Question

LZW CODING

LZW coding the initial dictionary is given: Index Symbol space 3 R. Decode the received sequence: 3,1,4,6,8,4,2,1,2,5,10. Continue building the dictionary while decoding. There is one place you could be confused. The appearance of 8 in the above sequence is not a mistake: remember that in the dictionary before adding 3-character pattern, you add 2-character pattern. That is, while decoding and before referring to index 8, you will add entries 7 and 8.

Answer 1

The LZW stands for Lempel-Ziv-Welch commpression algorithm. This algorithm is alossless alogrithm. LZW Algorithm is optionally used in TIFF and PDF and mostly used in GIF. LZW compression mostly works by grouping the symbols into strings ,converting the strings into codes and reading the sequence of symbols.

The received sequence is 3,1,4,6,8,4,2,1,2,5,10.

After adding 7 and 8 before reffering to 8 the received sequence becomes 3,1,4,6,7,8,8,4,2,1,2,5,10.

Index	Symbol
1	A
2	space
3	R
4	T

The table given below helps to decode the received output and finds the original string.

Received	Decode	Index	Entry	Index	Partial Entry
3	R	-	-	5	R-
1	A	5	RA	6	A-
4	T	6	AT	7	T-
6	AT	7	TA	8	AT-
7	TA	8	ATT	9	TA-
8	ATT	9	TAA	10	ATT-
8	ATT	10	ATTA	11	ATT-
4	T	11	ATTT	12	T-
2	space	12	Tspace	13	space-
1	A	13	spaceA	14	A-
2	space	14	Aspace	15	space-
5	RA	15	spaceR	16	RA-
10	ATTA	16	RAA	17	ATTA-

The decoded string is RATATTAATTATTTspaceAspaceRAATTA (it is the decode part of the table ).

space can be denoted as "_".

After that the resultant string can be written as RATATTAATTATTT_A_RAATTA.