Application of Discrete Structures and Numerical Sequences in Block Codes

The purpose to compress information using composition of universal codes with the recursive algorithm of original data recovery was achieved in this work. It obtains compression coefficient higher than in symbolic coding. Proposed method of time coding has reasonable values of compression coefficient and its purpose is coding with compression. For this purpose, entirely new kind of universal coding with the polybasic numeral system was created. The presented method is subtype of universal codes and has an advantage over the Huffman coding for compression, because there is no need to know the exact probability distribution that gives us the characters in the initial data stream and it is a subspecies of the universal coding. The Huffman coding requires exact probability distribution. But when we talk about universal coding it is sufficient to know only the relative order of these probabilities (symbol, are more often, the second of the most common symbol, etc.) withal. Created coding method can be applied in mobile communication and in means of closed communication, if it will be used with block codes, which doesn’t scatter symbol frequencies, because it meets modern requirements for cyphering.

Publication year: 
2014
Issue: 
6
УДК: 
512.715:512.772.1:688.321
С. 68–75.Іл. 1. Бібліогр.: 7 назв.
References: 

1. S. Ristov and E. Laporte, “Ziv lempl compression of huge natural languadge data tries using suffix arrays”, 10th Annual Symp. ACM. Experimentation, Combinatorial Pattern Matching, UK, Warwick University, M. CrocheІ more and M. Paterson, eds. Berlin: Springer, 1999, pp. 196—211.
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3. K. Sayood, Introduction to Data Compression, 3rd ed., Morgan Kaufman, 2006, p. 315.
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5. H. Yamamoto, “A new recursive universal code of the positive integers”, IEEE Trans. Inform. Theory, vol. 46, pp. 717—723, 2000.
6. Скуратовський Р. В. Комбінована λ,ν-адична система числення і деякі математичні об’єкти, які з нею пов’язані // Студентскі фіз.-мат етюди. — 2003. — С. 45—50.
7. Стахов А.П. Коды золотой пропорции. — М.: Радио и связь, 1994. — 152 с.

References [transliteration]: 

1. S. Ristov and E. Laporte, “Ziv lempl compression of huge natural languadge data tries using suffix arrays”, in 10th Annual Symp. ACM. Experimentation, Combinatorial Pattern Matching, UK, Warwick University, M. Crochemore and M. Paterson, eds. Berlin: Springer, 1999, pp. 196–211.
2. Metody szhatii͡a bez poter' / D. Vatolin, A. Ratushni͡ak, M. Smirnov, V. I͡Ukin. – M.: Dialog-MIFI, 2002. – 384 s.
3. K. Sayood, Introduction to Data Compression, 3rd ed., Morgan Kaufman, 2006, p. 315.
4. Skuratovs'kiĭ R.V. Metod bystrogo taĭmernogo kodirovanii͡a tekstov // Kibernetika i sistemnyĭ analiz. – 2013. – # 1. – S. 154–160.
5. H. Yamamoto, “A new recursive universal code of the positive integers”, IEEE Trans. Inform. Theory, vol. 46, pp. 717–723, 2000.
6. Skuratovs′kyĭ R.V. Kombinovana - - adychna systema chyslenni͡a i dei͡aki matematychni obi͡ekty, i͡aki z nei͡u povi͡azani // Studentski fiz.-mat eti͡udy. – 2003. – S. 45–50.
7. Stakhov A.P. Kody zolotoĭ proport͡sii. – M.: Radio i svi͡az', 1994. – 152 s.

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