We give an algorithm to decide whether a given regular omega-language is equal to P-omega for some prefix-free language P. We emphasize the differences between the case of finite prefix-free omega-generators and the c...
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We give an algorithm to decide whether a given regular omega-language is equal to P-omega for some prefix-free language P. We emphasize the differences between the case of finite prefix-free omega-generators and the case of infinite prefix-free omega-generators.
This paper describes a lookup table for the addressing of an optimally shaped constellation. The method is based on partitioning the subconstellations into shaping macro-shells of integer bit rate and increasing avera...
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This paper describes a lookup table for the addressing of an optimally shaped constellation. The method is based on partitioning the subconstellations into shaping macro-shells of integer bit rate and increasing average energy. The macro-shells do not need to have an equal number of points. A lookup table is used to select a subset of the partitions in the cartesian product space. By devising appropriate partitioning/merging rules, we obtain suboptimum schemes of very low addressing complexity and small performance degradation. The performance is computed using the weight distribution of an optimally shaped constellation.
We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain new up...
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We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain new upper bounds for automata with a short word of small rank. The results are applied to make several improvements in the area. In particular, we improve the upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an n-state synchronizing decoder has a reset word of length at most O(nlog(3)n). In addition to that, we prove that the expected reset threshold of a uniformly random synchronizing binary n-state decoder is at most 0(nlogn). We prove the Cerny conjecture for n-state automata with a letter of rank <= 3 root 6n-6. In another corollary, we show that the probability that the Cerny conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states, and that the expected value of the reset threshold is at most n(3/2-o(1)). Moreover, all of our bounds are constructible. We present suitable polynomial algorithms for the task of finding a reset word "of length within our bounds. (C) 2016 Elsevier Inc. All rights reserved.
The paper addresses the overflow/underflow problem encountered when limiting the bit length of the exponent field of a computer arithmetic real-number representation. Two systems are presented and compared. To suppres...
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The paper addresses the overflow/underflow problem encountered when limiting the bit length of the exponent field of a computer arithmetic real-number representation. Two systems are presented and compared. To suppress this defect, it was proposed that the bit length be varied according to the absolute value of the number to be represented. Among such representations with variable-length exponent field is Hamada's system, known as URR (Universal Representation of Real numbers). The level-index system, on the other hand, proposes to define the `level' using the absolute value of the number to be represented and the representation system selected on the basis of the defined level.
For every natural number n >= 2 and every finite sequence L of natural numbers, we consider the set UDn(L) of all uniquely decodable codes over an n-letter alphabet with the sequence L as the sequence of code word ...
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For every natural number n >= 2 and every finite sequence L of natural numbers, we consider the set UDn(L) of all uniquely decodable codes over an n-letter alphabet with the sequence L as the sequence of code word lengths, as well as its subsets PRn(L)and FDn(L) consisting of, respectively, the prefix codes and the codes with finite delay. We derive the estimation for the quotient vertical bar UDn(L)vertical bar/vertical bar PRn(L)vertical bar, which allows to characterize those sequences L for which the equality PRn(L) = UDn(L) holds. We also characterize those sequences L for which the equality FDn(L) = UDn(L) holds. (C) 2016 Elsevier B.V. All rights reserved.
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.
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
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