A Compression Technique Based On Optimality Of LZW Code (OLZW)
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1 2012 Third International Conference on Computer and Communication Technology A Compression Technique Based On Optimality Of LZW (OLZW) Utpal Nandi Dept. of Comp. Sc. & Engg. Academy Of Technology Hooghly ,West Bengal, India nandi.3utpal@gmail.com Jyotsna Kumar Mandal Dept. of Comp. Sc. & Engg. University of Kalyani Nadia , West Bengal, India jkm.cse@gmail.com Abstract A lossless dictionary based data compression technique has been proposed in this paper which is based on the optimality of LZW code. The compression process is started with empty dictionary and if the next symbol to be encoded is already in dictionary, length of symbol code is determined by the highest symbol code in the dictionary and encoded with the code in the dictionary. Otherwise, the symbol is encoded with 8-bit ASCII code. Some of the limitations of LZW compression technique have been eliminated in the proposed compression technique. Comparisons are made between proposed technique and two different version of LZW data compression technique which shows that the proposed technique works well for small size files particularly. Keywords- Data compression; compression ratio; LZW; dictionary-based compression; OLZW I. INTRODUCTION Data compression techniques [7, 8] are deployed to reduce the number of bits used to store or transmit information which are divided into two major families; lossless [1-8] and lossy [8]. Loss-less compression consists of whose techniques guaranteed to generate an exact duplicate of the input file/stream after compress/expand cycle. But, the lossy data compression concedes a certain loss of accuracy in exchange for greatly increased compression. A dictionarybased loss-less data compression technique [1, 2, 8] is proposed in this paper based on LZW technique [1]. Initially, the dictionary is empty. Therefore, the available code values are started from 1 instead of 256 as in LZW. If the next symbol to be encoded is already in dictionary, length of symbol code is determined by the highest symbol code in the dictionary and is encoded with symbol code of the symbol in the dictionary with calculated length. But, the symbol to be encoded not in dictionary is encoded with 8-bit ASCII code. Thus, some of the weaknesses of LZW technique are overcome. The LZW coding technique and its limitations are discussed in section II. The proposed coding technique is discussed in section III in details. Results are given in section IV and conclusions are drawn in section V. II. THE LZW TECHNIQUE AND IT S LIMITATIONS The LZW coding technique was developed by Terry Welch in The method starts by initializing the dictionary to all 256 symbols in the alphabet. Therefore, the first 256 entries of the dictionary (0 to 255) are occupied before any data is input and the next free code value started from 256. The method reads symbols one by one and accumulates them into a string S. After each symbol is input and is concatenated to S, the dictionary is searched for string S. As long as the S is found in the dictionary, the process continues. At a certain point, adding the next symbol C causes the search to fail. The string S is in the dictionary but, string SC (Symbol C concatenated to S) is not. At this point, the encoder outputs the dictionary pointer that points to string S, saves string SC (which is now called phrase) in the next available dictionary entry and initializes string S to symbol C. This is now repeated for remaining symbols until end of symbol. The decoding process is also started by initializing the dictionary to all 256 symbols in the alphabet. Then, it reads its input stream (which consists of pointers to the dictionary) and uses each pointer to retrieve uncompressed symbols from its dictionary and write them on its output file/stream. It does not need to receive the dictionary from compressor. It builds its dictionary in the same way as the encoder. That is, encoder and decoder are synchronized. One version of LZW coding (LZW12) uses a fixed size 12 bit code to encode each phrase of the dictionary. But, 12 bits code size allows for a 4K phrase dictionary which is not enough for large file/stream. LZW is improved by increasing the size of the dictionary. The more powerful improved version of LZW coding (LZW15V) contains several enhancements. First, it expands the maximum code size to 15 bits. Second, it starts encoding with 9 bit codes, working its way up in bits size only as necessary. Finally, it flushes the dictionary when the dictionary is filled up with phrases. But, there are some limitations remaining in the improved version of LZW. First, in LZW technique, the dictionary is initialized to all the symbols in the alphabet at the beginning of the encoding processes. Some symbols in the dictionary may not be used during encoding of some files/streams. But, the unused symbols occupy some code values that cannot be used for other necessary phrases of dictionary. Available code values can be represented by more bits compare to code values of unused symbols. It increases the size of compressed file/stream. Another problem is that at the beginning of the encoding process, the next available code value (256) can be represented by at least 9 bits. Because, first 256 code values (0 to 255) are occupied by 256 symbols of the alphabet. These large length available codes of phrases increase the size of compressed file/stream. To overcome these /12 $ IEEE DOI /ICCCT
