[IR] Dictionary Coding

【数据压缩】LZ77算法原理及实现

【数据压缩】LZ78算法原理及实现

Lempel–Ziv–Welch

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年发表的论文《A Universal Algorithm for Sequential Data Compression》中提出。

基于统计的数据压缩编码，比如Huffman编码，需要得到先验知识——信源的字符频率，然后进行压缩。但是在大多数情况下，这种先验知识是很难预先获得。

因此，设计一种更为通用的数据压缩编码显得尤为重要。LZ77数据压缩算法应运而生，其核心思想：利用数据的重复结构信息来进行数据压缩。

LZ77: referring to previously processed data as dictionary 利用内部信息作为字典。

在提出基于滑动窗口的LZ77算法后，两位大神Jacob Ziv与Abraham Lempel于年在发表的论文中提出了LZ78算法；

与LZ77算法不同的是LZ78算法使用动态树状词典维护历史字符串。

LZ78: use an explicit dictionary 字典是外置的。

LZ系列压缩算法均为LZ77与LZ78的变种，在此基础上做了优化。

• LZ77：LZSS、LZR、LZB、LZH；
• LZ78：LZW、LZC、LZT、LZMW、LZJ、LZFG。

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LZW Encoding:

　　Video: https://www.youtube.com/watch?v=nW7OARbr7OI

"TO BE OR NOT TO BE OR TO BE OR NOT"

Idea:

以下是我们已知的字典。

再动态补充新发现的pattern字典，从27开始编号，如下所示：

current	next	code	dictionary
T	O	20	TO	27	TO BE OR NOT TO BE OR TO BE OR NOT
O	B	15	OB	28	TO BE OR NOT TO BE OR TO BE OR NOT
B	E	2	BE	29	TO BE OR NOT TO BE OR TO BE OR NOT
E	O	5	EO	30	TO BE OR NOT TO BE OR TO BE OR NOT
O	R	15	OR	31	TO BE OR NOT TO BE OR TO BE OR NOT
R	N	18	RV	32	TO BE OR NOT TO BE OR TO BE OR NOT
N	O	14	NO	33	TO BE OR NOT TO BE OR TO BE OR NOT
O	T	15	OT	34	TO BE OR NOT TO BE OR TO BE OR NOT
T	T	20	TT	35	TO BE OR NOT TO BE OR TO BE OR NOT
TO	B	27	TOB	36	TO BE OR NOT TO BE OR TO BE OR NOT
BE	O	29	BEO	37	TO BE OR NOT TO BE OR TO BE OR NOT
OR	T	31	ORT	38	TO BE OR NOT TO BE OR TO BE OR NOT
TOB	E	36	TOBE	39	TO BE OR NOT TO BE OR TO BE OR NOT
EO	R	30	EOR	40	TO BE OR NOT TO BE OR TO BE OR NOT
RN	O	32	RNO	41	TO BE OR NOT TO BE OR TO BE OR NOT
OT	#	34	N/A	N/A	TO BE OR NOT TO BE OR TO BE OR NOT
Input		Output

这里共16行，也就是原来的24字节 --> 16字节。

LZW Decoding:

code	prev	output	dictionary
20		T			TO BE OR NOT TO BE OR TO BE OR NOT
15	T	O	TO	27	TO BE OR NOT TO BE OR TO BE OR NOT
2	O	B	OB	28	TO BE OR NOT TO BE OR TO BE OR NOT
5	B	E	BE	29	TO BE OR NOT TO BE OR TO BE OR NOT
15	E	O	EO	30	TO BE OR NOT TO BE OR TO BE OR NOT
18	O	R	OR	31	TO BE OR NOT TO BE OR TO BE OR NOT
14	R	N	RN	32	TO BE OR NOT TO BE OR TO BE OR NOT
15	N	O	NO	33	TO BE OR NOT TO BE OR TO BE OR NOT
20	O	T	OT	34	TO BE OR NOT TO BE OR TO BE OR NOT
27	T	TO	TT	35	TO BE OR NOT TO BE OR TO BE OR NOT
29	TO	BE	TOB	36	TO BE OR NOT TO BE OR TO BE OR NOT
31	BE	OR	BEO	37	TO BE OR NOT TO BE OR TO BE OR NOT
36	OR	TOB	ORT	38	TO BE OR NOT TO BE OR TO BE OR NOT
30	TOB	EO	TOBE	39	TO BE OR NOT TO BE OR TO BE OR NOT
32	EO	RN	EOR	40	TO BE OR NOT TO BE OR TO BE OR NOT
34	RN	OT	RNO	41	TO BE OR NOT TO BE OR TO BE OR NOT
<Output>		<Input>

可见与encoding时表格一一对应的关系。

就是还原表格的过程。