Synchronizing codewords of q-ary Huffman codes

Abstract The databases of genomic sequences are growing at an explicative rate because of the increasing growth of living organisms. Compressing deoxyribonucleic acid (DNA) sequences is a momentous task as the databases are getting closest to its threshold. Various compression algorithms are developed for DNA sequence compression. An efficient DNA compression algorithm that works on both repetitive and non-repetitive sequences known as “HuffBit Compress” is based on the concept of Extended Binary Tree. In this paper, here is proposed and developed a modified version of “HuffBit Compress” algorithm to compress and decompress DNA sequences using the R language which will always give the Best Case of the compression ratio but it uses extra 6 bits to compress than best case of “HuffBit Compress” algorithm and can be named as the “Modified HuffBit Compress Algorithm”. The algorithm makes an extended binary tree based on the Huffman Codes and the maximum occurring bases (A, C, G, T). Experimenting with 6 sequences the proposed algorithm gives approximately 16.18 % improvement in compression ration over the “HuffBit Compress” algorithm and 11.12 % improvement in compression ration over the “2-Bits Encoding Method”.

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Design and analysis of dynamic Huffman codes

Journal of the ACM ◽

10.1145/31846.42227 ◽

1987 ◽

Vol 34 (4) ◽

pp. 825-845 ◽

Cited By ~ 205

Author(s):

Jeffrey Scott Vitter

Keyword(s):

Huffman Codes

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Huffman Codes

Foundations of Coding ◽

10.1002/9781118033265.ch2 ◽

2011 ◽

pp. 17-24

Keyword(s):

Huffman Codes

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The Number of Huffman Codes, Compact Trees, and Sums of Unit Fractions

IEEE Transactions on Information Theory ◽

10.1109/tit.2012.2226560 ◽

2013 ◽

Vol 59 (2) ◽

pp. 1065-1075 ◽

Cited By ~ 9

Author(s):

Christian Elsholtz ◽

Clemens Heuberger ◽

Helmut Prodinger

Keyword(s):

Huffman Codes ◽

Unit Fractions

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The WARM-UP Algorithm: A Lagrangian Construction of Length Restricted Huffman Codes

SIAM Journal on Computing ◽

10.1137/s009753979731981x ◽

2000 ◽

Vol 30 (5) ◽

pp. 1405-1426 ◽

Cited By ~ 6

Author(s):

Ruy Luiz Milidiú ◽

Eduardo Sany Laber

Keyword(s):

Warm Up ◽

Huffman Codes ◽

Lagrangian Construction

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A QUADRATIC UPPER BOUND ON THE SIZE OF A SYNCHRONIZING WORD IN ONE-CLUSTER AUTOMATA

International Journal of Foundations of Computer Science ◽

10.1142/s0129054111008039 ◽

2011 ◽

Vol 22 (02) ◽

pp. 277-288 ◽

Cited By ~ 24

Author(s):

MARIE-PIERRE BÉAL ◽

MIKHAIL V. BERLINKOV ◽

DOMINIQUE PERRIN

Keyword(s):

Upper Bound ◽

The State ◽

Additional Property ◽

Prefix Code ◽

Deterministic Automaton ◽

Huffman Codes ◽

Synchronizing Word ◽

Černý’S Conjecture

Černý's conjecture asserts the existence of a synchronizing word of length at most (n - 1)2 for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p·ar = q·as for some integers r, s (for a state p and a word w, we denote by p·w the state reached from p by the path labeled w). As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n2). This applies in particular to Huffman codes.

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