2 limitations, a coding technique is proposed and described in section III. III. OPTIMALITY OF LZW CODES AND THE PROPOSED COMPRESSION TECHNIQUE Optimality of LZW codes can be achieved by starting the encoding process with empty dictionary. First phrase to be entered into the dictionary should has code values 1 which can be represented using only single bit. The 2 nd and 3 rd phrases to be entered into the dictionary should have code values 2 and 3 and can be represented by 2 bits. Similarly, 3 bits are required for 4 th to 7 th phrases to be entered into the dictionary and so on. This is in contrast to LZW coding where fist 256 phrases entered initially into the dictionary are represented by 8bits per phrase. Therefore, significant reduction of number of bits can be done by optimization of LZW codes. This concept is applied in the proposed technique. The proposed coding technique is started with a empty dictionary initially. Any symbol or phrase that is not used should not be in the dictionary. Therefore, the first available phrase code value is 1. The code assignment of phrase is started with code value 1 that can be represented using only one bit long. The encoding process read symbols one by one. If the next phrase to be encoded is already in dictionary, length (say, x) of phrase code is determined by the highest phrase code in the dictionary. If the highest phrase code in the dictionary is h, then the value of x is one that satisfy 2 x-1 <=h<2 x. Then, the phrase is encoded with x bits phrase code of the corresponding phrase in the dictionary. In this way, the optimization of phrases code is done. But, the symbol to be encoded not in dictionary is encoded with 8-bit ASCII code and entered into the dictionary as a new phrase with next available code value. A 1 bit flag is used to distinguish above two possibilities. The proposed technique is termed as A compression technique based on optimality of LZW code (OLZW). The advantage of the proposed technique is that it does not bring any symbol until needed and encoding of phrase code is done by optimum code length, not the fixed length code. The complete OLZW compression and decompression algorithms are shown in Fig. 1 and Fig. 2 respectively. For example, let us consider a file/stream containing the message- BPQSBPQBPQQBPQ ABPQTB (say, MSG1). The compression steps of MSG1 using OLZW technique are shown in table I. The first symbol B is input. But, B is not in dictionary. Therefore, the encoder outputs ASCII code of B with single bit flag 0 and the symbol B is kept as new phrase with code value 1 in dictionary. Similarly, the encoder outputs ASCII codes of P, Q, S with corresponding flags 0 for input P, Q, S respectively and the symbols P, Q, S are kept with code value 2, 3, 4 respectively. The next symbol B is input which is already in dictionary. Then, the next symbol (P) is input. But, the string BP is not in dictionary. The encoder outputs code of B (i.e.1) from dictionary represented by 3 bits with single bit flag 1.Then, the next symbol (P) is input. But, the string BP is not in Initially, the dictionary is empty and initialize next_code=1,s=null, Flag=0; C=first character from input file/stream; Add C to dictionary with code value as While (not end of input file/stream) do C=next character from input file/stream; If (S+C is in dictionary), then Flag=1; S=S+C; Add S+C to dictionary with code value as If (Flag=0), then S=NULL; x=find_code_length (next_code-1); Output flag with x bits code for C from dictionary; If(C is not in dictionary), then Flag=0; Add C to dictionary with code value as S=C; Flag=1; End while; If (Flag=1), then x= find_code_length (next_code-1); Output flag with x bits code for S from dictionary; End; Figure 1. OLZW compression algorithm. dictionary. The encoder outputs code of B (i.e.1) from dictionary represented by 3 bits with single bit flag 1. As the highest code value of dictionary is currently 4, the length of the code is 3 bits long. The string BP is kept in dictionary as new phrase with code value 5 and initializes string as P. The symbol P is already in dictionary. The next symbol Q is input. But, the string PQ is not in dictionary. Similarly, the encoder finds the code length as 3 bits and outputs code of P represented by 3 bits with single bit flag 1. All other symbols are encoded similarly until end of file. Finally, a special code value 0 is output for End_Of_File marker. The compressed message of MSG1 is 0B0P0Q0S1<1>1<2>1<3> 1<5>1<3>1<7>1<6>0A1<8>0T 1<0> (say, MSG2). Size of MSG1 is 20x8 bits = 160 bits. Size of MSG3 is (1x15+3x4+4x5+8x6) bits = 95 bits. The compression ratio 167
