DNA Inspired Bi-directional Lempel-Ziv-like Compression Algorithms
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1 DNA Inspired Bi-directional Lempel-Ziv-like Compression Algorithms Transmission Systems Group (TrSys) Attiya Mahmood Nazia Islam Dawit Nigatu Werner Henkel 1
2 Outline Inspiration Description of Bi-directional Algorithms: LZ77, LZ78, and LZW84 Results Conclusion 1
3 Inspiration Bi-directional Reading and Lempel-Ziv-like Processes in the DNA Bi-directional processes: DNA Replication, Transcription, Translation Lempel-Ziv-like process: Alternative Splicing 2
4 Bi-directional Processes: Replication DNA has two ends in the two strands: 3 to 5 Bi-directionality in reading in complementary strands Figure: DNA replication ( node=photos/graphics&id=85151) 3
5 Bi-directional Processes: Gene Expression Transcription Figure: mrna Transcription Process en.wikipedia.org/wiki/transcription(genetics) 4
6 Bi-directional Processes: Gene expression Translation >gi :c Escherichia coli str. K-12 substr. W3110, Complete genome ATGAATGTTAATTACCTGAATGATTCAGATCTGGATTTTCTTCAGCATTGTAGTGAGGAACAGTTGGCAAATTTC GCCCGATTGCTCACCCATAATGAAAAAGGCAAAACTCGCCTCTCCAGCGTACTGATGCGCAACGAACTGTTAAATC GATGGAAGGGCATCCCGAGCAACATCGCCGCAACTGGCAGCTGATTGCCGGAGAATTACAGCATTTTGGTGGCGAT AGTATCGCCAACAAACTGCGCGGACACGGTAAATTGTATCGGGCCATTTTGCTCGATGTTTCAAAGCGATTGAAGC TGAAAGCCGACAAAGAGATGTCTACGTTTGAAATTGAGCAACAGTTACTGGAACAATTTCTGCGTAATACCTGGA AGAAAATGGACGAGGAACATAAGCAGGAGTTTCTGCACGCGGTCGATGCCAGGGTGAATGAGCTGGAAGAGCTGC TGCGCTGCTGATGAAAGACAAATTATTGGCAAAAGGTGTGTCGCATTTGCTTTCCAGCCAACTGACCCGCATTTTA CGCACCCACGCAGCAATGAGCGTACTTGGGCATGGTTTGCTGCGCGGCGCGGGGCTGGGAGGCCCTGTAGGTGCGG CACTAAATGGGGTTAAAGCGGTCAGCGGCAGCGCCTATCGCGTGACGATTCCAGCCGTACTGCAAATCGCCTGCCT GCGCCGGATGGTTAGCGCCACTCAGGTCTGA Figure: Genes htga and yaaw in overlapping position on opposite strands (nucleotide sequence of gene yaaw of E. coli K12.) 5
7 Alternative Splicing Figure: Alternative splicing ( 6
8 Bi-directional Lempel-Ziv-like Algorithms Bi-directional matching criterion Cost: 1 bit direction flag Flag bit 0 : regular direction Flag bit 1 : reverse direction 7
9 Bi-directional LZ77 Data traversed in: memory and look ahead buffers Size of buffers limited Output: (position, length, non-matching character, flag) text block to be compressed: ecabbaced Encoder Output 0,0,e,0 0,0,c,0 0,0,a,0 0,0,b,0 3,4,d,1 String at specified index e c a b baced 8
10 Bi-directional LZ77 Output: (position, length, non-matching character, flag) text block to be compressed: ecabbaced Encoder Output 0,0,e,0 0,0,c,0 0,0,a,0 0,0,b,0 3,4,d,1 String at specified index e c a b baced 9
11 Bi-directional LZ77 Output: (position, length, non-matching character, flag) text block to be compressed: e cabbaced Encoder Output 0,0,e,0 0,0,c,0 0,0,a,0 0,0,b,0 3,4,d,1 String at specified index e c a b baced 10
12 Bi-directional LZ77 Output: (position, length, non-matching character, flag) text block to be compressed: ec abbaced Encoder Output 0,0,e,0 0,0,c,0 0,0,a,0 0,0,b,0 3,4,d,1 String at specified index e c a b baced 11
13 Bi-directional LZ77 Output: (position, length, non-matching character, flag) text block to be compressed: ecab baced Encoder Output 0,0,e,0 0,0,c,0 0,0,a,0 0,0,b,0 3,4,d,1 String at specified index e c a b baced 12
14 Bi-directional LZ78 Dictionary based approach Dictionary size limited Output: (index, next non-matching character, flag) text block to be compressed: ecbebbec Encoder Encoder String at Decoder dictionary Output specified index dictionary 1: e 0,e,0 e 1: e 2: c 0,c,0 c 2: c 3: b 0,b,0 b 3: b 4: eb 1,b,0 eb 4: eb 5: bec 4,c,1 bec 5: bec 13
15 Bi-directional LZ78 Output: (index, next non-matching character, flag) text block to be compressed: ecbebbec Encoder Encoder String at Decoder dictionary Output specified index dictionary 1: e 0,e,0 e 1: e 2: c 0,c,0 c 2: c 3: b 0,b,0 b 3: b 4: eb 1,b,0 eb 4: eb 5: bec 4,c,1 bec 5: bec 14
16 Bi-directional LZ78 Output: (index, next non-matching character, flag) text block to be compressed:ecbebbec Encoder Encoder String at Decoder dictionary Output specified index dictionary 1: e 0,e,0 e 1: e 2: c 0,c,0 c 2: c 3: b 0,b,0 b 3: b 4: eb 1,b,0 eb 4: eb 5: bec 4,c,1 bec 5: bec 15
