[IR] Arithmetic Coding

Statistical methods的除了huffman外的另外一種常見壓縮方式。

 

Huffman coding的非連續數值特性成爲了沒法達到香農極限的先天沒法彌補的缺陷，但Arithmetic coding給出了better solution。

固然，最好的東西每每伴隨着各類專利。

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2012年以後，貌似能夠有一部分能夠用了呢。

 

Encoding:

每一個字符分配一個Range，size就是其比例（Probability）。

Algorithm:

Set low  to 0.0
Set high to 1.0

While there are still input symbols do
get an input symbol
　　code_range = high - low.
　　high = low + range*high_range(symbol)
　　low  = low + range*low_range (symbol)
End of While
output low or a number within the range

  

Decoding:

第四行：0.72167752, Low:0.6, High:0.8, 那麼，下一個char會是什麼？

range=0.8-0.6=0.2

encoded number = (0.72167752-0.6)/0.2 = 0.6083876 --> L

 

Algorithm:

get encoded number

Do
　　find symbol whose range straddles the encoded number
　　output the symbol
　　range = symbol high value - symbol low value
　　subtract symbol low value from encoded number
　　divide encoded number by range
until no more symbols

 

 

優化技巧：

 

其實，0.45即能解碼成功。

大大地提升了壓縮率。

 

Bzip2 and JPG use Huffman as AC protected by patents
PackJPG using AC shows 25% of size saving

 

關於專利：

U.S. Patent 4,122,440 — (IBM) Filed 4 March 77, Granted 24 October 78 (Now expired)U.S. Patent 4,286,256 — (IBM) Granted 25 August 81 (Now expired)U.S. Patent 4,467,317 — (IBM) Granted 21 August 84 (Now expired)U.S. Patent 4,652,856 — (IBM) Granted 4 February 86 (Now expired)U.S. Patent 4,891,643 — (IBM) Filed 15 September 86, granted 2 January 90 (Now expired)U.S. Patent 4,905,297 — (IBM) Filed 18 November 88, granted 27 February 90 (Now expired)U.S. Patent 4,933,883 — (IBM) Filed 3 May 88, granted 12 June 90 (Now expired)U.S. Patent 4,935,882 — (IBM) Filed 20 July 88, granted 19 June 90 (Now expired)U.S. Patent 4,989,000 — Filed 19 June 89, granted 29 January 91 (Now expired)U.S. Patent 5,099,440 — (IBM) Filed 5 January 90, granted 24 March 92 (Now expired)U.S. Patent 5,272,478 — (Ricoh) Filed 17 August 92, granted 21 December 93 (Now expired)