3 is {1-(95/160)}x100% = 40.62%. The decompression steps of MSG2 using OLZW technique are shown in table II. First flag is input. As flag=0, the decoder inputs 8 bits ASCII code of a symbol B and output the same. As the next three flags are also 0, decoder does the same operation. The next flag is 1. Therefore, decoder calculates code length as 3 and inputs 3 bits to obtain the code value (1). Then, the code value is translated into phrase B from dictionary and outputs phrase B. Similarly, all other codes are decoded depending on the value of flags until code value of end of file /stream is not read. Initially, the dictionary is empty and initialize next_code=1, S=NULL; Flag= First one bit from compressed file/stream. While (not end of compressed file/stream) do If (Flag=0), then C=next 8 bits from compressed file/stream; Add S+C to the dictionary with code value as Output C; If(C is not in dictionary), then Add C to dictionary with code value as End if S=NULL; P=0; x= find_code_length (next_code-1); C=next 8 bits from compressed file/stream; Y= translation of C; Output phrase Y; If (P=1), then Add (S + first character of Y) to dictionary with code value as S=Y; P=1; Flag= next one 1 bit from compressed file/stream; End while; End ; Figure 2. OLZW decompression algorithm IV. RESULTS AND COMPARISMS The comparison among LZW12, LZW15V (two version of LZW) coding and proposed OLZW coding have been made in table III. The graphical representations of compression ratios of LZW12, LZW15V and proposed OLZW coding techniques for different increasing size C source file, text files, document files and java files each of five are shown in Fig. 3, Fig. 4, Fig. 5 and Fig. 6 respectively. For all type of small files, the compression ratios are better than LZW12 and LZW15V for most of the time. Also, the compression ratios of OLZW for large size files are better than LZW12 and close to the compression ratios of LZW15V, but not so well for some time. V. CONCLUSION The proposed OLZW technique eliminates some of the problems of the LZW coding and enhances the performance of the same. The proposed technique works very well for particularly small size files most of the time than two versions of LZW (i.e. LZW12 and LZW15V). And the performances of OLZW are not so poor for large size files also. It offers better compressions for large size files than LZW12 most of the time. The compression rates of OLZW for large size files are not as well as LZW15V, but close to it. The proposed technique has a great scope of modifications to make it suitable for large size files also by populating the dictionary with combination of character of phrase instead of the phrase itself and removing phrases not used for longest period of time if the dictionary gets full. It can also be used for image compression. TABLE I. (in dict?) COMPRESSION OF MSG1 USING OLZW Flag Output (length) value Dictionary B B (N) 0 B (8) 1 B P P (N) 0 P (8) 2 P Q Q (N) 0 Q (8) 3 Q S S (N) 0 S (8) 4 S B B (Y) P BP (N) 1 1(3) 5 BP P (Y) Q PQ (N) 1 2(3) 6 PQ B QB (N) 1 3(3) 7 QB B (Y) P BP (Y) Q BPQ (N) 1 5(3) 8 BPQ Q QQ (N) 1 3(4) 9 QQ B QB P QBP (N) 1 7(4) 10 QBP P (Y) Q PQ (Y) A PQA (N) 1 6(4) 11 PQA A (N) 0 A (8) 12 A B B (Y) P BP (Y) Q BPQ (Y) T BPQT (N) 1 8(4) 13 BPQT T (N) 0 T (8) 14 T <EOF> (Y) 1 0(4) 168
4 TABLE II. DECOMPRESSION OF MSG2 USING OLZW Flag value (length ) Output phrase value Dictionary 0 B (8) B 1 B 0 P (8) P 2 P 0 Q (8) Q 3 Q 0 S (8) S 4 S 1 1(3) B 1 2(3) P 5 BP 1 3(3) Q 6 PQ 1 5(3) BP 7 QB 1 3(3) Q 8 BPQ 1 7(4) QB 9 QQ 1 6(4) PQ 10 QBP 0 A (8) A 11 PQA 12 A 1 8(4) BPQ 0 T (8) T 1 0(4) 13 BPQT 14 T Figure 4. Compression ratios of text files TABLE III. COMPARISON OF COMPRESSION RATIOS File Name File Size in Bytes LZW12 %compression LZW15V Proposed OLZW y1.c y2.c y3.c y4.c y5.c x1.txt x2.txt x3.txt x4.txt x5.txt z1.doc z2.doc z3.doc z4.doc z5.doc j1.java j2.java j3.java j4.java j5.java Figure 5. Compression ratios of document files Figure 6. Compression ratios of java files VI. ACKNOWLEDGMENT The authors extend sincere thanks to the department of Computer Science and Engineering and PURSE Scheme of DST, Govt. of India and Academy Of Technology, Hooghly, West Bengal, India for using the infrastructure facilities for developing the technique. Figure 3. Compression ratios of C source files REFERENCES [1] M. Nelson, LZW Data Compression, in Dr. Dobb s Journal, Vol. 14, No. 10, October 1989, pp [2] J. Ziv, A. Lempel, A universal algorithm for sequential data compression, in IEEE Transactions on Information Theory, Vol. 23, No. 3, May 1977, pp
5 [3], Region based Huffman(RB H) Compression Technique with Interchange, Malayasian Journal of Computer Science(MJCS), Malayasia,Vol.23, No. 2, September 2010, pp [4], A. Kumar, A Compression Technique Based on Optimality of Huffman Tree (OHT), in Proceedings of 12 th International Conference of IEEE on Advanced Computing and Communications - ADCOM-2004, December 15-18, 2004, Ahmedabad, India, pp [5] J. Ziv, and A. Lempel, Compression of individual sequences via variable-rate coding, in IEEE Transactions on Information Theory, Vol. 24, No.5, September 1978, pp [6], and R.Gangopadhayay, Implementation of Two Data Compression Schemes, in Proc. First International Workshop on Telematics, NERIST, India, 1995, pp [7] H. K. Reglebati, An Overview of Data Compression Techniques, in IEEE Computer, April 1981,pp [8] M. Nelson, The Data Compression Book,ed. Second, India, BPB Publications, [9] Welch, Terry, A Technique for High-Performance Data Compression, in IEEE Computer, Vol. 17, No.6, June 1984, pages [10] Y. Kanitkar, C project, ed.second, India, BPB Publications,
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