is simple form of data compression.
 consecutive runs of data are stored as single data value .
 Each count(indicating how many times that data is repeating) .
 It is useful for compressing simple graphic images .
EXAMPLE:
Input: ZZZZZZZZZZZZCZZZZZZZZZZZZCCCZZZZZZZZZZZZZZZZZZZZZZZZC
Output:
12ZC12Z3C24ZC
6/18/2017 9ECE /MIT/2009

10. III.ARITHMETIC CODING
 Mathematical compression.
Based on the coding of a input sequence using a rational number in ranges [0,1).
 Doesn´t use a discrete number of bits for each.
The main idea behind Arithmetic coding is to assign each symbol an interval.
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11. 3.PROBLEMS OF HUFFMAN AND THE NEED OF ARITHMETIC
CODING , GENERAL COMPARISON?
ARITHMETIC CODING
• Huffman coding
 Less efficiency
 less edible.
……… .....in contrast
Faster
Enough storage
• Arithmetic Coding
 redundancy much reduced.
Can be used with any model
conjunction , adaptiveness ,sharp in any
model.
…………………………Dis advantage AC
 Too slow because mathematical
operations .
Significant amount of memory.
6/18/2017 11ECE /MIT/2009

12. CONTND….
1.5 Figure comparison between Huffman And Arithmetic coding 6/18/2017 12ECE /MIT/2009

13. 4.ARITHMETIC ENCODING STEPS
• To code symbol s ,where symbols are numbered from 1 to n and symbol I has the
probability pr[i];
• low bound = 𝑖=0𝑝𝑟
𝑠−1
[𝑖]
• High bound = 𝑖=0𝑝𝑟
𝑠−1
[𝑖]
• Range=high-low
• Low=low + range *(low bound)
• High=low + range *(high bound)
6/18/2017 13ECE /MIT/2009

14. CONTND----
• Consider encoding the name MIT CAMPAS Again, we need the frequency of all the
characters in the text
• char freq.
• Space 0.1
• A 0.2
• C 0.1
• I 0.1
• M 0.2
• P 0.1
• S 0.1
• T 0.1
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15. CONTND----
• . character probability range
• space 0.1 [0.00, 0.10)
• A 0.2 [0.10, 0.30)
• C 0.1 [0.30, 0.40)
• I 0.1 [0.40, 0.50)
• M 0.2 [0.50, 0.70)
• P 0.1 [0.70, 0.80)
• S 0.1 [0.80, 0.90)
• T 0.1 [0.90, 1.00)
•
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16. CONTND----
• . ENCODING THEWORD MIT CAMPAS
• chr low high
• 0.0 1.0
• M 0.5 0.7
• I 0.54 0.55
• T 0.549 0.550
• Space 0.5490 0.5491
• C 0.54903 0.54941
• A 0.549301 0.549033
• M 0.5493015 0.5493017
• P 0.54930164 0.54930166
A 0.549301643 0.549316466
S 0.5493016438 0.5493016439
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17. CONTND
• .The final low value, 0.5493016438 will uniquely encode the name MIT CAMPAS.
• which in binary is approximately [0.11010 00000, 0.11010 01100).We can uniquely
identify this interval by outputting 1101000.
• Another example Encoding
suppose the alphabet is (a, e, i, O, u, !I, and a fixed model is used with
probabilities shown in Table I. Imagine trans mitting the message eaii! .
 Initially, both encoder and decoder know that the range is [0, 1).
 After seeing the first symbol, e, the encoder narrows it to [0.2, 04, the range the
model allocates to this symbol.
The second symbol, a, will narrow this new range to the first one-fifth of it,
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18. CONTND…
• .
Figure 1.7 frequency of alphabets
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19. CONTND…
• 1.8 Graphical representation of Arithmetic coding.
6/18/2017 19ECE /MIT/2009

20. HOW THE ARITHMETIC DECODER WORKS?
 Decoder detects the last suffix o.23355.
Relative to the fixed model of Table I,
.The entropy of the five-symbol message eaii! Is taking logarithm of each term would
be 4.22 .
6/18/2017 20ECE /MIT/2009

21. GENERALLY……..
 Arithmetic coding typically has a better compression ratio than Huffman coding, as it
produces a single symbol rather than several separate code words.
 Arithmetic coding is a lossless coding technique.
Few disadvantages of arithmetic coding.
I . whole code word must be received to start decoding the symbols.
 If corrupt bit in the code word, the entire message could become corrupt.
II .There is a limit to the precision of the number which can be encoded, thus limiting
the number of symbols to encode within a code word.
 There also exists many patents upon arithmetic coding, so the use of some of the
algorithms also call upon royalty fees.
6/18/2017 21ECE /MIT/2009

22. CONTND…
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