Binary error-correction encoding using the two-base numeration system with the radices 2 and 3 is proposed. Properties and error-correcting capabilities of such codes for one and two errors are analyzed. A special kin...
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Binary error-correction encoding using the two-base numeration system with the radices 2 and 3 is proposed. Properties and error-correcting capabilities of such codes for one and two errors are analyzed. A special kind of the (2,3) code, namely, the lower (2,3) code is introduced to provide error-correcting properties.
The combinatorial structure ofn-prefix-suffix languages, calledn-ps-codes in this paper, is investigated. Ann-ps-code is a language, each of whose subsets of cardinality at mostnis a prefix code or a suffix code.
The combinatorial structure ofn-prefix-suffix languages, calledn-ps-codes in this paper, is investigated. Ann-ps-code is a language, each of whose subsets of cardinality at mostnis a prefix code or a suffix code.
We consider the problem of constructing and transmitting the prelude for Huffman coding. With careful organization of the;required operations and an appropriate representation for the prelude, it is possible to make s...
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We consider the problem of constructing and transmitting the prelude for Huffman coding. With careful organization of the;required operations and an appropriate representation for the prelude, it is possible to make semistatic coding efficient even when S, the size of the source alphabet, is of the same magnitude as m, the length of the message being coded. The proposed structures are of direct relevance in applications that mimic one pass operation through the use of semistatic compression on a block-by block basis.
The construction of thin maximal bifix codes of degree 1 or 2 is clear and simple. In this paper, a class of thin maximal bifix codes of degree 3 which contains all finite maximal bifix codes of degree 3 is investigat...
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The construction of thin maximal bifix codes of degree 1 or 2 is clear and simple. In this paper, a class of thin maximal bifix codes of degree 3 which contains all finite maximal bifix codes of degree 3 is investigated. The construction of such codes is determined. It is well known that for any positive integers d and k, there are finitely many finite maximal bifix codes of degree d over a k-letter alphabet. But the enumeration problem is unsolved in general. In this paper, we show that for any positive integer k, there is a bijection from the set of all finite maximal bifix codes of degree 3 over a k-letter alphabet onto the set of all directed acyclic graphs with k vertices, and then, the enumeration problem of finite maximal bifix codes of degree 3 is solved.
An effective procedure for deciding permutativeness of one-directional cellular automata on the one-sided full shift is presented. It is then implemented in C++, and used to test permutativeness of elementary cellular...
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An effective procedure for deciding permutativeness of one-directional cellular automata on the one-sided full shift is presented. It is then implemented in C++, and used to test permutativeness of elementary cellular automata (those of radius 3). (C) 2009 Elsevier Inc. All rights reserved.
Some important properties of speech are considered from the point of view of the theory of error correcting codes. It has found experimentally that the properties of Russian words encoded in terms of phonemes are larg...
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Some important properties of speech are considered from the point of view of the theory of error correcting codes. It has found experimentally that the properties of Russian words encoded in terms of phonemes are largely similar to the properties of the so-called prefix codes. In the prefix codes, no code word is a prefix of another word. According to the theory of coding, for any prefix code exists an algorithm of unambiguous decoding where no pause or special symbol-delimeter separates code words. Apparently, word segmentation in the continuous speech signal is provided mainly by the use of the prefix property. Phoneme probability in Russian follows the Mandelbrot law. This finding is evidence in favour of the assumption that the probability is determined by the "complexity" or "expense" of phoneme generation. Speech recognition for a large vocabulary requires much time for access to word templates. Thus, a preliminary sorting of the templates is necessary to restrict a number of candidates for final recognition. The preliminary sorting can be executed by means of word coding by few phonemic cues. Auditory experiments with speech masked by white noise have revealed the most reliable cues. These cues are "vowel, voiced, nasal, fricative". About 150 templates were left after the fast sorting procedure for approximately 100,000 templates in the vocabulary of 10,000 of the most frequent English words. Speech recognition rate obtained by an automatic recognition system must be compared with potentially achievable rate. The potential rate of word recognition for various S/N ratios can be computed with the use of methods developed in the theory of coding. It can be argued that an optimal machine for automatic speech recognition should find robust the same cues which humans find robust. The potential rate for words encoded in terms of independent distinctive features is closer to the subjective reliability of word perception than the rate for words encoded by phonemes. (C
We introduce a strongly infix code. A code X is a strongly infix code if X is an infix code and any catenation of two words in X has no proper factor in X, which is neither a left factor nor a right factor. We show th...
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We introduce a strongly infix code. A code X is a strongly infix code if X is an infix code and any catenation of two words in X has no proper factor in X, which is neither a left factor nor a right factor. We show that the class of strongly infix codes is closed under composition, and, as the dual result, that the property to be strongly infix is inherited by a component of a decomposition.
In this note, we present some results about parses of codes. First we present a sufficient condition of a bifix code to have the bounded indicator. Next we consider a proper parse, introduced notion. We prove that for...
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In this note, we present some results about parses of codes. First we present a sufficient condition of a bifix code to have the bounded indicator. Next we consider a proper parse, introduced notion. We prove that for a strongly infix code, the number of proper parses is at most three under some condition. We also prove that if a code X has a unique proper parse for each word under the same condition, then X is a strongly infix code.
We consider syntactic congruences of some codes. As a main result, for an infix code L, it is proved that the following (i) and (ii) are equivalent and that (iii) implies (i), where P-L is the syntactic congruence of ...
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We consider syntactic congruences of some codes. As a main result, for an infix code L, it is proved that the following (i) and (ii) are equivalent and that (iii) implies (i), where P-L is the syntactic congruence of L. (i) L is a P-L2-class. (ii) L-m is a P-Lk-class, for given two integers m and k with 1 less than or equal to m less than or equal to k. (iii)L* is a P-L*-class. Next we show that every (i), (ii) and (iii) holds for a strongly infix code L. Moreover we consider properties of syntactic conguences of a residue W(L) for a strongly outfix code L.
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