17 Bi-directional LZ78 Output: (index, next non-matching character, flag) text block to be compressed:ecbebbec Encoder Encoder String at Decoder dictionary Output specified index dictionary 1: e 0,e,0 e 1: e 2: c 0,c,0 c 2: c 3: b 0,b,0 b 3: b 4: eb 1,b,0 eb 4: eb 5: bec 4,c,1 bec 5: bec 16
18 Bi-directional LZ78 Output: (index, next non-matching character, flag) text block to be compressed:ecbebbec Encoder Encoder String at Decoder dictionary Output specified index dictionary 1: e 0,e,0 e 1: e 2: c 0,c,0 c 2: c 3: b 0,b,0 b 3: b 4: eb 1,b,0 eb 4: eb 5: bec 4,c,1 bec 5: bec 17
19 Bi-directional LZ78 Output: (index, next non-matching character, flag) text block to be compressed:ecbebbec Encoder Encoder String at Decoder dictionary Output specified index dictionary 1: e 0,e,0 e 1: e 2: c 0,c,0 c 2: c 3: b 0,b,0 b 3: b 4: eb 1,b,0 eb 4: eb 5: bec 4,c,1 bec 5: bec 18
20 Bi-directional LZW84 Initialized dictionary Output: (index, flag) text block to be compressed: ecabaced Encoder Encoder String at Decoder dictionary Output specified index dictionary 27: ec 5,0 e 27: e? 28: ca 3,0 c 27: ec; 28: c? 29: ab 1,0 a 28: ca; 29: a? 30: bac 29,1?a 29: a?; 30:?a? 31: ced 27,1 ce 30:?ac; 31: ce? 19
21 Bi-directional LZW84 Output: (index, flag) text block to be compressed:ecabaced Encoder Encoder String at Decoder dictionary Output specified index dictionary 27: ec 5,0 e 27: e? 28: ca 3,0 c 27: ec; 28: c? 29: ab 1,0 a 28: ca; 29: a? 30: bac 29,1?a 29: a?; 30:?a? 31: ced 27,1 ce 30:?ac; 31: ce? 20
22 Bi-directional LZW84 Output: (index, flag) text block to be compressed:ecabaced Encoder Encoder String at Decoder dictionary Output specified index dictionary 27: ec 5,0 e 27: e? 28: ca 3,0 c 27: ec; 28: c? 29: ab 1,0 a 28: ca; 29: a? 30: bac 29,1?a 29: a?; 30:?a? 31: ced 27,1 ce 30:?ac; 31: ce? 21
23 Bi-directional LZW84 Output: (index, flag) text block to be compressed:ecabaced Encoder Encoder String at Decoder dictionary Output specified index dictionary 27: ec 5,0 e 27: e? 28: ca 3,0 c 27: ec; 28: c? 29: ab 1,0 a 28: ca; 29: a? 30: bac 29,1?a 29: a?; 30:?a? 31: ced 27,1 ce 30:?ac; 31: ce? 22
24 Bi-directional LZW84 Output: (index, flag) text block to be compressed:ecabaced Encoder Encoder String at Decoder dictionary Output specified index dictionary 27: ec 5,0 e 27: e? 28: ca 3,0 c 27: ec; 28: c? 29: ab 1,0 a 28: ca; 29: a? 30: bac 29,1?a 29: a?; 30:?a? 31: ced 27,1 ce 30:?ac; 31: ce? 23
25 Bi-directional LZW84 Output: (index, flag) text block to be compressed:ecabaced Encoder Encoder String at Decoder dictionary Output specified index dictionary 27: ec 5,0 e 27: e? 28: ca 3,0 c 27: ec; 28: c? 29: ab 1,0 a 28: ca; 29: a? 30: bac 29,1?a 29: a?; 30:?a? 31: ced 27,1 ce 30:?ac; 31: ce? 24
26 Bi-directional LZW84 Output: (index, flag) text block to be compressed:ecabaced Encoder Encoder String at Decoder dictionary Output specified index dictionary 27: ec 5,0 e 27: e? 28: ca 3,0 c 27: ec; 28: c? 29: ab 1,0 a 28: ca; 29: a? 30: bac 29,1?a 29: a?; 30:?a? 31: ced 27,1 ce 30:?ac; 31: ce? Last dictionary entry cannot be used for reverse reading 25
27 Bi-directional LZW84: Symmetry Text compression: ASCII characters in initialized dictionary Bit pattern symmetry Use flag bit to indicate inverted bit pattern Initial dictionary is half the size of original counterpart 26
28 Results Audio [F] Audio [FR] Image [F] Image [FR] Text [F] Text [FR] Compression Ratio N SB Figure: Comparison of conventional and modified LZ77 27
29 Results Audio [F] Audio [FR] Image [F] Image [FR] Text [F] Text [FR] Compression Ratio N SB Figure: Comparison of conventional and modified LZ78 28
30 Results Compression Ratio Audio [F] Audio [FR] Image [F] Image [FR] Text [F] Text [FR] Finite Dictionary Size Figure: Comparison of conventional and modified LZW84 29
31 Conclusion Proposed algorithm has better performance, when there is some symmetry in data Employ this for DNA compression using conjugate reverse relations which may use non-binary flags Analytical treatment of how this differs from the original Lempel-Ziv algorithm properties 30
32 Thank You! 31
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