[IR] Arithmetic Coding

Statistical methods的除了huffman外的另一种常见压缩方式。

Huffman coding的非连续数值特性成为了无法达到香农极限的先天无法弥补的缺陷，但Arithmetic coding给出了better solution。

当然，最好的东西往往伴随着各种专利。

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2012年之后，貌似可以有一部分可以用了呢。

Encoding:

每个字符分配一个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, 那么，下一个char会是什么？

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

优化技巧：

其实，0.45即能解码成功。

大大地提高了压缩率。

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

关于专利：

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)